photoproduction of the -meson o the deuteron · 2016. 1. 31. · abstract the photoproduction of...

Project Thesis

Photoproduction of the η -Meson

o� the Deuteron

by

Marie-Luise Wille

Supervisor: Prof. Dr. Bernd Krusche

Department of Physics, University of Basel

January 2008

Abstract

The photoproduction of η-mesons o� deuteron was studied with the Crystal Ball

and TAPS detectors at MAMI facility for photon beams in the range from 603 to

1400 MeV. The η-mesons are detected via following decay mode: η → 3π0 → 6γ.

The invariant mass spectra as well as the total cross sections of the inclusive, the

quasi-free proton and the quasi-free neutron reactions are presented.

Acknowledgement

I want to thank Prof. Bernd Krusche for o�ering me such an interesting project

at the new MAMI facility. I appreciate his endless patience very much, as it took

me a long time to get into C++ programming and the ROOT system. Special

thanks go also to Dominik, who always supported me with my questions, without

his help I think I would be lost. Thanks also to all members of the group: Igal,

Thierry, Bene, Fabien, Francis, Yasser, Guiseppe and Therese. Finally I would

like to thank my parents, my sister Corinna and my boyfriend Robert who helped

me in the last months, so I could concentrate on my project thesis.

Contents

1. Introduction 1

2. Theory 3

2.1. The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2. The Quark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3. Decay and branching ratio of the η - meson . . . . . . . . . . . . 7

2.4. Nucleon Resonances . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5. Meson production and isospin amplitudes . . . . . . . . . . . . . . 11

2.6. The goal of this work . . . . . . . . . . . . . . . . . . . . . . . . . 13

3. Experimental Setup 15

3.1. The MAMI facility . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2. The Glasgow-Mainz photon tagger . . . . . . . . . . . . . . . . . 16

3.3. The detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4. Data Analysis 21

4.1. Production Thresholds . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2. Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3. Eta Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3.1. Intermediate state analysis . . . . . . . . . . . . . . . . . . 24

4.3.2. Missing mass analysis . . . . . . . . . . . . . . . . . . . . . 25

4.3.3. Applied cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.4. Applied �ts . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4. Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5. Results and discussion 33

5.1. Eta identi�cation . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2. The total cross sections . . . . . . . . . . . . . . . . . . . . . . . . 35

5.3. Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . 39

A. Cross section data 41

B. Tagger energy calibration 45

i

ii Contents

C. Invariant Mass Spectra 49

D. Missing Mass Spectra 53

Bibliography 57

List of Tables

2.1. Overview of the lepton classi�cations . . . . . . . . . . . . . . . . 3

2.2. Overview of the quark classi�cation . . . . . . . . . . . . . . . . . 4

2.3. Properties of the Interactions . . . . . . . . . . . . . . . . . . . . 4

2.4. Quark properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5. Properties of the non-strange mesons . . . . . . . . . . . . . . . . 8

2.6. Widths of some resonances . . . . . . . . . . . . . . . . . . . . . . 8

3.1. Main parameters of MAMI . . . . . . . . . . . . . . . . . . . . . . 15

4.1. Experimental Parameters . . . . . . . . . . . . . . . . . . . . . . . 21

4.2. Photon energies of the tagger channels . . . . . . . . . . . . . . . 32

4.3. Numerical values for calculating the cross section . . . . . . . . . 32

iii

List of Figures

2.1. Pseudoscalar nonet . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2. Decay scheme of the η meson . . . . . . . . . . . . . . . . . . . . 7

2.3. First excited states of the nucleon . . . . . . . . . . . . . . . . . . 9

2.4. Cross section of the total nucleon photoabsorption . . . . . . . . . 10

2.5. Total cross section of the proton and the neutron . . . . . . . . . 11

3.1. The MAMI facility . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2. Overview of the experimental setup . . . . . . . . . . . . . . . . . 17

3.3. The Glasgow-Mainz photon tagger . . . . . . . . . . . . . . . . . 17

3.4. Photograph of Crystal Ball and TAPS . . . . . . . . . . . . . . . 18

3.5. The Crystal Ball and TAPS . . . . . . . . . . . . . . . . . . . . . 19

4.1. Relative timing of Crystal Ball and Tagger . . . . . . . . . . . . . 23

4.2. 3π0 invariant mass spectrum from 6 neutral hits . . . . . . . . . . 26

4.3. Angular distribution of the neutron . . . . . . . . . . . . . . . . . 27

4.4. 3π0 invariant mass spectrum from 7 neutral hits . . . . . . . . . . 27

4.5. 3π0 invariant mass spectrum with missing mass cuts . . . . . . . . 28

4.6. Tagging e�ciencies of the enabled tagger channels . . . . . . . . . 31

4.7. Total number of photons per tagger channel . . . . . . . . . . . . 31

5.1. Total 3π0 invariant mass spectrum . . . . . . . . . . . . . . . . . 34

5.2. Quasi-free proton(neutron) 3π0 invariant mass spectrum . . . . . 34

5.3. 3π0 missing mass spectrum . . . . . . . . . . . . . . . . . . . . . . 35

5.4. Total cross section times εdet . . . . . . . . . . . . . . . . . . . . . 35

5.5. Total cross section . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.6. Scaled quasi-free neutron and proton cross section . . . . . . . . . 37

