nuclear and particle physics - η0 mesons oﬀ the deuteron near … · 2016. 1. 31. · extremely...

Photoproduction of

η′ Mesons off the Deuteron

near Threshold

by

Dominik Werthmuller

Submitted in partial fulfillment of the

requirements for the degree of

Master of Science in Physics

at the

University of Basel

September 2007

Abstract

Meson photoproduction allows the identification of unknown nucleon resonances, aswell as the further investigation of the known resonances. The A2 collaboration at theMainzer Mikrotron (MAMI) performs that kind of experiments. Thanks to an energyupgrade to 1.5 GeV of the electron accelerator (‘MAMI C’) photons of energies up toEγ = 1.4 GeV can now be produced via bremsstrahlung tagging. Therefore the η′

meson, having a production threshold of Eγ = 1204.55 MeV on the deuteron, can beproduced for the first time.

The first goal of this work was the identification of the η′ in the first test data takenin May 2007. It will be shown that 60 η′ events could be reconstructed. The secondgoal was the determination of the inclusive cross section of d(γ, η′)X. Although someapproximations had to be made due to the limited time frame of this work, the crosssection near threshold could be extracted.

Acknowledgments

I would like to thank Prof. Bernd Krusche for offering me the opportunity of analyzingbrand new data and giving me the chance to continue my work in the interesting fieldof meson photoproduction. I appreciated his great patience and support very much.Thanks go also to all members of the group, especially Bene, Fabien, Francis, Yasserand last but not least Thierry and Igal who always helped me in resolving my questions.

Further I would like to thank all my friends who supported me during this demand-ing time. Special thanks go to my fellow sufferer and roommate Lukas for the livelydiscussions about physics and other matters.

Finally I would like to express my gratitude to my parents who enabled me to studyphysics and never lost their patience with me.

Contents

1 Introduction 11.1 Nucleon resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Meson photoproduction 72.1 Properties of pseudoscaler mesons . . . . . . . . . . . . . . . . . . . . . 72.2 Kinematics of the free production . . . . . . . . . . . . . . . . . . . . . . 102.3 Kinematics of the production off nuclei . . . . . . . . . . . . . . . . . . . 10

2.3.1 Coherent production . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Incoherent production . . . . . . . . . . . . . . . . . . . . . . . . 112.3.3 Quasifree production . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 η′ photoproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Present data for the free production . . . . . . . . . . . . . . . . 152.4.2 Production off the deuteron . . . . . . . . . . . . . . . . . . . . . 152.4.3 The goal of this work . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Experimental setup 173.1 The MAMI electron accelerator . . . . . . . . . . . . . . . . . . . . . . . 173.2 The Glasgow photon tagger . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 The Crystal Ball detector . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4 Particle identification detector . . . . . . . . . . . . . . . . . . . . . . . . 213.5 The TAPS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.6 Data taking and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Data analysis 254.1 Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Time calibration and random subtraction . . . . . . . . . . . . . . . . . 274.3 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3.1 Particle identification detector . . . . . . . . . . . . . . . . . . . 294.3.2 Other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.5 η′ reconstruction in the 6γ channel . . . . . . . . . . . . . . . . . . . . . 32

4.5.1 Final state analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5.2 Intermediate state analysis . . . . . . . . . . . . . . . . . . . . . 33

v

vi Contents

4.5.3 Intermediate state meson mass correction . . . . . . . . . . . . . 344.5.4 The η → 3π0 background channel . . . . . . . . . . . . . . . . . . 354.5.5 Missing mass analysis . . . . . . . . . . . . . . . . . . . . . . . . 364.5.6 Cut overview and evolution of the 2π0η invariant mass . . . . . . 38

4.6 Extraction of the inclusive d(γ, η′)X cross section . . . . . . . . . . . . . 394.6.1 Calculation of the target density . . . . . . . . . . . . . . . . . . 394.6.2 Determination of the photon number . . . . . . . . . . . . . . . . 404.6.3 Determination of the number of produced η′ mesons . . . . . . . 424.6.4 Final cross section formula . . . . . . . . . . . . . . . . . . . . . 44

5 Results and discussion 455.1 η′ identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2 The inclusive d(γ, η′)X cross section . . . . . . . . . . . . . . . . . . . . 465.3 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A Inclusive cross section data of d(γ, η′)X 49

B Tagger energy calibration 51

References 53

List of Figures

1.1 Cross section of the total nucleon photoabsorption . . . . . . . . . . . . 31.2 First excited states of the nucleon . . . . . . . . . . . . . . . . . . . . . 41.3 Nucleon resonances scheme . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 LO Feynman diagrams contributing to η photoproduction . . . . . . . . 72.2 The nonet of the pseudoscaler mesons . . . . . . . . . . . . . . . . . . . 82.3 Decay scheme of the η′ meson . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Part.-spect.-model of the quasifree η′ photoprod. off the deuteron . . . . 122.5 Quasifree threshold for the η′ photoproduction off the deuteron . . . . . 14

3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 MAMI floor plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Photograph of the Glasgow photon Tagger . . . . . . . . . . . . . . . . . 203.4 Photograph of the Crystal Ball detector . . . . . . . . . . . . . . . . . . 223.5 Photograph of the TAPS detector . . . . . . . . . . . . . . . . . . . . . . 23

4.1 Cosmics spectrum of a TAPS module . . . . . . . . . . . . . . . . . . . . 264.2 Relative timing of Crystal Ball and Tagger . . . . . . . . . . . . . . . . 284.3 ∆E to E plot of a PID element . . . . . . . . . . . . . . . . . . . . . . . 304.4 Visualization of the η′ decay into six photons . . . . . . . . . . . . . . . 324.5 6γ intermediate state invariant mass . . . . . . . . . . . . . . . . . . . . 334.6 η signal in the 3π0 invariant mass spectrum . . . . . . . . . . . . . . . . 354.7 Missing mass spectrum of the quasifree η′ production . . . . . . . . . . . 374.8 Evolution of the 2π0η invariant mass throughout the analysis cuts . . . 384.9 Tagging efficiencies of the enabled tagger channels . . . . . . . . . . . . 414.10 Total number of photons per tagger channel . . . . . . . . . . . . . . . . 414.11 η′ signal fits for the determ. of the number of measured η′ mesons . . . 43

5.1 Final 2π0η invariant mass spectrum . . . . . . . . . . . . . . . . . . . . 465.2 Cross section of d(γ, η′)X times detection efficiency . . . . . . . . . . . . 475.3 Inclusive cross section of d(γ, η′)X . . . . . . . . . . . . . . . . . . . . . 48

vii

Chapter 1

Introduction

After the discovery of the proton in 1919 by Rutherford and the neutron in 1932 byChadwick the constituents of the atomic nucleus (nucleons) were finally discovered.Along with the longer known electron the elementary building blocks of matter werebelieved to be identified. However in the following years more and more particles wereexperimentally found. Particularly the number of the strongly interacting particles,the ‘hadrons’, was so extensive by 1960 that one spoke of a ‘particle zoo’. As the onlyexisting classification the lighter hadrons were called ‘mesons’ whereas the heavier oneswere called ‘baryons’.

In 1961 Gell-Mann introduced the so-called ‘Eightfold Way’ in which the mesonsand baryons were combined into groups of e.g. eight particles (‘octets’) or ten parti-cles (‘decuplets’). In addition the particles were arranged in these multiplet in strictgeometrical patterns according to their charge and strangeness. After the predictionof the undiscovered Ω− baryon using the Eightfold Way this classification was widelyaccepted, although the justification of this system was unknown.

A first hint was again given by Gell-Mann and independently Zweig who proposedthat the hadrons were made of even more elementary particles, so-called ‘quarks’. Three‘flavours’ of quarks were introduced: the ‘up’ quark u, the ‘down’ quark d and the‘strange’ quark s. In addition with their antiparticles u, d, s they form the hadrons:The mesons consist of one quark and one antiquark (qq), while the baryons consistof three quarks (qqq). In the later years three additional flavors were introduced andfound in experiments performed with new, more powerful accelerators. Table 1.1 showsall quark flavors of today’s Standard Model along with their most important properties.

Using the quark model the Eightfold Way could be derived easily. However noexperimental evidence was found until the late sixties that corroborated this theory.Thanks to technological progress the construction of particle accelerators reaching thenecessary energies to prove the quark model was possible. Starting at SLAC and laterat CERN the most prominent hadron, the proton, was tested for a substructure usingdeep inelastic scattering. The results of this experiments indeed could be interpretedusing constituent particles which Feynman and Bjorken named ‘partons’. Finally the

1

2 Chapter 1. Introduction

Symbol NameMass [MeV]

Q/|qe|current quark constituent quark

u up 1.5 - 3 ≈ 300 +2/3d down 3 - 7 ≈ 300 −1/3s strange 95 ≈ 450 −1/3c charm 1250 +2/3b bottom 4200 −1/3t top 174 000 +2/3

Table 1.1: Quark flavors in the Standard Model and their most important properties. The lighterquarks show a massive difference of their current quark and their constituent quark mass. The currentquark mass denotes the mass of a ‘bare’ quark, i.e. the mass at q2 →∞. The constituent quark massis the effective mass of a quark bound in a hadron. [1, 2]

development of Quantum Chromodynamics (QCD) allowed to identify these partonsas quarks and gluons. [3]

Forty years after the these first break troughs in a deeper comprehension of matter,the structure of the nucleon is still not understood. With QCD, the theory of thestrong force, a powerful tool is available to describe the interaction of quarks andgluons due to their color charge. Unfortunately a characteristic property of the strongforce prevents an application in the calculation of the nucleon. The mediator bosonsof the strong interaction, the gluons, carry the color charge themselves, unlike e.g. theneutral photons of the electromagnetic interaction. In the end this leads to the fact thatthe coupling ‘constant’ of the strong interaction αs is in fact not constant, but variesextremely with the momentum transfer q2 of a reaction. In the first limit q2 →∞ thephenomenon called ‘asymptotic freedom’ lets αs vanish asymptotically. As in QuantumElectrodynamics (QED) problems can be solved very exact using perturbation theory,because αs 1. Results predicted by QCD in the high energy regime were successfullyconfirmed by high energy collider experiments. At the other end where q2 → 0 thecoupling becomes very strong. This ‘confinement’ is the reason that quarks cannotexist as single particles but only bound in hadrons. Consequently αs is here very largeand thus there is no way to solve low energy problems in QCD perturbatively. Howeverthe nucleon and its first excited states are located exactly in this low energy regime.In the future one will maybe be able to circumvent this problems using lattice gaugecalculations. As of today this technique is still at the beginning of its development andmostly limited by the computational performance of even up-to-date computer systems.

Therefore nucleons and their excited states are described by effective models in-corporating effective degrees of freedom. For example in the simple constituent quarkmodel three equivalent constituent quarks build up a baryon. These constituent quarksmust somehow gain a lot of ‘mass’ via interaction energy because the bare ‘currentquarks’ are much lighter (see table 1.1). Theorists are trying to explain this fact us-ing different models and approaches for the interactions. However only experimental

1.1. Nucleon resonances 3

100

200

300

400

500

600

Photon energy [GeV]

0.5 0.51.0 1.01.5 1.52.0 2.02.5 2.5

1,21,2 1,51,5 1,81,8 2,12,1 2,42,4

Invariant mass [GeV]

[b]

( ,p) ( ,n)

Fig. 1.1: Cross section of the total proton (left hand side) and neutron (right hand side) photoab-sorption. The data points (green) are fitted with several Breit-Wigner shaped resonances (blue) and aslowly rising background function giving the total fit curve (black). [6]

evidence can decide on the accuracy of a model. Therefore its essential to measureas much properties of different nucleon states as possible, such as number of excitedstates, excitation energies, quantum numbers and state transitions. But on the otherhand also theoretical input is needed for the experimental work, thus progress is madeiteratively by achieving new results on both sides. [4, 5]

1.1 Nucleon resonances

Because of the direct relation between the number of excited states and the numberof effective degrees of freedom in a model the knowledge of the excitation spectrumis of crucial importance. Unfortunately this is not easily accessible in experiments.Due to the dominant decay of the resonances by strong interaction via meson emissionthe resonances are very short-lived. This leads to very large width of several hundredMeV so that the close lying resonances overlap strongly. Figure 1.1 showing the totalphotoabsorption on the proton and the neutron illustrates this difficulty. With theexception of the ∆-resonance at 1232 MeV the overlap of the resonances is large andtheir positions and widths are hard to extract.