5.7. Total cross section results from [8] . . . . . . . . . . . . . . . . . . 37

5.8. The neutron-proton cross section ratio . . . . . . . . . . . . . . . 38

C.1. Total 3π0 invariant mass spectrum in dependence of the tagger

channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

C.2. Quasi-free proton 3π0 invariant mass spectrum . . . . . . . . . . . 50

C.3. Quasi-free neutron 3π0 invariant mass spectrum . . . . . . . . . . 51

v

vi List of Figures

D.1. Total 3π0 missing mass spectrum in dependence of the tagger chan-

nels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

D.2. Quasi-free proton 3π0 missing mass spectrum . . . . . . . . . . . 54

D.3. Quasi-free neutron 3π0 missing mass spectrum . . . . . . . . . . . 55

1. Introduction

During the last years the MAMI facility in Mainz, Germany, was upgraded to

higher energies. In 2007 the new MAMI C accelerator was completed and a

high intensive electron beam up to 1.5 GeV can be produced. Since years is

the investigation of electromagnetic excitation of nucleon resonances of central

interest. In this work the data of the �rst test measurements in May 2007 are

analyzed. The nucleons are excited with a high energy photon beam, which is

produced via Bremsstrahlung. The dominant decay channel of nucleon resonances

is the hadronic decay via the emission of mesons. Thus it is useful to investigate

those resulting mesons. This so-called photoproduction is done with a 'tagged'

photon beam, i.e. the incident photon energy is known.

The photoproduction of η-mesons is an excellent tool to study the S11(1535)

resonance and with the new energy range, even higher resonances above the

S11(1535) resonance region could be observed. Detailed results are already avail-

able for the photoproduction o� protons [3], [5], in contrast to photoproduction

o� neutrons. Since no free neutron target exists, light nuclei like deuteron (as

in this experiment) are taken as neutron targets. The investigation of nucleon

resonances o� the neutron has two reasons: �rst, to reveal the isospin structure

of the electromagnetic excitations of the nucleon; second, it seems that the elec-

tromagnetic coupling of some resonances is stronger to the neutron than to the

proton. Therefore it is necessary and very helpful to analyze the resonances on

the neutron. Determining the cross section ratio of the neutron and the proton

shows that proton and neutron cannot be treated equally, especially not for higher

energies.

After this short introduction a theoretical overview is given in chapter 2. The

experimental setup is brie�y described in chapter 3 and followed by a description

of the data analysis and techniques in chapter 4. In chapter 5 the main results are

presented and discussed. In this work the di�erent cross sections of the inclusive,

the quasi-free proton and the quasi-free neutron are determined as well as the

neutron-proton cross-section ratio.

1

2. Theory

2.1. The Standard Model

The standard model of elementary particles and interactions is a theory, where

(almost) all known elementary particles and their interactions are well described.

Elementary particles have no known internal structure, i.e. they are pointlike.

Nowadays one assumes that all matter is made up by three di�erent types of

elementary particles: leptons, quarks and their interaction particles. Leptons

and quarks are the matter constituents and spin 12particles, i.e. half integer spin

and so called fermions. There are three lepton families (or generations), classi�ed

by their charge (Q), electron number Le , myon number Lµ and the tauon number

Lτ as follows:

lepton Q Le Lµ Lτ

e -1 1 0 0νe 0 1 0 0µ -1 0 1 0νµ 0 0 1 0τ -1 0 0 1ντ 0 0 0 1

Table 2.1: Overview of the lepton classi�cations. [7]

For each lepton exists an antilepton (denoted with an '+') with opposite sign,

the positron e+ for example has a charge of +1 and electron number -1. Therefore

there are 12 leptons all together. Similar to the leptons exist three quark families

(table 2.2) containing up (u), down (d), charm (c), strange (s), top (t) and bottom

(b) quark. The quarks have besides their charge six '�avors', which are classi�ed

by upness (U), downness (D), charm (C), strangeness (S), truth (T) and beauty

(B).

Each quark has as well its own antiquark (denoted with a bar over the particle

symbol, for example antiup: u) again with opposite sign. As each quark carries

three types of color charge, there are 36 quarks in total. Note: Particle and

antiparticle have identical mass and spin but opposite charges. Some electrically

neutral bosons (e.g. Z0, γ) are their own antiparticle.

3

4 Chapter 2. Theory

quark Q I IZ C S T Bu 2/3 1/2 1/2 0 0 0 0d -1/3 1/2 -1/2 0 0 0 0c 2/3 0 0 1 0 0 0s -1/3 0 0 0 -1 0 0t 2/3 0 0 0 0 1 0b -1/3 0 0 0 0 0 -1

Table 2.2: Overview of the quark classi�cations and charges Q (in units of e). Upness anddownness are not listed in the table as they are rarely used. For example is the up-quark theonly one with C=S=T=B=0 and Q=2/3, therefore it is unnecessary to mention that U=1 andD=0. Instead of U and D, the isospin I and the z-component IZ are listed. [7]

The interaction between matter is described in the standard model by gauge

bosons, the force carriers. Bosons are integer spin particles, i.e. spin = 0, 1,

2, ... . The interaction particles di�er in vector bosons (γ, W+, W−, Z0, gluon)

with spin 1 and the not yet observed higgs boson with spin 0. Three of the four

fundamental interactions, i.e. weak, electromagnetic and strong interaction can

be described by vector bosons (table 2.3).

2.2. The Quark Model

Quarks and gluons cannot be isolated - they are con�ned in color-neutral parti-

cles called hadrons. Hadrons are therefore not elementary and decay via strong

interaction. In 1961, Murray Gell-Mann postulated the so called eightfold way,

which arranged the hadrons in geometric schemes, dependent from charge and

strangeness. Hadrons are divided as well into fermions and bosons which are

called baryons, if made of three quarks (qqq), and mesons, if made of a quark-

antiquark pair (qq). Quarks have the additive baryon number 1/3, antiquarks

-1/3, thus baryons have the baryon number B = 1 and mesons have a neutral

Property Gravitational Weak Electromagnetic Strong

Interaction Interaction Interaction Interaction

(Electroweak)

Acts on: Mass-Energy Flavor Electric Charge Color Charge

Particles All Quarks, Leptons Charged Quarks, Gluonsexperiencing: Electrically

Particles Graviton W+,W−, Z0 γ Gluonsmediating: (not yet observed)

Table 2.3: Properties of the Interactions. [6]

2.2. The Quark Model 5

quark charge Q Mass [MeV]current quark constituent quark

u 2/3 1.5 - 3 ≈ 300d -1/3 3-7 ≈ 300s -1/3 95 ≈ 450c 2/3 1250b -1/3 4200t 2/3 174 000

Table 2.4: Quark �avors, their charges and masses. The current quark mass correspond to a'nude' quark, while the constituent quark mass is the e�ective mass of a quark, which is boundin a hadron. [15]

baryon number B = 0. The most familiar baryons are proton (uud) and neu-

tron (udd), which are made of the lightest quarks. I will now concentrate on

the lightest mesons, i.e. quark-antiquark pairs containing u-, d-, and s-quarks.

In comparison to the heavy quark-antiquark pairs, the so called 'Quarkonia' like

cc and bb, mesons of light qq are more complicated to describe, because the

constituent masses don't di�er a lot (see table 2.4).

As a meson is composed of two quarks with spin s = 1/2, the total spin S can

be 1 (parallel spins) or 0 (antiparallel spins). L is the orbital angular momentum

quantum number and the higher L is, the higher is usually the mass for the

meson. L and S form the total angular momentum quantum number J with

| J |=| L + S |. Another quantum number is the parity P with P = (−1)(L+1)

and the charge conjugation or C-parity (for neutral systems) C = (−1)(L+S).

For the lightest mesons there is no relative orbital angular momentum, thus

L = 0. For L = 0 follows that P = -1 and JP can obtain two di�erent values.

Mesons with JP = 0− are called pseudoscalar mesons and mesons with JP = 1−

are called vectormesons.

We are just considering the lightest quark combinations of u, d and s quarks,

so we follow the SU(3) symmetry group and we get nine possible qq combination

(nonet) grouped into an octet and a singlet:

3⊗ 3 = 8⊕ 1

As the η is part of the pseudoscalar mesons, I only concentrate on the pseu-

doscalar nonet where the mesons are arranged as follows (2.1):

6 Chapter 2. Theory

Figure 2.1: The pseudoscalar meson nonet. [14]

The SU(3) octet consists of:

• 1 isospin triplet: I = 1, S = 0

I3 meson quark content-1 π− du0 π0 1√

2(uu− dd)

1 π+ ud

• 2 isospin doublets: I = 1/2, S = ±1

S = +1 I3 meson quark content-1/2 K0 ds+1/2 K+ us

S = -1 I3 meson quark content-1/2 K− su

+1/2 K0 sd

• 1 isospin singlet: I = 0, S = 0 η8 = 1√6(uu + dd− 2ss)

The SU(3) singlet consists of: I = 0, S = 0 η1 = 1√3(uu + dd + ss)

Due to their same quantum numbers the η8 and η1 state mix with an mixing

angle θ ≈ −20◦ and form the two observed particles η(547) and η′(958):

|η〉 = cos θ|η8〉 − sin θ|η1〉|η′〉 = sin θ|η8〉+ cos θ|η1〉

2.3. Decay and branching ratio of the η - meson 7

that means that the η - meson is the dominant octet state and the η′ - meson is

the dominant singlet.

2.3. Decay and branching ratio of the η - meson

The η - meson has a mass of 547.51 MeV and a mean life time of 5.1 · 10−19 s and

decays mainly in two photons (39.38%) or three pions (32.51%) (see 2.5). In this

work just the η → π0π0π0 decay is considered, because for the η → γγ decay the

peak to background ratio was too low, so no clear peak could be determined. The

π0 decays to 98.798% into two photons so we can calculate the total branching

ratio of the eta decay.

η (39.38±0.26) % 2γ

(32.51±0.28)%

π0 π0 π0

2γ 2γ 2γ

(98.79±0.032)%

6 γ (31.35±0.27)%

Figure 2.2: Decay scheme of the main decays of the η meson. The total branching ratio forthe here considered η → 6γ adds up to 31.35%. [15]

The ratio and the error of the η → π0π0π0 → 6γ decay is calculated as follows:

ratio r = 32.51% · (98.79%)3 = 31.35%

error ∆r = r ·√

( 0.28%32.51%

)2 + 3 · (0.032%98.79%

)2 = 0.27%

8 Chapter 2. Theory

meson IG JPC mass [MeV] mean life time (s) main decayπ− , π+ 1− 0− 139.57 2.6 · 10−8 µ±νµ

π0 1− 0−+ 134.98 8.4 · 10−17 γγη 0+ 0−+ 547.51 5.1 · 10−19 γγ

π0π0π0

π+π−π0

η′ 0+ 0−+ 957.78 3.3 · 10−21 π+π−ηρ0γ

π0π0γ

Table 2.5: Properties of the non-strange members of the pseudoscalar nonet. For a multiplett

with isospin I is G de�ned (only for non-strange members) by G = (−1)IC. [15]

2.4. Nucleon Resonances

In order to investigate the structure of the nucleon it is useful to excite them

and analyze what happens, when the excited states, i.e. resonances, fall back to

the ground state. In this work the excitation is done with high energy photons.