A level scheme of the first excited states of the nucleon is shown in figure 1.2. Thenotation is equivalent to the notation used in atomic spectroscopy. The letter standsfor the relative orbital angular momentum L between the nucleon and the emittedmeson (S=0, P=1, D=2, ...). The two subscript numbers represent the double of theisospin 2I and the double of the total angular momentum 2J . Finally the mass of the

4 Chapter 1. Introduction

1000

1200

1400

1600

P11(939)

P11(1440)

D13(1520)S11(1535)

S11(1650)D15(1675)D13(1700)

P33(1232)

P33(1600)S31(1620)

D33(1700)

Mass [MeV/c2]N(I=1/2) ∆(I=3/2)

η ρ π

50%

0.06

%

Notation:

L2I2J ; L=0(S),1(P),2(D),...

Fig. 1.2: First excited states of the nucleon. The level scheme is divided into isospin 1/2 states (lefthand side) and isospin 3/2 states (right hand side). Decays via π emission are represented by the solidblue arrows, η emission by the dashed red arrows and ρ emission by the curled green arrows. Thethickness of the arrows represents the branching ratios of the corresponding decay. [5]

resonance is indicated in parentheses. The level scheme is divided into so-called N∗

states with isospin 1/2 (left hand side) and ∆ states having an isospin of 3/2 (righthand side). Different arrows indicate the different decays (see figure caption for moredetails). The resonances can be classified into two regions: The ‘∆-resonance region’around the ∆(1232) resonance, which is the best known excited state of the nucleon,and the more complicated ‘second resonance region’ reaching from 1350 to 1600 MeV.Due to isospin conservation the ∆(1232) resonance can only decay via π emission tothe nucleon ground state. This holds true for all direct decays of ∆ resonances tothe ground states. However decays via double meson emission (e.g. ηπ) are of courseallowed. The N∗ states can either decay via emission of π, ρ, η or η′ to the groundstate or via π emission to a ∆ state, if the kinematical thresholds and the angularmomentum selection rules are fulfilled.

Historically most of the knowledge about the nucleon resonances was obtained bypion scattering experiments. Because of the hadronic vertex these reactions benefitfrom large cross sections. However they also feature two major drawbacks. First, asdiscussed before, a strong interaction vertex is not that easy to handle at low energy.Second, resonances that couple only weakly to the πN channel run the risk of not beingdetected. The latter point motivated to look for other methods of resonance excitation.

1.1. Nucleon resonances 5

1000

1200

1400

1600

1800

2000

2200

2400

P11(939)

P11(1440)

D13(1520)S11(1535)

S11(1650)D15(1675)F15(1680)D13(1700)P11(1710)P13(1720)P13(1900)

F17(1990)F15(2000)D13(2080)S11(2090)P11(2100)G17(2190)D15(2200)H19(2220)G19(2250)

P33(1232)

P33(1600)S31(1620)

D33(1700)P31(1750)S31(1900)F35(1905)P31(1910)P33(1920)D35(1930)D33(1940)F37(1950)F35(2000)S31(2150)

H39(2300)D35(2350)F37(2390)H3,11(2420)

Mass/(MeV/c2)N(I=1/2) ∆(I=3/2)

exp expQM QM

Fig. 1.3: Nucleon resonances scheme. The scheme is divided into isospin 1/2 states (left hand side)and isospin 3/2 states (right hand side). Experimentally found states are labeled ‘exp’ and classifiedaccording to [1]: four or three stars (solid lines), two stars (dashed lines) and one star (dotted lines).The states predicted by a quark model are labeled ‘QM’. Resonances with no experimental counterpartare represented by dashed lines. Taken from [7].

Namely there was already evidence of an experimental bias, because theory predictedmuch more resonances as were observed in these experiments (problem of ‘missingresonances’). This is illustrated in figure 1.3 where experimentally found resonancesare compared to resonances predicted by a quark model. Particularly near 2 GeV a lotmore resonances are predicted than have been found.

As it will be discussed in the next chapter the method of meson photoproductionoffers an alternative way to look for the missing resonances as well as to investigate theproperties of the already known resonances more deeply.

Chapter 2

Meson photoproduction

An alternative way for the study of nucleon resonances is provided by meson photopro-duction. Thanks to QED the electromagnetic interaction vertex is better understoodand the photon is only coupling to the spin-flavor degrees of freedom of the quarks.But also this methods has its disadvantages: The electromagnetic reactions have muchsmaller cross sections than their hadronic counterparts and are usually accompaniedby non-resonant background reactions. Figure 2.1 shows for example the leading orderFeynman diagrams contributing to η photoproduction off the nucleon. To separate theresonance contributions from the rest coming from Born terms and vector meson ex-change terms it is necessary to use reaction models which may add model dependenciesto the results.

The study of meson photoproduction requires the the knowledge of the meson prop-erties. Some basic facts, especially concerning the pseudoscaler meson, will be men-tioned briefly in section 2.1. Afterwards the calculation of the free production thresholdis shown in section 2.2. Section 2.3 discusses the production off nuclei, anticipating somefacts of the η′ photoproduction off the deuteron (section 2.4.2) that was the main topicof this work.

2.1 Properties of pseudoscaler mesons

Meson consists of a quark-antiquark-pair (qq). Because the quarks carry a spin of1/2 a two quark system can couple to either spin 1 or spin 0. In case of the lightestmesons the orbital angular momentum is L = 0. In addition the intrinsic parity of the

η ηγ γ

N NN* N

N N

η ηγ γ

N NN* N

N N

ηρ, ω

γ

N N

Fig. 2.1: Leading order Feynman diagrams contributing to η photoproduction. Besides the trueresonance terms also Born terms and vector meson exchange term are contributing. Taken from [5].

7

8 Chapter 2. Meson photoproduction

S1

1

-1

-1

0

0 IZ

!!" #

#’!+

K

K K

K_o

o

o

+

-

Fig. 2.2: The nonet of the pseudoscaler mesons. The meson are arranged according to their z-component of the isospin Iz and their strangeness S. Taken from [4].

quarks is opposite, thus the total parity is P = (−1)L+1 = −1. Therefore two groupsof mesons can be build: The ‘vector mesons’ having JP = 1− and the ‘pseudoscalermesons’ having JP = 0−. Because the decays of the nucleon resonances are dominatedby π and η emission, and one goal of this work was the identification of the η′, only thepseudoscaler mesons should be discussed here in detail.

According to group theory1 the 3 × 3 = 9 combinations of two of lightest quarksu, d, s are building an octet and a singlet. The flavor wave functions of the non-strangemembers can be written as

|π+〉 = |ud 〉

|π0 〉 =1√2|uu− dd 〉

|π−〉 = |ud 〉

|η8〉 =1√6|uu+ dd− 2ss 〉

|η1〉 =1√3|uu+ dd+ ss 〉

whereas the |η8〉 state belongs to the octet and the |η1〉 to the singlet. This two statesare not observed directly in nature. Due to their same quantum numbers the two statesmix:

|η〉 = cos Θ · |η8〉 − sinΘ · |η1〉 ≈ |η8〉|η′〉 = sinΘ · |η8〉+ cos Θ · |η1〉 ≈ |η1〉

1symmetry group SU(3) because of the isospin 1/2 of the u and d quarks and the strangeness of thes quark

2.1. Properties of pseudoscaler mesons 9

Meson IG JPC Mass life timedecay

[MeV] [s]

π± 1− 0− 139.57 2.6 ×10−8 weakπ0 1− 0−+ 134.98 8.4 ×10−17 el.mag.η 0+ 0−+ 547.51 5.1 ×10−19 el.mag. / strong suppr.η′ 0+ 0−+ 957.78 3.3 ×10−21 strong / el.mag.

Table 2.1: Basic properties of non-strange pseudoscaler mesons. [1]

The mixing angle lies around Θ ≈ −15, or Θ ≈ −22 if a perfect SU(3) flavor symmetryis assumed [8, 9]. Hence the truly observed η is approximately an octet state and the η′

is a singlet state. Without mixing one would expect that the singlet has the lower masssince it has only ss in the wave function while the octet has 2ss. Due to the mixingthis is reversed and the singlet η′ becomes the far ‘heavier’ meson.

The π+, π0 and the π− build an isospin triplet. The complete nonet of the pseu-doscaler mesons is shown in figure 2.2 and the basic properties of the non-strangepseudoscaler mesons in table 2.1. Figure 2.3 shows a more detailed decay scheme ofthe η′. In this work the η′ → π0π0η → 6γ decay with a total branching ratio of 8.0%was used to identify the η′.

Fig. 2.3: Decay scheme of the η′ meson. In this work the strong decay of the the initial η′ (green)through the intermediate state π0π0η (blue) to 6 photons (red) was analyzed. The total branchingratio for this decay adds up to 8.0%. [1]


2.2 Kinematics of the free production

The threshold energy for meson photoproduction off the free proton can be calculatedby looking at the kinematics of the reaction. The initial state in the lab frame consistsof the incoming photon with four-momentum k and the proton with four-momentumpp, assumed to be at rest:

k = (Eγ , ~k), ~k = (0, 0, Eγ) (2.1)

pp = (mp, 0) (2.2)

Thus the total invariant mass squared in the initial state is

s = (k + pp)2 = 2Eγmp +m2p (2.3)

At threshold√s has to be large enough to produce the masses of the final state particles:

√sthr = mp +mm (2.4)

Using equation (2.3) and (2.4) the threshold photon energy Ethrfreeγ can be calculated:

Ethrfreeγ = mm +

m2m

2mp(2.5)

In case of η′ photoproduction the threshold for the production off the free proton is

Ethrfreeγ (γ + p→ η′ + p) = 1446.6 MeV

2.3 Kinematics of the production off nuclei

In the photoproduction off nuclei one distinguishes three different types of reactions.They will be presented in the following section and discussed in more detail for the η′

photoproduction off the deuteron that was studied in this work. More details about η′

photoproduction can be found in section 2.4.

2.3.1 Coherent production

In the coherent reaction the meson is produced off the whole nucleus, i.e. the totalproduction amplitude is the coherent sum of the production amplitudes of all nucleons.The nucleus remains intact and in the ground state, as it was before the reaction. Incase of η′ photoproduction off the deuteron the coherent reaction is therefore

γ + d→ η′ + d

Due to the two particle final state the energy of the produced meson is clearly definedfor fixed photon energies and polar angles.