The advantage of photons is, that they are completely absorbed by the nucleon,

thus the energy transfer is equal to the photon energy. All nucleon resonances

can decay via strong interaction by emission of a meson to the ground state. The

strong interaction indicates a very short lifetime of the resonances which is usually

around 10−23 s, hence their widths are very large. Typical widths are between

100-300 MeV (see table 2.6) and therefore a overlapping of adjacent resonances

may occur. Figure 2.3 is a level scheme, which shows the nucleon in its ground

state and some of the excited states in dependence of their masses. Resonances

are divided into N - resonances with isospin I=1/2 (on the left hand side) and

the ∆ - resonances with I = 3/2 (on the right hand side).

Resonance (mass in MeV) Width [MeV]P33(1232) 120P11(1440) 350D33(1520) 120S11(1535) 150S31(1620) 150S11(1650) 150

Table 2.6: The full widths of some resonances. [15]

2.4. Nucleon Resonances 9

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),...

Figure 2.3: First excited states of the nucleon. The level scheme is divided into isospin 1/2states (left hand side) and isospin 3/2 states (right hand side). Decays via π emission arerepresented by the solid blue arrows, η emission by the dashed red arrows and ρ emission bythe curled green arrows. The thickness of the arrows represents the branching ratios of thecorresponding decay. [3]

The ground state of a nucleon is denoted as N(939), respectively N(938). Ex-

cited states, for example the well known ∆ - resonance P33(1232), describes the

relative orbital angular momentum of the emitted meson and the nucleon during

the decay. The letters S, P, D, ... correspond (analog to the atomic spectroscopy)

to the orbital angular momentum l = 0, 1, 2, ... . The indices describe the dou-

bled isospin and spin. A from the above mentioned resonance emitted π0 - meson

has then the relative orbital angular momentum l = 1 and the resonance itself

has the isospin I = 3/2 and spin J = 3/2. The value in braces indicates the

mass in MeV, here 1232 MeV. In �gure 2.3 are the possible decays via π0 or η

emission indicated with arrows, while the thickness shows the relative frequency

of the decay. ∆-resonances cannot decay via η-meson emission, because this has

an isospin I = 0 and the strong interaction conserves the isospin. Therefore we

can see, that special mesons serve as a �lter for certain resonances. For example

the η-meson is characteristic for the S11(1535) resonance.

10 Chapter 2. Theory

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)�

Figure 2.4: Total photoabsorption cross section on the proton (left hand side)and on the neutron (right hand side) photoabsorption. The data points (green)are �tted with several Breit-Wigner shaped resonances (blue) and a slowly ris-ing background function giving the total �t curve (black). From left to right:P33(1232), P11(1440), D13(1520), S11(1535), F15(1680) (proton only) and F37(1950). [4]

As mentioned before resonances are overlapping and this fact makes it di�cult

to identify and investigate individual states, as demonstrated in �gure 2.4. Figure

2.4 shows the total photoabsorption cross section for the reaction γN → NX on

the proton and on the neutron. As one can easily see they are not identical.

It follows that some resonances couple strongly to a proton, while they couple

weakly to a neutron and vice-versa. From quantum mechanical considerations

one may suggest that the neutron/proton cross section ratio σn/σp should be

2/3:

σn/σp =Q2

u + Q2d + Q2

d

Q2u + Q2

u + Q2d

=4/9 + 1/9 + 1/9

4/9 + 4/9 + 1/9= 2/3 (2.1)

This is of course just a hypothesis and just implies that there is a di�erence

between the two cross sections. A resulting 2/3 ratio does not necessarily mean

that this hypothesis is correct.

For the photoproduction of η-mesons (see �g. 2.5) both reactions are dominated

by the S11(1535) resonance and the cross section ratio σn/σp is randomly ≈ 2/3

for photon energies of Eγ = 800 MeV. But for higher energies the ratio starts to

increase due to the higher laying resonances which may couple strongly to the

neutron. In �gure 2.5 the quasi-free neutron cross section shows a bump around

2.5. Meson production and isospin amplitudes 11

Figure 2.5: Quasi-free proton total cross section (green squares) as a function of the incidentphoton beam energy compared to the quasi-free neutron total cross section (blue triangles).Insert: neutron-proton cross section ratio. [8]

Eγ = 1 GeV. This resonance is not yet identi�ed but di�erent models already

predict some solutions. It is suggested to be the very narrow P11(1670) or a

normal P11 resonance, or a combination of S11(1650) and/or P11(1710) and cusp

e�ects, just mentioning some of them. For detail see [8] and [1].

2.5. Meson production and isospin amplitudes

For the mesonproduction o� the deuteron two di�erent production mechanism

are important:

1. Coherent production:

γ + d → η + d

correspondent four-momenta:

k + pi → q + pf

with k = (Eγ, ~k) pi = (Eid, ~p

id) q = (Eη, ~pη) pf = (Ef

d , ~pfd)

where i and f indicate the initial and �nal states.

In the coherent production the incomming photon interacts with all nucle-

ons. The nucleus stays intact and remains in the ground state.

12 Chapter 2. Theory

In the not mentioned incoherent production is the nucleus also intact but

in an excited state. As the deuteron has no excited states this process is

not important in this work.

2. Quasi-free production:

γ + d → η + ppart + nspect

γ + d → η + npart + pspect

correspondent four-momenta:

k + pi → q + p1f + p2

f

with k = (Eγ, ~k) pi = (Eid, ~p

id) q = (Eη, ~pη)

p1f = (Ef

N1, ~pf

N1) p2

f = (EfN2

, ~pfN2

)

where N1 is the recoil nucleon (proton or neutron) and N2 is the spectator

nucleon (neutron or proton). In this participant-spectator model the meson

is produced o� one target nucleon (participant) while the other nucleon is

not participating in this reaction (spectator). The nucleon is here considered

as quasi-free, i.e. una�ected from the remaining nucleus.

The investigation of the η-photoproduction o� the deuteron is useful to analyze

the isospin structure of the S11(1535)-resonance with the help of the di�erent

cross sections. The cross sections of the quasi-free and coherent η-production

can be separated into an isoscalar and an isovector part, the so called isospin

amplitudes. As the electromagnetic interaction at the beginning of the reaction

does not conserve the isospin, transitions with ∆I = 0 or ∆I = 1 are possible.

From the known isospin of the η-meson and the participating nucleons one can

derive following relations:

σp ∼ |As + Av|2 (2.2)

σn ∼ |As − Av|2 (2.3)

σd ∼ |As|2 (2.4)

where σn and σp describe the quasi-free η-photoproduction cross sections on

the proton respectively neutron and σd the coherent cross section. As and Av

describe the isoscalar and the isovector production amplitudes. For the σn/σp

ratio follows:

2.6. The goal of this work 13

σn

σp

=|As − Av|2

|As + Av|2(2.5)

Due to quantum mechanical assumption the neutron-proton cross section ratio

should be equal to 2/3. A constant ratio implies that a resonance is dominating.

2.6. The goal of this work

In this work a coincidence measurement of η-mesons and the recoil nucleons is

done in order to extract the ratio σn/σp as a function of the incident photon

energy Eγ. The �rst step is the determination of a clear eta signal out of six

or seven neutral events. Afterwards the total cross sections of the inclusive, the

quasi-free proton and the quasi-free neutron reaction is calculated, to get �nally

the neutron-proton cross section ratio.

3. Experimental Setup

3.1. The MAMI facility

The Mainzer Mikrotron (MAMI) experienced several upgrades to gain higher en-

ergies during the years. Since spring 2007 the new 'MAMI C' facility is ready

for test measurements of the A2 collaboration. The electron accelerator consists

now of the three mikrotrons of 'MAMI B' plus the new HDSM (Harmonic Dou-

ble Sided Mikrotron). In the mikrotrons the electrons are accelerated by normal

Cu-cavities (f=2.45 GHz).

The electrons are produced in a photo gun and then accelerated in a linear accel-

erator (LINAC) up to 3.5 MeV. From there they enter the �rst (quite small) race

track mikrotron RTM 1 with a B-�eld of 0.10 T. After 18 turns the electrons have

an energy of 14.9 MeV and leave the mikrotron in order to enter the next one,

RTM 2, with B = 0.55 T. There they stay for 51 turns till they have 180 MeV

ready to go to the RTM 3 with B = 1.28 T, where they can stay for maximal 90

turns. When the electrons leave the RTM 3 they can have an energy up to 855

MeV. In the newly built HDSM the electrons are accelerated up to 1508 MeV.

The reason for a HDSM instead of a 'normal' mikrotron is simple: it is double

sided because it had to �t into the current hall size (a RTM would be six times

larger) and harmonic (two di�erent frequencies 4.90 GHz and 2.45 GHz) for more

beam stability. The parameters of the accelerators are summarized in table 3.1.

MAMI is a continuous wave machine with a 100% duty factor electron beam.

This is especially useful for coincidence experiments to reduce time dependent

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 �eld - 0.1026 T 0.5550 T 1.2842 T 1.53-0.95 T

weight of magnets - 4.2 t 92.3 t 911.6 t 1030 t

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

Table 3.1: Main parameters of the accelerators. [10]

15

16 Chapter 3. Experimental Setup

Figure 3.1: MAMI �oor plan. The electrons are produced in an electron cannon in the mostouter left hall. Afterwards they are accelerated by an injector LINAC and three RTMs. Afterpassing through the HDSM the beam reaches an energy of 1508 MeV. Finally the beam isguided into the A2 experimental hall. Taken from [10].

background, which is here done. The electron beam can be passed to four experi-

mental halls. For this experiment the beam is used in the real photon hall, where

the A2 collaboration is working and the Crystal Ball and TAPS calorimeters are

used.

3.2. The Glasgow-Mainz photon tagger

The electron beam produces an intense beam of real photons through bremsstrahlung

in a thin metal foil radiator. In this process the scattered electrons are analyzed in

the Glasgow Tagger, a magnetic spectrometer. The energy of the bremsstrahlung

photons vary between 0 and the maximum electron energy, i.e. the resulting

bremsstrahlung spectrum is continuous and shows a 1/Eγ distribution. To nar-

row the photon beam for the target a collimator behind the radiator foil is used

(see �gure 3.2 and 3.3). To determine the energy of one single photon, one takes

into account, that the photon energy could be calculated with the di�erence of

the electron energies before and after the scattering process:

3.2. The Glasgow-Mainz photon tagger 17

Figure 3.2: Overview of the experimental setup with Tagger Crystal Ball and TAPS. [13]

Eγ = Ebeam − E′

e− (3.1)

The determination of electron energy E′

e− is done by the Glasgow-Mainz-

Tagger, a dipole magnet with plastic scintillators in the focal plane (see �gure

3.3). The electrons are de�ected on di�erent orbits depending on their energy and

detected by the scintillators. Non scattered electrons are led to a beam dump.

e⁻ beamdump

tagging field

Figure 3.3: Schematic view of the photon tagger. [12]

18 Chapter 3. Experimental Setup

3.3. The detectors

Figure 3.4: Photograph of the detector system. The photon beam is comming from the rightentering Crystal Ball and �nally hitting TAPS, which is installed 1.5 m behind CB in forwarddirection.