2.3. Kinematics of the production off nuclei 11

In comparison to the production off the free proton (see section 2.2) the thresholdin the coherent production is reduced. This is due to the fact that the recoil massis larger and thus the recoil energy smaller. Consequently the threshold of the totalinvariant mass for the η′ production is achieved at lower photon energy. Using thedeuteron mass instead of the proton mass in equation (2.5) results in

Ethrcohγ (γ + d→ η′ + d) = 1202.3 MeV

Coherent cross sections are usually small because they are lowered compared to thefree cross sections by the form factors of the nuclear target2. In case of η productionoff the deuteron a further reducing was observed due to the small isoscaler contribution[5]. Because the η′ possesses the same relevant quantum numbers as the η the coherentcross section for η′ off the deuteron is expected to be small too. Hence in this work,using low statistic data, no special extraction of the coherent part of the η′ productionwas conducted.

2.3.2 Incoherent production

The incoherent production is similar to the coherent case. The difference is that thetarget nucleus is in an excited state after the reaction took place:

γ +A→ η′ +A∗

The nucleus decays later to the ground state electromagnetically via photon emission.Hence the meson energy for a fixed photon energy and polar angle take several smallervalues than in the coherent case representing the excitation spectrum of the nucleus.The cross section for incoherent production is usually small.

The photoproduction off the deuteron denotes a special case because the deuteronpossesses no excited state. Therefore the hereby defined incoherent production resultsin a breakup of the deuteron. As the breakup happens also in case of quasifree produc-tion (see next paragraph) it has to be said that no difference between incoherent andquasifree production could be made in this work. All breakup reactions were assumedto be quasifree.

2.3.3 Quasifree production

In the participant-spectator-model of the quasifree production the meson is producedoff one nucleon (participant) of the target nucleus. The other nucleons (spectators) areassumed to not take part in the reaction. The scattered participant is knocked out ofthe nucleus which results in a three particle final state:

γ +A→ η′ +Npart + (A− 1)

2Sometimes (e.g. π0 production at low energies) the form factor is compensated by the A2-factorresulting from the coherent addition of amplitudes. Then coherent production can be dominant.


Fig. 2.4: Participant-spectator-model of the quasifree η′ photoproduction off the deuteron. On theleft hand side the initial state is illustrated. The incoming photon is interacting with the participantnucleon that carries the Fermi momentum ~pF . The spectator nucleon carries the opposite momentum−~pF in both the initial and the final state, because it is assumed not to take part in the reaction. Inthe final state (at threshold) on the right hand side also the produced η′ is shown.

This leads to a distributed meson energy around the value of the free production that isadditionally broadened by the Fermi momentum of the participant nucleon. The Fermimomentum is also responsible for the reduction of the photon threshold energy com-pared to the free production. Nevertheless the coherent threshold plus the separationenergy is the kinematically lowest possible threshold (see below). As mentioned abovethe quasifree production is expected to be the dominant reaction in η′ photoproduction.Therefore some aspects of the quasifree η′ production will be discussed in detail in thefollowing part.

Figure 2.4 illustrates the situation of quasifree η′ photoproduction off the deuterondescribed by the so-called participant-spectator-model. The incoming photon is onlyinteracting with the participant nucleon p while the spectator nucleon s is not takingpart in the reaction. Naturally either the proton or the neutron can play the role ofthe participant or the spectator, respectively:

γ + d→ η′ + ppart + nspect

γ + d→ η′ + npart + pspect

The initial state kinematics in the lab frame is set up as follows: The participanthaving the mass mp and energy Ep is carrying a Fermi momentum of ~pF . The spectatorwith mass ms and energy Es carries therefore a Fermi momentum of −~pF so that thetotal deuteron with mass md is at rest. Requesting energy and momentum conservationwe have

pd = pp + ps =

(Ep

~pF

)+

(Es

−~pF

)=

(md

0

)(2.6)

Because the energy of the spectator is

Es =√m2

s + ~p 2F (2.7)

2.3. Kinematics of the production off nuclei 13

and the deuteron binding energy Bd is neglected in this model3 (thus md = mp +ms)the energy of the participant is

Ep = md −√m2

s + ~p 2F 6=

√m2

p + ~p 2F (2.8)

and hence the participant is off-shell.The calculation of the quasifree production threshold is similar to free case (see

2.2). Starting with the initial state

k = (Eγ , ~k), ~k = (0, 0, Eγ) (2.9)

pp = (Ep, ~pF ) (2.10)

the square of the total invariant mass s is calculated:

s = (k + pp)2 = E2γ + 2EγEp + E2

p − (~k + ~pF )2 (2.11)

Using Ep from (2.8) and ~k from (2.9) we get

s = m2d +m2

s + 2Eγ

(md −

√m2

s + ~p 2F

)− 2md

√m2

s + ~p 2F − 2EγpF, z (2.12)

In the final state the same condition at threshold as for the free case is used√sthr = mp +mη′ (2.13)

where mp is the on-shell mass of the participant. Combining (2.12) and (2.13) resultsin the threshold for quasifree η′ photoproduction:

Ethrq.f.γ =

(mp +mη′)2 −m2d −m2

s + 2md

√m2

s + ~p 2F

2(md − pF, z −

√m2

s + ~p 2F

) (2.14)

Eq. (2.14) has two important limits:

1. ~pF → 0If the Fermi momentum is zero the quasifree threshold Ethrq.f.

γ is equal to the freethreshold Ethrfree

γ of (2.5).

2. For Fermi momenta antiparallel to the incoming photon momentum the quasifreethreshold Ethrq.f.

γ reaches a minimum at the coherent threshold Ethrcohγ .

Figure 2.5 shows the dependence of the quasifree threshold Ethrq.f.γ of η′ photopro-

duction of the deuteron from the participant Fermi momentum. Here the proton wasassumed to be the participant. But for the production off the deuteron the curvelooks very much the same for the case where the neutron is the participant. The Fermi

3as the deuteron binding energy is only Bd = 2.2 MeV its negligence is acceptable


participant Fermi momentum [MeV]0 100 200 300 400 500

[MeV

]γth

r.E

1200

1250

1300

1350

1400

1450free threshold

coherent threshold

938 900 800 700participant off-shell mass [MeV]

Fig. 2.5: Quasifree threshold Ethrq.f.γ for the η′ photoproduction off the deuteron in dependence of

the participant Fermi momentum. The Fermi momentum was set antiparallel to the incoming photonmomentum and the proton was assumed to be the participant. The two limits of free and coherentproduction are indicated by the dashed lines (see text). Also the participant off-shell mass is indicated.

momentum was set antiparallel to the incoming photon momentum. The two limits dis-cussed above are clearly visible, whereas the rising of the threshold beyond its minimumat the coherent threshold is not part of the physical region. Also the correspondingoff-shell mass of the participant is indicated.

Because of the second limit of eq. (2.14) the threshold for the quasifree produc-tion can only be lowered by Fermi momentum down to the coherent threshold. Moreprecisely the lowest possible threshold is the coherent threshold plus the binding energy:

Ethrq.f.γ = Ethrcoh

γ +B (2.15)

In case of quasifree η′ photoproduction off the deuteron the threshold is:

Ethrq.f.γ

(γ + d→ η′ + ppart + nspect

γ + d→ η′ + npart + pspect

)= 1204.55 MeV

2.4. η′ photoproduction 15

2.4 η′ photoproduction

2.4.1 Present data for the free production

Photoproduction of π and η mesons have been already studied intensively by differentcollaboration like A2 at MAMI, SAPHIR and CB-ELSA at ELSA, CLAS at JLaband GRAAL at ESRF. Especially experiments involving η photoproduction offer thepossibility for selective investigations of isospin 1/2 resonances due to the zero isospinof the η (isospin filter). In addition certain background terms coupling to the mesoncharge are suppressed because the η is neutral. This is all also true for the η′ but thereare additional reasons that motivate η′ photoproduction experiments [10]:

• Because of the significant part of ss in the η′ wave function the nucleon can alsobe probed for ss components

• Gluonic coupling to the nucleon and the gluonic degrees of freedom may be probedbecause the η′ is the only pseudoscaler isosinglet meson

• The NNη′ coupling is not known very well

Unfortunately the cross section for η′ photoproduction is very small. Thereforehigh requirements are demanded of the experimental facilities, e.g. high beam currentsand large detector acceptances. Besides some older data of minor statistics [11, 12]there are currently only two published results of η′ photoproduction off the protonmeasured by the SAPHIR4 [13] and the CLAS [14] collaborations. Summarized, theCLAS collaboration analyzed 2 × 105 η′ events and suggests a coupling of the η′N

channel to the S11(1535) and the P11(1710) resonances5. Further also spin J = 3/2resonances seem to be important [15].

2.4.2 Production off the deuteron

Besides the goal of finding ‘missing’ resonances one also want to further investigatethe known resonances and determine its properties accurately. However the isospinstructure of the electromagnetic excitation, for example, can only be determined bymeasurements on the neutron. Since there is no sole neutron target neutrons bound inlight nuclei have to be used. The deuteron is an ideal candidate because the binding en-ergy is small and the nuclear structure is well understood. Thus neutron measurementscan be done by looking for quasifree reactions. Because the electromagnetic interactiondoes not conserve the isospin I but only its z-component Iz the helicity amplitudes can

4Compared to the high statistics CLAS data the cross sections extracted in the SAPHIR experimentare probably overestimated

5These two resonances are also known to couple to the ηN channel


be separated into an isospin conserving part (isoscaler) and an isospin violating part(isovector). In case of η′ photoproduction off the deuteron (I = 0, J = 1) the crosssections show the following relations

σp ∝ |AIS1/2 +AIV

1/2|2 (2.16)

σn ∝ |AIS1/2 −AIV

1/2|2 (2.17)

σd ∝ |AIS1/2|

2 (2.18)

where AIS1/2 is the isoscaler and AIV

1/2 the isovector part, respectively, and σd denotes thecoherent cross section. Measuring all three cross sections allows the determination of theamplitudes, however the extraction of σd requires some models to account for nucleareffects. σn was never measured, results of the CB-ELSA collaboration are expected tobe published soon [16]. Preliminary results show that σp is in good agreement with thedata from free production whereas the neutron data is somehow puzzling [17].

2.4.3 The goal of this work

Thanks to the latest upgrade the accelerator facility MAMI (see section 3.1) is now ableto produce η′ off the deuteron at threshold (max. tagged photon energy: ∼ 1400 MeV).Threshold measurements are especially useful to study the η′-nucleon interaction viafinal state interaction (FSI). Also data analysis is facilitated because background reac-tions involving additional meson production are kinematically not possible at threshold.

The goal of this work was to investigate the feasibility of such experiments usingvery early data that were taken during test measurements shortly after the completionof the accelerator upgrade. Therefore an attempt was made to identify η′ mesons andto calculate a first estimation of the inclusive cross section. The obtained results willbe discussed in chapter 5.

Chapter 3

Experimental setup

In this chapter the experimental setup currently used by the A2 collaboration at MAMIin Mainz, Germany, is described. Besides the electron accelerator the setup basicallyconsists of the photon tagger, the Crystal Ball detector and the TAPS detector. Figure3.1 gives an overview of the experimental situation: The electron beam is entering fromthe left hand side and hitting a metal foil (radiator) where photons are produced viabremsstrahlung. These photons are passing through a collimator towards the targetwhile the electrons are deflected by the magnetic field of the tagger and hit the so-called ‘detector ladder’ at a certain position according to their energy. The LD2 (liquiddeuterium) target is surrounded in a onion skin-like design by a particle identificationdetector (PID) and the Crystal Ball (CB) detector. The Two Arm Photon Spectrometer(TAPS) detector is installed in forward beam direction to compensate for the hole inCB.

3.1 The MAMI electron accelerator

The MAMI (Mainzer Mikrotron) electron accelerator facility at the Institut fur Kern-physik at the Johannes Gutenberg-Universitat in Mainz was built in the beginning ofthe 1980-ties. Through the years several upgrades were carried out to reach higherbeam energies. In 1990 the extension ‘MAMI B’ was installed allowing a maximumbeam energy of 855 MeV. After a construction period of six years the latest extension‘MAMI C’ was finally ready for experimental testing in spring 2007.