• The Crystal Ball detector

The Crystal Ball is a 672 element NaI detector covering 94% of 4π. Each el-

ement is shaped like a truncated pyramid and is approximately 41cm long and

connected to a photomultiplier. Photons incident on the ball produce an elec-

tromagnetic shower which deposits energy in a number of crystals. The target

is surrounded by a cylinder of scintillation counters that function as the charged

particle detector. Particle identi�cation of charged particles is done by a PID

(particle identi�cation detector) because no time-of-�ight method can be used

for particle identi�cation as the distance between target and Crystal Ball is too

short. The PID has a cylindrical shape with a diameter of 10 cm, which is in-

stalled between target and the Crystal Ball.

• The TAPS detector

TAPS (Two Arm Photon Spectrometer) is installed 1.5 m behind the target

and covers the angular range θ = 1◦ − 20◦ which is not covered by the Crys-

tal Ball. It consists of 384 hexagonally shaped BaF2 scintillation detectors each

25cm long corresponding to 12 radiation length. TAPS is used as a forward wall

detector and neutrons and charged particles could be identi�ed by pulse-shape

(PSA) and time-of-�ight (TOF) techniques with high e�ciency.

Further information and detailed description can be found in [13], [10], [12],

[11] and on the MAMI webpage.

3.3. The detectors 19

Figure 3.5: The Crystal Ball and TAPS detectors in the A2 hall at Mainz (with sectionsremoved to allow visibility of the detector elements. [11]

4. Data Analysis

The data used in this work was taken during the �rst test measurements of the

A2 collaboration from May 11th till May 21st 2007. The measurements were per-

formed to test the new 1.5 GeV beam of MAMI C on a liquid deuterium (LD2)

target. A deuterium target is chosen because no free neutron target exists. The

detailed experimental parameters are shown in table 4.1. Due to many problems

during the beamtime, just low data statistics could be achieved. All in all 80

data �les, including also recovered �les out of broken events, could be used for

the analysis, which is executed by the AcquRoot software. For more information

about AcquRoot which is based on the CERN ROOT framework check [2] and

[9]. The same calibration and analyze steps as in D. Werthmueller master thesis'

'Photoproduction of the η′ o� Deuteron' were used, on the one hand because he

used the same data set and on the other hand to proof that his data analysis is

correct, because for η are much more statistics available then for η′.

Parameter Value

electron beam current 1506 MeVbeam current 29 nA (30nA)radiator 10 µm Cucollimator diameter 4 mmactive tagger channels 0 - 223tagged photon energies 608 - 1399 MeVtarget type liguid deuterium (LD2)target length 47.6 mm ± 0.3 mmCB trigger multiplicity 2+CB trigger energy threshold Esum 500MeVsize of good raw data 130 GBbeamtime (good data) ∼ 26 h

Table 4.1: Experimental Parameters

21

22 Chapter 4. Data Analysis

4.1. Production Thresholds

For the measurements a deuterium target is used. The components, proton and

neutron, are bound inside the nuclei, which results in additional nuclear e�ect

and Fermi motion concerning the kinematics compared to a 'free' neutron target.

As the deuteron has no excited states, there are just two possible production

mechanism the coherent and the quasi-free production (see section 2.5)

The total center of momentum energy is

√s =

√(k + pi)2 =

√2Eγmd + m2

d (4.1)

To calculate the threshold photon energy Ethresγ , has to be large enough to

produce also the �nal state particles, namely md + mη. Thus

√sthres = mη + md =

√2Eγmd + m2

d (4.2)

Transforming the equation to Eγ one obtains the threshold energy:

Ethresγ = mη +

msη

2md

(4.3)

In case of the coherent production

Ethresγ (γ + d → η + d) = 627.42MeV

with mη = 547.51 MeV md = 1875.61 MeV

The threshold energy for the quasi-free production of the nucleus bound in the

deuteron is then according to eq. (4.3) calculated (with mp = 938.27 MeV and

mn = 939.56 MeV) to

Ethres

γ = 707.25 MeV (for the free proton)

Ethres

γ = 707.03 MeV (for the free neutron)

The threshold energies for the quasi-free production is a bit higher than the

coherent production energy due to the separation energy of the participating (and

knocked out) nucleon.

4.2. Calibration 23

4.2. Calibration

Before one can start with the 'real' analysis to obtain physical results, one has

to calibrate all detectors with an energy calibration in order to get a physical

quantity for a correspondent electronic signal or numerical output. Afterwards a

time calibration and a random subtraction for all detectors has to be done. The

calibrations were not part of this work as they were done before by D. Werth-

müller and F. Pheron, so I just give a short summary about it.

Each detector element is connected to a QDC (Charge to Digital Converter) and

a TDC (Time to Digital Converter). The QDC stores an event in the energy

(charge) correspondent digital channel, while the TDC records the timing signal

relative to the trigger. The TDC is important for a coincident analysis and the

later required random subtraction. After additional corrections the coincidence

peaks of TAPS, Tagger and Crystal Ball are aligned to 0 ns in the time spectra.

This peak represents coincidence events and is lying on a constant background

of random events. But as one cannot tell if a event is really coincidental or just

accidental, one has to sort the events according to their time. If the time belongs

to the background (prompt) regions then the values are stored in background

(prompt) spectra. The following random subtraction can be attained by sub-

tracting the prompt spectra and the corresponding background spectra see �gure

4.1.

[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: 2.76 ns

P1BG 2BG

Figure 4.1: Relative timing of Crystal Ball and Tagger. The true coincidental event peak(green) is lying on a slightly skew background of random events that is assumed to go oncontinuously under the peak. Because one cannot tell if a prompt event is really coincidental(green) or just accidental (red) one has to carry out a statistical removal using true randomevents left and right to the prompt peak (blue).


4.3. Eta Analysis

In the analysis following three reaction are taken into account:

1. γ + d → η + d

2. γ + d → η + p(n) (quasi-free proton)

3. γ + d → η + n(p) (quasi-free neutron)

As most of the recoil nucleons of quasi-free reactions are in forward direction

and having a polar angle of less than ∼ 20◦, that means they are �ying towards

TAPS, they could not be detected because TAPS could not be used in this test

measurements, due to some problems with the time spectra. Those recoil nucleons

with a larger angle could be detected but the statistics is of course very low.

Furthermore only the protons could be detected by the PID inside Crystal Ball,

for 'detecting' neutrons (PID recognize just charged particles) one tries to analyze

seven neutral hits and takes the 6γ + n solution via χ2 selection. The results in

this case have to be improved by making an angle selection. Summarizing the

�rst analysis steps for the three reactions:

1. only events with six neutral hits are considered

2. only events with seven hits in total are considered, while six hits are neutral

and one hit is charged.

3. only events with seven neutral hits are considered and the neutron is iden-

ti�ed with χ2 - test. According to I. Jaegle [8] only neutron candidates with

an laboratory angle θ below 70 degrees are accepted.

To suppress background coming from ηπ - production a missing mass cut is

applied to all reactions.

4.3.1. Intermediate state analysis

As said before we will only consider the η → π0π0π0 decay which occurs with a

probability of 32.51%, whereas the three π0 decay into 6 γ in total (with a proba-

bility of 98.8%). Now this 3 π0 intermediate state of the η decay is reconstructed

out of the six photons, from which one doesn't know which two photons belong

to which π0. In the analysis this is done via χ2 selection, with

χ2 = (mπ0 −mγ1γ2)2 + (mπ0 −mγ3γ4)

2 + (mπ0 −mγ5γ6)2 (4.4)

4.3. Eta Analysis 25

and mπ0 is the real π0 mass and mγγ the two photons invariant mass. The

solution with the minimal error of the invariant masses is then taken. Mass cuts

for the π0 from 110 to 160 MeV were applied and only those particles which ful�ll

those conditions were used as the 3π0 intermediate state for the ongoing analysis.

In order to avoid a smeared signal in the later analysis a meson mass correction

has to be done. The meson Energy E is normalized to the real meson mass mm

and the momentum components pi are scaled so that E2cor = p2

cor +m2m is ful�lled

by the new four vectors:

E → Ecor =mm

mγγ

· E (4.5)

pi → pi,cor =

√E2

cor −m2cor

|~p|· pi (4.6)

4.3.2. Missing mass analysis

The missing mass cut is quite important in this analysis, because on the one

hand it suppresses background reactions producing multiple mesons and on the

other hand quasi-free reactions could be selected although the recoil nucleons are

not detected. Furthermore shows the missing mass spectrum the in�uence of the

Fermi motion. The missing mass is calculated by the following equation:

m2missing = (

∑Einit −

∑Efinal)

2 − (∑

~pinit −∑

~pfinal)2 (4.7)

= ∆E2 −∆~p2 (4.8)

where the summation of the energies E and the momenta ~p is over all initial

and �nal state particles, i.e.

∆E = Eγ + mp − Eη (4.9)

∆~p = ~pγ − ~pη (4.10)

while the photon momentum ~pγ is only in z - direction, Eγ is the beam energy,

mp is the proton mass and Eη and ~pη are the energy and momenta of the recon-

structed η. Consequently the missing mass for the quasifree η-photoproduction1

is:

mmissing =√

(Eγ + mp − Eη)2 − (~pγ − ~pη)2

In this analysis the mass of the expected 'missing' particle (here mp ) is sub-

1for coherent η-photoproduction the deuteron mass md is taken instead of mp


tracted from the right side, so if the particle is there the missing mass should

result in 0 MeV.

If the missing particle is the neutron, then mp is substituted by the neutron mass

mn.

4.3.3. Applied cuts

With just a few cuts, a quite clear η peak in the 3π0 invariant mass spectrum

is obtained. Only events with six or seven neutral hits or six neutral and one

charged hit are selected. After collecting the best combination of 6γ to 3π0 via

χ2 - test a mass cut on the π0 intermediate state particle between 110 MeV and

160 MeV is applied (�gure 4.2). As one can see in �gure 4.2, the data statistics

for the 6γ + p case is much lower then for the 6γ alone case. To improve the

mass resolution the π0 mass is used as a constrain. In case of the seven neutral

hits an additional cut for the neutron is applied. Only neutron candidates with

a laboratory angle below 70 degrees are accepted. A later η cut from 500 MeV

to 600 MeV is done in order to select the events for the excitation function.

invariant mass [MeV]0π30 200 400 600 800 1000 1200

Cou

nts

per

bin

[a.u

.]

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

η

6 neutral hits


Cou

nts

per

bin

[a.u

.]

0

200

400

600

800

1000

1200

1400

1600

1800

2000

η

6 neutral and 1 charged hit

Figure 4.2: The resulting 3π0 invariant mass spectrum reconstructed from six neutral hits(left side) and six neutral plus one charged hit (right side). The grey spectrum shows the'uncutted' spectrum after the χ2-test. The red (yellow) area shows the in�uence of the cut onthe π0 mass. The black dotted line represents the real η mass.