Figure 3.2 shows the floor plan of the MAMI facility. Unpolarized and polarizedelectrons are produced by an electron cannon (for polarized electrons a special GaAsPcrystal is used). In a first step the electrons are accelerated in a LINAC (linear acceler-ator) to 3.97 MeV. Afterwards they are flying through a cascade of so-called racetrackmicrotrons (RTM).

In an RTM, that has a rectangle-like ground view, a LINAC (at MAMI: cavityresonator/clystron based) is installed on one of the longer sides. On the two smallersides two dipole magnet are facing each other. The electrons follow oval tracks and are

17

18 Chapter 3. Experimental setup

Fig. 3.1: Overview of the experimental setup. See text for more details.

once accelerated in the LINAC and twice deflected by 180 degrees in the magnets atevery circulation. Due to the gain of kinetic energy the radii of the semi-circles in themagnets are getting larger and larger with every turn. Having reached the most outertrack after a certain number of turns the electron beam is extracted and led to the nextone.

The beam energy reaches 14.9 MeV after passing through RTM1, 180 MeV afterRTM2 and 855 MeV after RTM3 (‘MAMI B’). The latest accelerator stage ‘MAMIC’ is not an RTM, but a very similar device called HDSM (harmonic double sidedmicrotron). An HDSM possesses four magnets in each corner and one LINAC installedon each of the two longer sides. The reason to set up an HDSM instead of an RTMwas due to the limited hall size the device had to fit in: To generate a beam of thesame energy in an RTM the magnets would be six times larger than they are in theHDSM. The final energy of the electron beam after all accelerator stages is 1.506 GeV.Table 3.1 gives an overview of the most important parameters of the MAMI acceleratorsystem.

Parameter Injector RTM1 RTM2 RTM3 HDSM

extration energy 3.97 MeV 14 MeV 180 MeV 855 MeV 1508 MeV# of turns - 18 51 90 43

magnetic field - 0.1026 T 0.5550 T 1.2842 T 1.53-0.95 Tweight of magnets - 4.2 t 92.3 t 911.6 t 1030 t

linac length 4.93 m 0.80 m 3.55 m 8.87 m 8.57 / 10.10 m

Table 3.1: Main parameters of MAMI [18]

3.1. The MAMI electron accelerator 19

Fig. 3.2: MAMI floor plan. The electrons are produced in an electron cannon in the most outer lefthall. Afterwards they are accelerated by an injector LINAC and three RTMs. After passing through theHDSM the beam reaches an energy of 1508 MeV. Finally the beam is guided into the A2 experimentalhall. Taken from [18].

MAMI is a CW (continuous wave) machine. This means that the time differencebetween two electron beam packages is smaller than the detector time resolution. Be-cause of this the beam is ‘seen’ in the detectors as a continuos current. This fact isoften described by the so-called ‘duty factor’ that has in this case a value of 100%.The opposite of a CW machine is a pulsed machine where single beam packages canbe resolved in the detector. Pulsed machines are used in experiments where very highbeam currents (∼ 1A) are needed. Due to technical limitations (cooling, losses, ...)such high currents cannot be achieved in CW machines. Nevertheless pulsed machinesare not suitable for coincidence experiments because the accidental background riseswith the square of the beam intensity.

In the case of photoproduction experiments a high beam current is desirable becauseof the mostly small cross sections of the investigated reactions. In addition to that atime coincidence analysis should be possible. The CW machine at MAMI providesan excellent beam quality and currents up to 100 µA and is therefore one of the bestaccelerator available to perform studies in this area. Further information about MAMIcan be found in [18].


Fig. 3.3: Photograph of the Glasgow photon Tagger (View to target). Between the large blue dipolemagnets the focal plane detector ladder can be seen (along the line of cooling fans). Shielding indirection to the target is provided by blocks of concrete.

3.2 The Glasgow photon tagger

Photoproduction experiments require a high energy photon beam. One method tocreate such a beam with an electron accelerator is ‘bremsstrahlung tagging’. In thismethod the electron beam is led to a metal foil where photons can be produced viabremsstrahlung. If the beam energy Ebeam and the energy of the electron Ee− after thefoil is known, the photon energy is simply

Eγ = Ebeam − Ee− (3.1)

So if the energy of the bremsstrahlung producing electron is measured, the correspond-ing photon is ‘tagged’, i.e. its energy is known. This job is done by a device naturallycalled ‘tagger’ which is installed just after the radiator foil. The tagger at MAMI wasconstructed by the Glasgow group [19, 20], a photograph of the device is shown infigure 3.3. In this apparatus the electrons enter a magnetic field provided by a largedipole magnet and are deflected laterally. In addition to that their trajectories are splitup according to their kinetic energy. After being bent by about 90 degrees they hit aplastic scintillator detector array installed in the focal plane whereas their hit positionin the array depends on the deflection and thus on their kinetic energy. Accordingto eq. (3.1) electrons that produced very high energetic bremsstrahlung photons have

3.3. The Crystal Ball detector 21

small kinetic energies, so they reach only the nearest elements in the detector ladder.Electrons hitting the furthest end of the ladder have lost little energy and are henceassigned to low energy photons. Finally electrons that have not radiated at all aredirected to a beam dump (see figure 3.1).

The detector ladder consists of 352 plastic scintillators coupled to photomultipliers.Each element is arranged perpendicular to the corresponding electron track and overlapswith its two neighbor elements. Thanks to this background hits can be reduced byapplying a coincidence cut on two elements because a true electron should always hitboth. The energy resolution depends on the width of the scintillators and is around 2MeV. However there is another, smaller detector ladder called ‘tagger microscope’ thatcan be positioned at a region of interest in case a better resolution is desirable (e.g.photoproduction at threshold). With this detector a resolution of about 400 keV canbe achieved.

Because the photon flux behaves as a typical ∼ 1/Eγ bremsstrahlung distributiona lot of low energy photons are produced. For this experiment one is not interestedin these photons, however they will be recored by the data acquisition contributing tothe dead time of the detector system. In order to maximize the beam current and thusthe photon flux the high electron energy (low photon energy) detector elements wereswitched off. In the first period of data taking only photon energies starting at 807MeV were tagged. In the second period the threshold was set to 607 MeV.

3.3 The Crystal Ball detector

The Crystal Ball (CB) [21] is a segmented calorimeter detector initially constructedfor experiment at SLAC. Later it was moved to DESY and is now finally locatedat MAMI. It was designed to detect neutral particles with great angular acceptancecovering around 94% of the solid angle. CB is a so-called 4π-detector. In the sphericalshape 720 inorganic NaI(Ti) crystals of 40.6 cm height (∼ 16 radiation lengths) areinstalled pointing towards the center of the sphere. In the range of 0 to 20 and 160to 180 degrees of the polar angle (with respect to the center) no crystal are installedthus providing the entrance and exit windows for the beam. The inner radius of thesphere is 25 cm and the outer radius is 66 cm. The detector is divided into a top anda bottom hemisphere that are booth vacuum sealed because the NaI(Ti) crystals arehighly hygroscopic. Each crystal is separated from the others by reflecting foils andconnected to a photomultiplier. A photograph of CB in its red housing can be seen infigure 3.4.

3.4 Particle identification detector

Because of the short distance between the target and the Crystal Ball and the insuf-ficient time resolution of the Na(Ti) crystals no time-of-flight methods can be usedfor particle identification. Therefore a particle identification detector (PID) [22] was


Fig. 3.4: Photograph of the Crystal Ball detector. The two hemisphere (silver) are installed in the redmetal housing. Each crystal is read out by a photomultiplier (black tubes) that are connected throughthe red and blue cables to the data acquisition system and the high voltage supply.

constructed to identify charged particles. It consists of 24 plastic scintillators of thesize 31 cm × 13 mm × 2 mm which form a cylinder of 10 cm diameter. The PID isinstalled between the target and the Crystal Ball detector. More details about particleidentification using the PID is given in section 4.3.1.

3.5 The TAPS detector

One block of the universal TAPS detector system (Two Arm Photon Spectrometer) [23]is used in Mainz as forward wall detector to cover the hole in CB and is installed 1.5m behind the target (see photograph in figure 3.5). It consists of hexagonally shapedinorganic BaF2 crystals that are in the current configuration first arranged in trianglesof 64 elements. 6 of this triangles are then combined to a hexagonal wall resulting in384 detectors. Each element is 25 cm long (12 radiation lengths) and the diameter of

3.6. Data taking and analysis 23

Fig. 3.5: Photograph of the TAPS detector. TAPS is installed 1.5 m behind the target in forwarddirection to cover the hole in CB. It consists of 384 BaF2 crystals that form a hexagonal wall.

the inscribed circle is 5.9 cm). In front of each crystal a 5 mm thick NE102A plasticscintillator is installed that serves as a veto detector for the corresponding element. Allcrystals and all vetos are read out by separate photomultipliers.

Due to the special scintillation properties of BaF2 a so-called pulse shape analysiscan be conducted to identify different types of particles. More details about this canbe found in section 4.3.2.

3.6 Data taking and analysis

The data analyzed in this work was taken from May 11 to May 21 2007. This wasthe first beamtime where the new 1.5 GeV beam was tested on the liquid deuteriumtarget. The main parameters of the experiment are show in table 3.2. Two taggingefficiency measurements were performed (see section 4.6.2). Unfortunately the datayield was not very high because many problems occurred. To get as much statistics as


Parameter Value

electron beam energy 1508 MeVbeam current 20 nA (30 nA)radiator 10 µm Cucollimator diameter 4 mmactive tagger channels 0-223 (0-175)tagged photon energies 608-1399 MeV (807-1399 MeV)

target type liquid deuterium (LD2)target length 47.6 mm ± 0.3 mm

CB trigger multiplicity 2+CB trigger energy threshold Esum > 500 MeV

size of good raw data 169 GBbeam time (good data) ∼33 h

Table 3.2: Experimental parameters

possible it was tried to recover good events out of broken data files. Finally 102 datafiles corresponding to a beamtime of ∼33 h could be used for the analysis.

The data analysis was conducted using the software AcquRoot [24]. AcquRoot isthe successor of ACQU, the formerly used data acquisition and analysis software ofthe A2 collaboration. AcquRoot is written in C++ and based on the CERN ROOTframework [25]. It offers the access and the control of all detector data. Thanks to theobject-oriented design the software can be easily adapted and expanded.

Chapter 4

Data analysis

Extracting physical results from the raw data recorded by the data acquisition systemrequires several steps. First of all the detectors have to be calibrated to associate theirelectronic signal or numerical output to a physical quantity. The energy calibration willbe described in section 4.1. Unfortunately TAPS could not be used in this work becauseof some problems concerning that detector which could not be resolved within the timeframe of this work. In section 4.2 the time calibration and the random subtractionis presented. Once reliable information is available particles can be distinguished andidentified by the their characteristic detector signatures. Section 4.3 gives an overviewof the basic techniques. A short introduction to the event simulation can be found insection 4.4. Finally when the types and physical quantities of all particles are known thereaction channel of interest can be investigated (section 4.5). This last step includes theremoval of as much background data as possible to obtain a clear signal so a statementabout a physical observable can be made. At the end the extraction of the inclusived(γ, η′)X cross section is explained in section 4.6.

4.1 Energy calibration

Each photomultiplier of a crystal element in either Crystal Ball or TAPS is read outseparately by a QDC (Charge to Digital Converter). Depending on the integratedcurrent (or charge) the QDC stores an event in the corresponding digital channel. Therelation between the deposited energy in the crystal and the channel number (i.e. theaccumulated charge) is approximately linear. So if one wants to determine the relationbetween channel number and energy one has to know the energy of at least two channels.

Due to the geometrical differences between Crystal Ball and TAPS different waysof energy calibrations were used for the two detectors.

TAPS TAPS was energy calibrated with the help of cosmic muon radiation. Thesemuons are the so-called ‘hard’ component of the secondary cosmic radiation which isproduced in the earth’s atmosphere by the primary cosmic radiation [26]. They have

25

26 Chapter 4. Data analysis

channel number0 100 200 300 400 500 600 700

Cou

nts

per

bin

[a.u

.]

1

10

210

310

410pedestal

min.-ionizing cosmics peak

Fig. 4.1: Cosmics spectrum of a TAPS module. Superimposed on a background the minimum ionizingpeak of the cosmic muon radiation can be identified at around channel 230 corresponding to 37.7 MeV.The pedestal is located around channel 100 corresponding to 0 MeV.

an average energy of ≈ 4 GeV [1] and are according to the Bethe-Bloch equation forthe most part minimum ionizing particles. Knowing the diameter of a TAPS module(5.9 cm [23]) and the minimum energy loss in BaF2 (dE/dx|min = 6.37 MeV/cm [1]) apeak around 37.6 MeV can be expected. The exact position of the peak at 37.7 MeVwas determined by M. Robig-Landau [27].

Fig. 4.1 shows the raw QDC channel spectrum of a TAPS module. Indeed a peaklying on a rather large background can be observed around channel 230 providing thefirst point necessary for the energy calibration. The second point is the pedestal aroundchannel 100 which correspond to no true signal but just electronic noise. This point ofcourse corresponds to 0 MeV.

In addition to the described calibration one should later perform a second calibra-tion step using reconstructed meson masses. This corrects for electromagnetic showerleakages in the detector and losses in the electronics. That kind of calibration was notdone in this work.

Crystal Ball As mentioned in the introduction Crystal Ball cannot be calibratedwith cosmic muon radiation. This is because the detector elements in Crystal Ball arenot positioned horizontally as are all elements in TAPS but are arranged sphericallyaround the center of the detector. The described calibration in the following paragraph

4.2. Time calibration and random subtraction 27

was not part of this work and was already done before.The first step in the energy calibration of Crystal Ball was done using the 4.438 MeV

γ-source 241Am/9Be. The aim was to place the measured peak in every detector elementinto the same region of the ADC spectrum by adjusting the high voltage of the elements’photomultipliers. But the photons that have to be detected in the experiment possessmuch more energy. Therefore high energetic photons must be taken for a more precisecalibration. They were found in the reaction γp → pπ0 → pγγ which is kinematicallyoverdetermined. Knowing the beam energy and the emission angle of the π0 the energyof the decay photons was calculated and compared to the measured value. In mostcases one photon produces a hit cluster and deposits its energy in several neighboringcrystals. Thus the calibration factors for the crystals have to be calculated iterativelybecause a change of this factor for one crystal has always an influence on its neighbors.

Tagger The relationship between the element number in the Tagger’s focal planedetector ladder and the electron energy can be obtained by a computer program. Usingray tracing techniques this program computes the trajectories of the electrons in themagnetic field and calculates the mean electron energy for every detector element. Theactual field strength is measured with the help of an NMR probe that is installed insidethe tagger magnet and constantly monitored during data taking.

4.2 Time calibration and random subtraction

For a coincidence analysis one must have a timing signal of all detectors involved inthe particle detection. Therefore each detector is connected to a TDC (Time to DigitalConverter) that records the timing signal produced by the trigger. There is a constantTDC channel to time relationship, namely 100 ps per channel for TAPS and 117 psfor Crystal Ball and the Tagger. In a typical time spectrum a peak representing thecoincidental events is lying on a flat, constant background coming from random events.

As a preparation for the later required random subtraction all coincidence peaksin the time spectra of TAPS and Tagger were aligned at 0 ns. The magnitude of theshift was obtained by fitting the peak in each spectrum with a gaussian and a linearbackground function. Due to the time walk effect in LEDs (Leading Edge Discrimina-tors) a so-called walk correction has to be done for Crystal Ball. This corrects for thefact that there is an energy dependent time shift, i.e. the time of smaller signals (lowenergy events) has to be shifted more than the time of stronger signals (high energyevents). After the walk correction, that was done by F. Pheron, the coincidence peakof Crystal Ball is also aligned to 0 ns.

Within the time window that is opened by the trigger also random hits in thedetectors are recorded. For instance, in this experiment the tagger registers in average38 hits per event. Of course only one belongs to the true coincidental electron thatproduced the photon which later possibly gave rise to a reaction in the target. Withthe help of the timing information the random hits can be identified and removed.


[ns]Tagger - tCB, avrgt-200 -150 -100 -50 0 50 100 150 200

Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250

300

350

400310×

FWHM: 2.88 ns

P1BG 2BG

Fig. 4.2: Relative timing of Crystal Ball and Tagger. The true coincidental event peak (green) is lyingon a slightly skew background of random events that is assumed to go on continuously under the peak.Because one cannot tell if a prompt event is really coincidental (green) or just accidental (red) one hasto carry out a statistical removal using true random events left and right to the prompt peak (blue).

Unfortunately this cannot be done for a single event but only statistically. The reasonfor this is that even in the coincidence peak there is a random background coming fromaccidental coincident hits. Therefore it is impossible to tell by just looking at the timeif a hit was coincidental or not. The trick works as follows: In the spectrum showingthe relative timing between the Tagger and Crystal Ball (average time of a photon hit)one defines three regions of interest (see figure 4.2):

1. A narrow region around the coincidence peak (prompt region), in this analysischosen from -2.5 ns to 2.5 ns (red and green areas)

2. A wider region in the random background to the right of the coincidence peak,in this analysis chosen from -200 ns to -100 ns (BG1)

3. A wider region in the random background to the left of the coincidence peak, inthis analysis chosen from 100 ns to 200 ns (BG2)

In the analysis one then loops over the hits in Tagger calculating the values for allspectra for each hit. Also the relative time of Tagger and Crystal Ball is calculatedfor every hit. If this time belongs to either one of the defined background regions thecalculated values are stored in designated background spectra. If the time belongs to the

4.3. Particle identification 29

prompt region the prompt spectra are filled. Afterwards the random subtraction can beachieved by subtracting the prompt spectra with a scaled version of the correspondingbackground spectrum. For this one assumes that the random background goes oncontinuously under the prompt peak. The scale factor s is the ratio of the backgroundarea in the prompt P (red) and the sum of the left and right true background areasBG1 and BG2 (blue):

s =P

BG1 +BG2(4.1)

In case of a flat background one gets this ratio easily just from the widths of the promptand random windows. This allows a random subtraction on-the-fly during the analysisusing a weighted histogram filling. In the data used in this analysis the backgroundwas rather skew1 so that the whole areas had to be calculated after all data have beenanalyzed. For this purpose a polynomial of second order combined with a gaussianwas fitted to the time spectrum. Afterwards the prompt background area could becalculated by integrating the polynomial background function. With the fit also theFWHM of the prompt peak being 2.89 ns could be determined. This value probablycould have been further optimized if more time was available for this work.

4.3 Particle identification

As mentioned in the introduction to this chapter TAPS was finally not used in the dataanalysis of this work. Therefore the only applied particle identification was provided bythe Particle Identification Detector (PID) installed in Crystal Ball. Its configurationwill be described in section 4.3.1. A short summary of other methods that could havebeen used with TAPS will follow in section 4.3.2.

4.3.1 Particle identification detector

With the PID (see section 3.4) charged particles can be detected. This is of courseuseful if one wants to identify charged reaction products (e.g. recoil nucleons) but alsothe detection of electrons helps to clean up the photon signal in Crystal Ball (electronveto). In this work the PID was configured to properly identify pions and protons.

Particles are identified by looking at their total deposited energy in Crystal Ball (i.eapproximately the total energy of the particle) and their energy loss in the thin plasticscintillators of the PID. If this two values are filled into a two-dimensional histogramfor every event characteristic patterns representing the different particle types emerge.The reason for this is the different energy-dependent energy loss that is described bythe Bethe-Bloch equation2. Figure 4.3 show the mentioned histogram for one PIDelement. As the lighter particle the pions deposit less energy (around 0.4 MeV) in

1The reason for this is probably the high intensity of the beam. Applying techniques described in[28] in a future analysis may improve the accuracy of the random subtraction.

2except for the electron


Cou

nts

per

cell

[a.u

.]

1

10

210

310

410

Energy deposit in CB cluster [MeV]50 100 150 200 250 300 350 400 450 500

Ene

rgy

depo

sit i

n P

ID e

lem

ent [

MeV

]

0

0.5

1

1.5

2

2.5

3

3.5

4

π

p

Fig. 4.3: ∆E to E plot of a PID element. Above around 100 MeV the energy loss of the pions isapproximately constant. The energy loss of the protons is falling with rising energy (see text). Thepolygon cut for the pions is represented by the dashed line, the solid line represents the proton cut.

the PID elements3. Starting at around 100 MeV pions are already minimum ionizingparticles. Therefore their energy loss remains at a constant level from 100 to 500 MeVof total energy. The heavier proton on the other hand is not yet minimum ionizing. Itsenergy loss shows a clear dependence on the total energy starting from 3.5 MeV at 50MeV and reaching 0.8 MeV after 350 MeV.

Having identified the regions of the protons and the pions cuts can be created bythe definitions of boundaries. To find the best ones it is possible to fit two-dimensionaldistributions to the data. Nevertheless considering both effort and yield the boundsof the two regions were created ‘manually’ by drawing polygons that include the tworegions (see figure 4.3). For each of the 24 PID elements one proton and one pionpolygon were defined. In the analysis the AcquRoot software checked these cuts forevery hit in Crystal Ball. If the energy loss-energy combination of a hit belongs to eitherone of the regions, a proton (or pion respectively) is assumed and the correspondingmass is used in the reconstructed four-vector of the particle. Otherwise a photon hit isassumed an the mass is set to zero.

3At higher energies the mass dependence of the energy loss is negligible

4.4. Simulation 31

4.3.2 Other methods

The following section gives an overview of other methods to identify particles, especiallywhen using TAPS. Due to the limited time frame they were not used in this work.

Veto detectors In front of every BaF2 crystal of TAPS a 5 mm thick plastic scin-tillator is installed. They serve as veto detectors to distinguish between charged andneutral particles. No energy or time information is available for this detectors as only‘hit’ (charged particle) or ‘no hit’ (neutral particle) is recorded.

Pulse shape analysis BaF2 possesses two scintillation components: The fast com-ponent has a life time of τ = 0.9 ns whereas the slow component decays within τ = 630ns. This two components are not equally excited by different types of particles. Forexample, massive particles like protons produce very little light through the fast com-ponent. By integrating the electronic signal of the photomultipliers over two differenttimes4 the individual strength of this two components is taken into account for theanalysis. One therefore can plot the long gate energy versus the short gate energyand after applying some cuts one is able to differentiate between proton/neutrons andphotons/electrons. Finally if also the veto detectors are used, proton and neutron hits(or electron and photon his, respectively) can be discriminated.

Time of flight analysis Charged particles can also be distinguished by their time offlight. Due to different masses the same reconstructed kinetic energy leads to differentvelocities and therefore to different times to pass a (possibly normalized) distance. Soif the deposited energy is plotted versus the time of flight separated bands representinge.g. pions, protons and α-particles can be found and used for particle identification.

4.4 Simulation

The Monte Carlo simulation of the Crystal Ball and TAPS detector system is writtenin FORTRAN and based on the software packages CERNLIB and GEANT3 of CERN[29, 30]. The simulation procedure is divided into two steps. First a HBOOK filecontaining all the kinematics, trajectories, particle types and the reaction vertex iscreated with the help of a FORTRAN-based event generator. In the second step thisfile is processed with the GEANT3 program where the passage of the particles throughthe experimental setup (tracking) and the detector response is simulated event-by-event. Also a visualization of every event can be created, figure 4.4 shows for exampleone event of the simulated η′ decay into six photons.

For this work the simulation was used to develop the data analysis as long no realdata was available. This was possible because the produced data of the simulation canbe used for the analysis in the same way as real data. The necessary data conversion is

4so-called short and long gate integration


1γ

2γ

3γ

4γ

5γ

6γ

Fig. 4.4: Visualization of the η′ decay into six photons. All particles are tracked through the exper-imental setup consisting of Crystal Ball, PID and TAPS. Photons are represented by the dashed bluelines, red solid lines represent charged particles (except muons). The electromagnetic showers in thedetector elements can be clearly seen.

handled automatically by the AcquRoot software. Therefore the same analysis (besidestiming related analysis steps) could be used for both simulation and real data. Secondlythe simulated line shape of the η′ peak in the 2π0η invariant mass and the obtainedoverall detection efficiency was later used in the analysis of the real data. For thispurpose 6 million events of the decay η′ → 2π0η → 6γ were processed.

4.5 η′ reconstruction in the 6γ channel

The goal of the procedure described in this section is to reconstruct the η′ in the 6γdecay channel:

η′ → π0π0η → 2γ 2γ 2γ = 6γ

Several steps are necessary to select good events and remove as much background aspossible. They will be presented in the following sections. An overview of the appliedcuts will be given in section 4.5.6. As a final result the η′ signal should be visible in the2π0η invariant mass so that the signal to background ratio can be estimated to finallyextract the cross section.

4.5. η′ reconstruction in the 6γ channel 33

4.5.1 Final state analysis

As discussed in section 2.4.2 the threshold for the production of an η′ meson andan additional meson (e.g. charged or neutral pion) is too high to be reached at thisexperiment. Therefore in a first step only the following three reactions are taken intoaccount in the analysis:

γ + d → η′ + d

γ + d → η′ + p+ nspect

γ + d → η′ + n+ pspect

The final state deuteron of the first coherent reaction was not detected in this work.As for the recoil nucleon of the quasifree reactions only the proton could possibly bedetected in the PID of Crystal Ball. However most part of the recoil nucleons areto be expected having a polar angle less than 20 degree and thus flying into TAPS[17]. Because TAPS was not used for this analysis also these recoil nucleons were notdetected. The neutrons anyway are much harder to detect. An attempt was made toidentify quasifree reactions on the neutron by looking for 7 neutral hits and taking thebest 6γ+n solution via a χ2 selection. Unfortunately with this method no clear signalcould be extracted. Hence only the final state containing 6 photons was used in thisanalysis.

intermediate state invariant mass [MeV]γ6100 200 300 400 500 600

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

0π η

600×

Fig. 4.5: 6γ intermediate state invariant mass for the best χ2 solutions. The filled π0 (blue) and η(green) histograms were background subtracted using a polynomial background function. The π0 peakis clearly visible while the η peak is only weak and was scaled for visibility by a factor of 600. The redsolid lines denote the applied invariant mass cuts, the dashed black lines denote the real meson masses.

4.5.2 Intermediate state analysis

In this step of the analysis the intermediate state particles of the η′ decay are recon-structed out of the 6 final state photons. The η′ decays with a probability of 20.8%into two π0 and one η which then all decay later to two photons (with probabilities


of 98.8% and 39.4%, respectively). Because one does not know which pairs of the 6photons belong to either the π0 or the η all 15×3 possible combinations5 are computedand finally the ‘best’ one is taken. By ‘best’ one means the solution that holds theminimal error of the invariant masses defined by the following χ2 function

χ2 = (mη −mγ1γ2)2 + (mπ0 −mγ3γ4)

2 + (mπ0 −mγ5γ6)2 (4.2)

where mη and mπ0 are the real π0 and η masses and the indices of the photons ofthe two photon invariant masses are changed for all combinations. Because of theη → 6γ background (see section 4.5.4) an equivalent χ2 is calculated for a possible 3π0

intermediate state:

χ2 = (mπ0 −mγ1γ2)2 + (mπ0 −mγ3γ4)

2 + (mπ0 −mγ5γ6)2 (4.3)

Figure 4.5 shows the intermediate state invariant mass of the best solutions de-termined with the χ2 method including the best solutions for the η → 6γ. The π0

peak is clearly visible while the η peak is completely hidden in the background. Thisbackground is first coming naturally because of the combinatorial selection as it is alsoappearing in the analysis of simulated data. Second other ‘not-real’ 6 photon hits con-tribute to the background, e.g. events where one photon escaped the detector and theother 6th hit was due to a secondary cluster or even another particle.

Finally to reconstruct the intermediate state mass cuts for π0 [110, 160 MeV] andthe η [500, 600 MeV] were applied. Thus only 3π0 and 2π0η intermediate states ofwhich every particle fulfilled the corresponding cut were used for further analysis.

4.5.3 Intermediate state meson mass correction

Figure 4.5 shows that the invariant mass of the intermediate state π0 and η is quitenear to the real value. But this hold only true for the average value. The invariantmass mγγ of a single event takes values from the lower to the upper bound of themass cut (see section 4.5.2). Because of this the energy resolution is rather bad andone obtains a smeared signal if one later uses the four-vector of this intermediate statemesons to reconstruct the primary meson. To avoid this problem the meson energy Eis normalized to the real meson mass mm. The momentum components pi are scaledso that E2

cor = p2cor +m2

m is fulfilled by the new four-vector:

E → Ecor =mm

mγγ· E (4.4)

pi → pi, cor =√E2

cor −m2m

| ~p |· pi (4.5)

5There exist 15 combinations of creating 3 pairs out of 6 elements. Because each pair could be theη we have 15× 3 combinations.


invariant mass [MeV]0π3460 480 500 520 540 560 580 600 620 640

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

70

Mean: 548.47

FWHM: 27.67

η

Fig. 4.6: η signal in the 3π0 invariant mass spectrum over all tagged photon energies. The peak wasfitted with a gaussian, the background with a second order polynomial. The red solid line representsthe total fit whereas the blue dashed line represents the polynomial background function. The blackdashed line indicates the position of the real η mass mη = 547.5 MeV.

4.5.4 The η → 3π0 background channel

The η decays to 3π0 with a probability of 32.5%. Because of the low productionthreshold and the much larger cross section compared to the η′ this reaction dominatesthe 6γ final state. Therefore it is necessary to analyze this channel as well to be ableof a clear separation of the η and the η′. Also the almost identical analysis could serveas a testing ground for the η′ analysis.

First the χ2 minimization, the invariant mass cuts (see section 4.5.2) and the mesonmass correction (see section 4.5.3) were done for the 3π0 intermediate state. In contrastto the η′ analysis a missing mass cut (see section 4.5.5) had to be done to suppressbackground coming from multi meson production reactions. The result of the obtained3π0 invariant mass over all tagged photon energies after the final random subtractionis shown in figure 4.6. A distinct peak lying very close to the correct position of the ηmass (mη = 547.5 MeV) can be seen. The background contribution is quite low andcan be fitted well with a polynomial of second order.

The result of the η reconstruction in the 3π0 channel looks promising. Thereforethe equivalent reconstruction of the η′ the 2π0η channel is expected to not have anysevere errors in the analysis.

The second outcome of this background channel analysis is the so-called ‘no η’ cut


of the η′ analysis: Whenever an η can be reconstructed out of a 3π0 intermediate state(say, if all π0 mass cuts are fulfilled) the η′ analysis is aborted. In other words: The η′

reconstruction requires that no η can be found. This cut suppresses some backgroundevents near the η′ peak in the 2π0η invariant mass and improves therefore the η′ signal(see section 4.5.6).

4.5.5 Missing mass analysis

A missing mass analysis can be useful for two reasons. First, if it is not possible todetect the recoil nucleon of the quasifree reaction, a missing mass cut can help toselect such reaction anyway. Second, background reactions producing multiple mesonscan be suppressed. The second reasons has no meaning in the case of η′ production atthreshold because it is kinematically not possible to produce additional particles6. But,regarding the first point, a missing mass analysis was mad because the recoil nucleonscould not be detected in the analysis of this work. As it turned out the cut was uselessas it just lowered statistics of the dominant quasifree reaction. Hence the missing masscut was not used. Nevertheless the missing mass spectrum shows the influence of theFermi motion and will be discussed at the end of this section.

The missing mass analysis starts by calculating the mass of the undetected particleusing the kinematics. Therefore one has to assume a specific reaction so that thecalculation can be made. In this case the quasifree η′ photoproduction was chosen (seesection 2.4.2)

γ + d→ η′ + p (n) + nspect (pspec)

with either the neutron or the proton as the spectator and the other nucleon as theparticipant. The missing mass was then calculated using the following equations:

mmissing =√

∆E2 −∆~p 2 (4.6)

∆E =∑

Ei −∑

Ef (4.7)

∆~p =∑

~pi −∑

~pf (4.8)

where Ei, ~pi and Ef , ~pf are the initial and final state energies and momenta. Thesummations in ∆E,∆~p are done over all initial and final state particles. As a result weget

∆E = Eγ +mp −Eη′

∆px = −pη′, x

∆py = −pη′, y

∆pz = Eγ −pη′, z

where mp is the proton mass7, Eγ the beam energy (photon momentum in z-direction)and Eη′ , ~pη′ the energy and momentum of the reconstructed η′.

6This is of course different in case of the η. In the η test-analysis a missing mass cut was applied(see 4.5.4).

7mp ≈ mn in this missing mass analysis


Missing mass [MeV]-800 -600 -400 -200 0 200

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12

14

Fig. 4.7: Missing mass spectrum of the quasifree η′ production. Due to the Fermi momentum of theparticipant nucleon the peak is shifted and broadened. At threshold these effects are even more distinctbecause high Fermi momentum nucleons are selected (see text).

For further considerations it is common to subtract the mass of the expected butmissing particle from the missing mass:

mmissing =√

∆E2 −∆~p 2 −mp (4.9)

Figure 4.7 shows the resulting missing mass spectrum. A broad distribution peakingat around -175 MeV can be seen. In the free production case one expects a narrowdistribution around 0. The difference is due to the influence of the Fermi motion insidethe deuteron. As it was shown in section 2.3.3 the off-shell mass of the participantdecreases with increasing Fermi momentum. Also the production threshold is lowerfor higher Fermi momenta. Therefore preferably nucleons with high momenta andstrongly shifted off-shell masses are selected in quasifree reactions at threshold. Figure2.5 illustrates this fact: The effective mass of a nucleon carrying a momentum of 400MeV (η′ production threshold) is ∼760 MeV resulting in a mass shift of almost -180MeV. The broadening of the peak is caused by the different directions of the Fermimomentum. However all the arguments are just qualitative. Only a simulation wouldallow a comparison of the exact peak shape.


invariant mass [MeV]η0π2700 800 900 1000 1100 1200 1300 1400 1500

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

’η2χafter best

mass cutsη/0πafter

after random subtr.

’ cutηafter ’no

2×

2×

Fig. 4.8: Evolution of the 2π0η invariant mass throughout the analysis cuts. The blue and the redhistograms were scaled by a factor of 2. The black dashed line indicates the position of the real η′ massmη′ = 958.8 MeV.

4.5.6 Cut overview and evolution of the 2π0η invariant mass

Table 4.1 gives an overview of the so far applied cuts in the data analysis. The ‘η′

mass’ cut will be discussed later in section 4.6.3.The influence of the several cuts applied to extract the η′ are visualized in figure

4.8. It shows the evolution of the 2π0η-invariant mass throughout the analysis process.The yellow histogram shows the invariant mass after the best 2π0η combinations wasselected via minimizing the χ2 function. The histogram has still a peak at the η massand no η′-signal is visible. The next cut is applied to intermediate state mesons massrequesting two π0 and one η. As it can be seen on the resulting green histogram this cutis the most effective one. It drastically removes all entries below 820 MeV and above1400 MeV leaving a distribution with a maximum at the η′ mass. However no clearpeak structure can be identified in this histogram. But after the random subtractionan isolated region of bins with maximal counts begin to emerge in the blue histograms.Finally the ‘no η’ cut reduces the number of entries at the edges of this region. Thus amore or less clear peak around the η′ mass lying on a rather large background can beidentified8. Figure 4.8 demonstrates also the very large loss of statistics when applying

8Nevertheless one can argue about the improvement of the signal by the ‘no η’ cut. The use of thiscut has to be further investigated.

4.6. Extraction of the inclusive d(γ, η′)X cross section 39

Cut Condition Applied to

π0 mass 110 MeV < m < 160 MeV interm. state meson

η mass 500 MeV < m < 600 MeV interm. state meson

‘no η’ no η can be reconstructed out of 6 photons initial meson

η′ mass915 MeV < m < 1000 MeV

initial η′ candidate⇒ accept event in excitation function

Table 4.1: Overview of the analysis cuts.

these different cuts – particularly if one considers that the blue and the red histogramswere scaled by a factor of 2.

4.6 Extraction of the inclusive d(γ, η′)X cross section

In general a cross section can be interpreted as the probability that a certain reactiontakes place and is commonly defined as

σ =#reactions

#beam particles×#target particles per area(4.10)

In the case of η′ photoproduction we want to know the cross section in dependance ofthe photon energy Eγ . Thus

σ(Eγ) =Nη′(Eγ)

Nγ(Eγ) ·Nd(4.11)

where Nη′(Eγ) is the number of produced η′ mesons and Nγ(Eγ) is the number ofincoming photons at the photon energy Eγ . Nd is the number of target deuterons perarea and is not depending on Eγ . The exact determination of these three requiredquantities will be scribed in the next sections. The final cross section formula is thenpresented in section 4.6.4.

4.6.1 Calculation of the target density

The number of target deuterons per area can be calculated easily if one knows thedensity and the atomic mass of liquid deuterium. The sole critical quantity of thecalculation is the target length l which has to be exactly known in every scatteringexperiment. The length of the A2 target cell was therefore measured using X-rayradiography. Using the numerical values presented in table 4.2 the target density canbe calculated:

Nd =NA

A· ρLD2 · l = (0.231± 0.00146) b−1 (4.12)

whereas traditionally the unit ‘barn’ is used: 1 b = 10−24 cm2.


Quantity Symbol Value

density of LD2 ρLD2 0.1624 g/cm3

deuterium atomic mass A 2.0145 g/molAvogadro constant NA 6.02214× 1023 mol−1

η′ → 6γ branching ratio Γ6γ/Γ (8.00 ± 0.46)%target length l (4.76 ± 0.03) cm

Table 4.2: Numerical values used in the cross section calculation.

4.6.2 Determination of the photon number

The number of detected electron hits Ne− in the tagger is counted by devices called‘scalers’. Every tagger channel has its own scaler thus the number of electron hits foreach tagged photon energy is known. But the number of electron hits is not equal tothe number of tagged photons that reach the target. This is because of the collimatorwhich prevents photons, that are out of the target diameter, to reach the target. Thecollimator is important, as one has to be sure that all tagged photons leaving the taggerpass really through the target and, in particular, do not hit the target container walls.

To determine the ratio of tagged photons reaching the target, a tagging efficiencymeasurement is done. Therefore a special lead glass detector is moved into the photonbeam that counts the photons in coincidence with the electron hits so that the taggingefficiency εtag(i) can be determined for every tagger channel i:

εtag(i) =Nγ(i)Ne−(i)

(4.13)

The beam intensity has to be lowered for this measurement in order not to saturate thelead glass detector and to reach an almost 100% detection efficiency for the photons.For this experiment two tagging efficiency runs were performed. Figure 4.9 shows theobtained average of the tagging efficiencies for all enabled tagger channels. In one tag-ging efficiency run only the first 176 channels were enabled thus only one measurementwas available for this channels.

The tagging efficiency is assumed to be stable and equal for higher beam intensities.Therefore the total number of photons Nγ(i) tagged by the tagger channel i can becalculated by multiplying the scaler value Ne−(i) of the channel by its tagging efficiencyεtag(i). The resulting histogram for all tagger channels is shown in figure 4.10. In theplot the tagger channel numbers were replaced by their corresponding energies (seeappendix B) to illustrated the typical ∼ 1/Eγ bremsstrahlung spectrum. The taggerchannels in the energy range of 600 to 800 MeV were not enabled during the wholebeamtime and thus have less counts.


Tagger channel0 20 40 60 80 100 120 140 160 180 200 220

Tag

ging

effi

cien

cy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1400 1300 1200 1100 1000 900 800 700 600 [MeV]γE

Fig. 4.9: Tagging efficiencies of the enabled tagger channels. The second axis indicates the corre-sponding photon energies. Two tagging efficiency runs were performed during the experiment.

[MeV]γE600 700 800 900 1000 1100 1200 1300 1400

]9 1

0×

per

tagg

er c

hann

el [

γN

0

5

10

15

20

25

30

35

40

45

γ1/E~

Fig. 4.10: Total number of photons per tagger channel in dependence of the photon energy. A typical∼ 1/Eγ bremsstrahlung curve was fitted to the data between 800 and 1400 MeV. The tagger channelsin the energy range of 600 to 800 MeV were not enabled during the whole beamtime and thus have lesscounts.


4.6.3 Determination of the number of produced η′ mesons

The cross section calculation using eq. (4.11) requires the determination of the totalnumber of produced η′ in dependence of the photon energy. As it will be shown inthis section, due to experimental limitations, several steps are necessary to obtain thisnumber.

In the analysis the final 2π0η invariant mass spectrum containing the η′ signal iscreated for every tagger channel i. Also the number of possible η′ mesons Nposs

η′ (i) wasstored for every tagger channel (excitation function). As a criterion for a possible η′

an event had to have an invariant mass between 915 and 1000 MeV (‘η′ mass cut’, seetable 4.1). In order to extract the exact number of measured η′ mesons Nmeas

η′ (i) in thisacceptance region, one would have to estimate the background in the invariant massspectrum of every tagger channel, as it will be explained in section 5.1. Due to the verylow statistics this was not possible. The background estimation was therefore done forthe summed spectra of multiple tagger channels and afterwards a linear interpolationswas used to estimate the η′ ratio rη′(i) for every tagger channel i. Then the number ofmeasured η′ mesons in a tagger channel i could be extracted:

Nmeasη′ (i) = Nposs

η′ (i) · rη′(i) (4.14)

To achieve the convergence of the fits a polynomial of the first order only was chosen toapproximate the background contributions. Also the simulated line shape of the η′ peakwas rebinned according to the binning of the histogram. These rough approximationscould perhaps result in an overestimation of the cross section. Nevertheless makingapproximations was inevitable to extract the information out of the low statistics data.The fits and the resulting η′ signal ratio function rη′(i) is shown in figure 4.11.

Having determined the number of measured η′ mesons Nmeasη′ (i) for every tagger

channel one has to apply two further corrections. First, not all of the produced η′

decay into the 6γ channel. Thus the branching ratio of the 6γ decay Γ6γ/Γ has to beconsidered (see figure 2.3). Second, the detection efficiency εdet corrects for losses inthe detector acceptance, the detector efficiency and the analysis efficiency. Actually,εdet depends on the photon energy and the direction of the η′ emission. Therefore it iscommon to create a ‘grid efficiency’ estimation for all energies and directions with thehelp of Monte Carlo simulations. Due to the limited time frame of this work no gridefficiency was simulated, but only an overall detection efficiency could be estimatedusing a single simulation9. Correcting for the branching ratio Γ6γ/Γ and the detectionefficiency εdet, the number of measured η′ mesons Nmeas

η′ (i) can be finally related to thereal number of produced η′ mesons Nη′(i):

Nmeasη′ (i) = Nη′(i) · Γ6γ/Γ · εdet (4.15)

9This matter will be discussed in more detail in section 5.2


invariant mass [MeV]η0π2

800 900 1000 1100 1200 1300

Cou

nts

per

bin

[a.u

.]

0

2

Channel 0 - 19

= 1399 - 1346 MeVγE


800 900 1000 1100 1200 1300C

ount

s pe

r bi

n [a

.u.]

0

1

2

Channel 20 - 39

= 1343 - 1287 MeVγE

invariant mass [MeV]η0π2800 900 1000 1100 1200 1300

Cou

nts

per

bin

[a.u

.]

0

2

Channel 40 - 59

= 1284 - 1228 MeVγE

invariant mass [MeV]η0π2800 900 1000 1100 1200 1300

Cou

nts

per

bin

[a.u

.]

0

2

Channel 60 - 99

= 1225 - 1097 MeVγE


800 900 1000 1100 1200 1300

Cou

nts

per

bin

[a.u

.]

0

1

Channel 100 - 129

= 1093 - 988 MeVγE

Tagger Channel0 50 100 150 200

Sig

nal r

atio

0

0.1

0.2

0.3

0.4

0.5

1400 1300 1200 1100 1000 900 800 700 600

[MeV]γE

Fig. 4.11: η′ signal fits for the determination of the number of measured η′ mesons Nmeasη′ . The solid

red lines are the fitted simulation line shapes of the η′ peak. The blue dashed lines are the estimatedbackground contributions. The last plot show the interpolated η′ signal ratio function rη′(i). See textfor more details.


4.6.4 Final cross section formula

After the three quantities in eq. (4.11) were determined as described in the previoussection the final cross section formula can be written using eq. (4.13) and (4.15) as

σ(Eγ) =Nmeas

η′ (Eγ)Ne−(Eγ) · εtag(Eγ) · Γ6γ/Γ · εdet ·Nd

(4.16)

whereas the photon energy of a specific tagger channel i is defined by the tagger energycalibration (see appendix B). The errors of the cross section ∆σ(Eγ) were calculated byusing the Gauss error propagation formula for the known errors of the target length andthe branching ratio (see table 4.2). Also the statistical error

√N of histogram entries

were propagated. In the histogram rebinning calculations all values were weighted withtheir errors.

Chapter 5

Results and discussion

This chapter presents the results of the η′ photoproduction experiment. The first goalof this work was the detection of η′ mesons which will be discussed in section 5.1. Thesecond goal was the determination of the inclusive cross section of d(γ, η′)X. Section5.2 shows the final outcome of the cross section extraction described in section 4.6.

5.1 η′ identification

After completing the data analysis described in section 4.5 the 2π0η invariant massspectrum was obtained as a first result. This spectrum is shown in figure 5.1. Eventswere accepted from the η′ production threshold at 1205 MeV up to the maximum taggedphoton energy at 1397 MeV. The peak was fitted using the line shape of the η′ peakobtained by the simulation (solid red curve). A second order polynomial was chosen toapproximate the underlying background distribution (dashed blue curve). The peak isat the right position but, due to the large background, not very pronounced.

The number of total identified η′ mesons was determined by integrating the contentof the 2π0η invariant mass spectrum above the estimated background. In this work

60 η′ events

could be reconstructed. Considering the length of the beamtime of ∼33 h this leads toan η′ detection rate of

∼1.8 η′ events / h

In future experiments this number could probably be increased by using a properlyconfigured and calibrated TAPS, better calibrations for the other detectors and moresophisticated techniques in the data analysis.

45

46 Chapter 5. Results and discussion

invariant mass [MeV]η0π2800 850 900 950 1000 1050 1100 1150 1200 1250

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6

7

8

9

’η

Fig. 5.1: Final 2π0η invariant mass spectrum for events from 1205 MeV to 1397 MeV. The η′ peakwas fitted using the simulated line shape of the peak (solid red curve) and a second order polynomialfor the background contribution (dashed blue curve). The black dashed line indicates the position ofthe real η′ mass mη′ = 958.8 MeV.

5.2 The inclusive d(γ, η′)X cross section

The inclusive cross section of d(γ, η′)X was calculated using eq. (4.16). As discussedin section 4.6.3 no ‘grid efficiency’ estimation was performed due to the limit time thatwas available for this work. Therefore, as a first result, not the cross section σ but theproduct of the cross section and the detection efficiency σ× εdet is shown in figure 5.2.Starting at the first tagged photon energy around 600 MeV the values are practicallyzero until 1000 MeV. Subsequently the errors are getting bigger. After 1100 MeV thevalues are definitely not zero anymore as they should be until production thresholdnear 1200 MeV. This could be due to combinatorial background because the thresholdfor a 2π0+η combination lies at 996 MeV. The rise of the values after the η′ productionthreshold is delayed and clearly starting not until 1280 MeV.

For the calculation of the real inclusive cross section of d(γ, η′)X the detectionefficiency was roughly approximated by the overall detection efficiency εdet = 9.4%obtained by the simulation. This is of course not very accurate, as a true efficiencydepends on the photon energy and the direction of the η′ emission. However the energyrange of less than 200 MeV is not very large and a certain value had to taken in orderto make a comparison to the existing data. Figure 5.3 shows the region of interest near

5.2. The inclusive d(γ, η′)X cross section 47

[MeV]γE600 700 800 900 1000 1100 1200 1300 1400

[nb]

det

ε × σ

0

5

10

15

20

com

bin.

thre

shol

dη0 π2

cohe

rent

/ br

eaku

p

Fig. 5.2: Cross section of d(γ, η′)X times the detection efficiency. The thresholds for coherent/quasifreeη′ production and the 2π0 + η combinatorial background are indicated by the dashed lines. Unit ofσ × εdet here is nanobarn.

the η′ production threshold up to the maximum tagged photon energy. The data wererebinned and the cross section was calculated for 12 photon energies. The exact valuesand the corresponding errors can be found in appendix A.

For comparison the preliminary cross section obtained by the CB-ELSA/TAPScollaboration [16] is shown in figure 5.3. The statistics of this data is around an orderof magnitude higher than that of the data used in this work. Although the cross sectionof this work is probably overestimated (see section 4.6.3) these results show an evensteeper rise after 1330 MeV.

As a comparison to a theoretical calculation the model prediction of the reggeizedη′-MAID model [31] is also drawn in figure 5.3. The numerics of this model was basedon the overestimated SAPHIR data [13]. Therefore the calculations were scaled to fitthe currently available data for the production off the free proton. It can be seen thatthe obtained cross section is well described except for the region near threshold and theregion above 1350 MeV. Due to an insufficient background removal the cross sectionis not zero below threshold. Even the error bars are not reaching zero. In the upperregion the cross section is too small. However the error bars are almost in agreementwith the theoretical value.

48 Chapter 5. Results and discussion

[MeV]γE1150 1200 1250 1300 1350 1400

b]µ [σ

0

0.05

0.1

0.15

0.2

0.25

0.3 this work

CB-ELSA/TAPS’-MAIDη

coherent

breakup

Fig. 5.3: Inclusive cross section of d(γ, η′)X. The figure show the results of this work (black circles), thepreliminary results of the CB-ELSA/TAPS collaboration [16] (blue triangles) and the model predictionof the η′-MAID model [31] (red curve). The threshold for the coherent and the quasifree breakupproduction are indicated by the dashed lines. Unit is microbarn.

5.3 Conclusion and outlook

In the first test measurement using the new accelerator stage ‘MAMI C’ at MAMI the η′

meson could be produced in the photoproduction off the deuteron. The η′ was identifiedand despite the short beamtime and the limited time frame of a master thesis a firstapproximation of the inclusive d(γ, η′)X could be calculated. Future investigationsof high statistics data with properly calibrated detectors and a more sophisticatedanalysis will surely contribute to the sparse knowledge of the η′ photoproduction andto the study of nucleon resonances.

Appendix A

Inclusive cross section

data of d(γ, η′)X

Eγ σ ∆σ

[MeV] µb µb

1161.2 0.013 0.007

1182.3 0.010 0.007

1203.0 0.014 0.007

1222.9 0.015 0.010

1243.0 0.021 0.009

1263.7 0.023 0.010

1284.0 0.033 0.013

1303.6 0.051 0.016

1324.2 0.072 0.024

1347.3 0.107 0.030

1367.3 0.117 0.025

1388.5 0.173 0.028

49

Appendix B

Tagger energy calibration

Ch Eγ ∆Eγ Ch Eγ ∆Eγ Ch Eγ ∆Eγ

[MeV] [MeV] [MeV] [MeV] [MeV] [MeV]0∗ 1398.64 2.00 30 1312.14 2.87 60 1224.68 3.071 1396.60 2.08 31 1309.29 2.83 61 1221.61 3.082 1394.48 2.16 32 1306.48 2.80 62 1218.52 3.093 1392.27 2.25 33 1303.69 2.78 63 1215.42 3.104 1389.98 2.33 34 1300.91 2.78 64 1212.32 3.115 1387.60 2.42 35 1298.12 2.79 65 1209.20 3.126 1385.14 2.51 36 1295.32 2.81 66 1206.07 3.147 1382.58 2.60 37 1292.50 2.83 67 1202.93 3.158 1379.93 2.69 38 1289.66 2.84 68 1199.77 3.169 1377.20 2.77 39 1286.81 2.85 69 1196.61 3.1710 1374.39 2.85 40 1283.95 2.86 70 1193.44 3.1811 1371.51 2.92 41 1281.09 2.87 71 1190.25 3.1912 1368.55 2.99 42 1278.21 2.88 72 1187.06 3.2013 1365.53 3.06 43 1275.33 2.89 73 1183.85 3.2114 1362.45 3.11 44 1272.43 2.90 74 1180.63 3.2215 1359.31 3.16 45 1269.52 2.91 75 1177.40 3.2316∗ 1356.13 3.20 46 1266.61 2.92 76 1174.17 3.2517 1352.92 3.23 47 1263.68 2.93 77 1170.92 3.2518 1349.68 3.25 48 1260.75 2.94 78 1167.65 3.2719 1346.42 3.26 49 1257.80 2.95 79 1164.38 3.2820∗ 1343.15 3.26 50 1254.84 2.96 80 1161.10 3.2921 1339.89 3.26 51 1251.87 2.97 81 1157.81 3.3022∗ 1336.65 3.23 52 1248.90 2.98 82 1154.50 3.3123 1333.43 3.21 53 1245.91 3.00 83 1151.19 3.3224 1330.24 3.17 54 1242.91 3.00 84 1147.86 3.3325 1327.10 3.12 55 1239.90 3.02 85 1144.53 3.3426∗ 1324.00 3.07 56 1236.88 3.03 86 1141.18 3.3527∗ 1320.96 3.02 57 1233.84 3.04 87 1137.82 3.3628 1317.97 2.96 58 1230.80 3.05 88 1134.46 3.3729 1315.03 2.91 59 1227.75 3.06 89 1131.08 3.38∗broken channels

51

52 Chapter B. Tagger energy calibration

Ch Eγ ∆Eγ Ch Eγ ∆Eγ Ch Eγ ∆Eγ

[MeV] [MeV] [MeV] [MeV] [MeV] [MeV]90 1127.69 3.39 135 965.15 3.81 180 786.79 4.0991 1124.29 3.40 136 961.34 3.82 181 782.70 4.1092 1120.88 3.41 137 957.52 3.83 182 778.60 4.1093 1117.46 3.42 138 953.69 3.83 183 774.50 4.1194 1114.03 3.44 139 949.85 3.84 184 770.39 4.1195 1110.59 3.45 140 946.00 3.85 185 766.28 4.1296∗ 1107.14 3.46 141 942.15 3.86 186 762.16 4.1297∗ 1103.68 3.47 142 938.29 3.86 187 758.04 4.1298 1100.21 3.48 143 934.42 3.87 188 753.92 4.1399 1096.73 3.49 144 930.55 3.88 189 749.79 4.13100∗ 1093.24 3.50 145 926.66 3.89 190 745.66 4.13101 1089.73 3.51 146 922.77 3.89 191 741.52 4.14102 1086.22 3.52 147 918.88 3.90 192 737.38 4.14103 1082.70 3.53 148 914.98 3.91 193 733.24 4.15104 1079.17 3.54 149 911.06 3.91 194 729.09 4.15105 1075.63 3.54 150 907.15 3.92 195 724.94 4.15106 1072.08 3.56 151 903.22 3.93 196 720.78 4.16107 1068.52 3.57 152 899.29 3.93 197 716.62 4.16108 1064.95 3.57 153 895.36 3.94 198 712.46 4.16109 1061.37 3.58 154 891.41 3.95 199 708.30 4.17110 1057.78 3.59 155 887.46 3.95 200 704.13 4.17111 1054.19 3.60 156 883.50 3.96 201 699.96 4.17112 1050.58 3.61 157 879.54 3.97 202 695.79 4.18113 1046.96 3.62 158 875.57 3.97 203 691.61 4.18114 1043.34 3.63 159 871.59 3.98 204 687.43 4.18115 1039.70 3.64 160∗ 867.61 3.99 205 683.25 4.18116 1036.06 3.65 161 863.62 3.99 206 679.06 4.19117 1032.40 3.66 162 859.63 4.00 207 674.87 4.19118 1028.74 3.67 163 855.63 4.00 208 670.68 4.19119 1025.07 3.68 164 851.62 4.01 209 666.49 4.20120 1021.39 3.68 165 847.61 4.02 210 662.29 4.20121 1017.70 3.69 166 843.59 4.02 211 658.09 4.20122 1014.00 3.70 167 839.57 4.03 212 653.89 4.20123 1010.29 3.71 168 835.54 4.03 213 649.69 4.20124 1006.58 3.72 169 831.51 4.04 214 645.48 4.21125 1002.85 3.73 170 827.47 4.04 215 641.27 4.21126 999.12 3.74 171 823.42 4.05 216 637.06 4.21127 995.38 3.75 172 819.37 4.05 217 632.85 4.21128 991.63 3.75 173 815.32 4.06 218 628.64 4.22129 987.87 3.76 174 811.26 4.06 219 624.42 4.22130 984.10 3.77 175 807.19 4.07 220 620.20 4.22131 980.33 3.78 176 803.12 4.07 221 615.98 4.22132 976.55 3.79 177 799.05 4.08 222 611.76 4.22133 972.76 3.80 178 794.97 4.08 223 607.54 4.22134 968.96 3.80 179 790.88 4.09

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