As mentioned before, most of the recoil nucleons are heading towards TAPS,

i.e. for a θ-angle smaller then 20 degrees. Those nucleons which have a larger

angle, can be detected with the Cristall Ball. The proton is than identi�ed via

PID, the neutron via χ2 - test. To improve the result an angular distribution is

done. According to Igal Jaegle's [8] work most of recoil neutrons should occur

below 70 degrees (see �gure 4.3). Thus additional cuts for the neutron are done

in the analysis (�gure 4.4).

• only neutron events with θ <70◦ are accepted

4.3. Eta Analysis 27

neutronθ0 20 40 60 80 100 120 140 160 180 200

Cou

nts

per

bin

[a.u

.]

0

500

1000

1500

2000

2500

3000

3500

4000

4500

cutsθ

Figure 4.3: The angular distribution of the neutron inside Crystal Ball. Between 0◦ and 20◦

no neutrons are detected because of the hole inside the CB. The dashed lines indicate the cutposition.

• only neutron events with θ <40◦ are accepted

invariant mass [MeV]0π3200 400 600 800 1000 1200

Cou

nts

per

bin

[a.u

.]

0

200

400

600

800

1000

1200

1400

1600

η

7 neutral hits


Cou

nts

per

bin

[a.u

.]

0

200

400

600

800

1000

1200

1400

1600

η

7 neutral hits

Figure 4.4: Evolution of the 3π0 invariant mass spectrum reconstructed from 7 neutral hits.The yellow area respresents the spectrum after the χ2-test. The green area is the resultingspectrum after the π0 cut and the pink area results after selecting only neutron events with θ<70◦ (left side) respectively θ <40◦ (right side). The black dotted line represents the real ηmass.

After the applying the θ-cut, the signal of the resulting (pink) spectra in �gure

4.4 is much more precise. The applied 40◦ cut gives on the one hand even a better

peak, but on the other hand a quite large statistics loss.

In order to reduce background, cuts on the missing mass are applied, too.

Three di�erent missing mass cuts were done (in three di�erent analysis) (�gure

4.5):

• from -200 MeV to ca. 150 MeV (depending on the tagger channel)

• from -200 MeV to 0 MeV

• from -200 MeV to the calculated peak position



Cou

nts

per

bin

[a.u

.]

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

η

6 neutral hits

MMCut: -200 MeV - 150 MeV


Cou

nts

per

bin

[a.u

.]

0

200

400

600

800

1000

1200

1400

η

7 neutral hits



Cou

nts

per

bin

[a.u

.]

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

η

6 neutral hits



Cou

nts

per

bin

[a.u

.]

0

200

400

600

800

1000

1200

1400

η

7 neutral hits



Cou

nts

per

bin

[a.u

.]

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

η

6 neutral hits

MMCut: -200 MeV - peak position


Cou

nts

per

bin

[a.u

.]

0

200

400

600

800

1000

1200

1400

η

7 neutral hits

MMCut: -200 MeV - peak position

Figure 4.5: Evolution of the 3π0 invariant mass spectrum reconstructed from 6 resp. 7 neutralhits. Left side: 6 neutral hits. The red area is the resulting spectrum after the missing mascut. Right side: 7 neutral hits. The pink area is the resulting spectrum after the missing masscut. Di�erent missing mass cuts were applied. Top row: MM cut from -200 MeV to ∼150 MeV,middle row: MM cut from -200 MeV to 0 MeV, bottom row: MM cut from -200 MeV to thecalculated peak position. The black dotted line represents the real η mass.

4.4. Cross section 29

As data statistics are high enough, the invariant mass and missing mass spectra

are displayed in steps of 10 tagger channels (see appendix C and D), i.e. di�erent

photon energies in a range of 35 MeV (see table 4.2 ). This is done in a so-

called 'Postanalysis', where all the speci�c changes, di�erent �ts, cross-section

calculation and other tuning are realized.

4.3.4. Applied �ts

To get a distinct peak positions, all histograms are �tted in di�erent ways.

• invariant mass spectra

The peak-function is �tted with a Gaussian �t function, with �xed parameters,

and the background-function is �tted by a second order polynomial. The total

�t function is the addition of both. The total �t function peaks in one value (the

η-peak ), which is slightly higher than the o�cial value of 547.51 MeV, probably

because of an insu�cient calibration.

• missing mass spectra

Like above, the peak-function is �tted with a Gaussian, but for the missing mass

spectra the �t of the background function is as well a Gaussian function for

higher energies, i.e. for Eγ > 966 MeV, otherwise it was �tted with a second

order polynomial. For lower energies the peak possition (which should be at 0

MeV) is shifted to the left (for energies lower than the η production threshold),

while for higher energies the peak position is shifted to the right, due to additional

meson production. The plotted peak position is then �tted with a third order

polynomial. The last �t is then used for the missing mass cut from -200 MeV to

the peak position in the analysis.

4.4. Cross section

In scattering experiments an important quantity is the cross section σ, which

denotes the probability that a reaction occurs. The dimension is an area, whereas

in particle physics usually the area is quite small and therefore the unit 'barn'

(1b = 10−24cm2) is used. The cross section, as a function of the energy of the

incoming particle, i.e. the photon, is than considered as:

σ(Eγ) =number of produced η mesons

number of incoming photons with Eγ × target particles per area(4.11)


that means:

σ(Eγ) =Nη(Eγ)

Nγ(Eγ) ·Nd

(4.12)

The tagging e�ciency εtag is the probability that a tagged photon reaches the

liquid deuterium target in coincidence with a election hit. Therefore εtag(i) can

be determined and measured for every tagger channel i:

εtag(i) =Nγ(i)

Ne(i)(4.13)

Reforming eq. 4.13, the total number of photons Nγ(i) tagged by the tagger

channel (i) can be determined. The plotted function in �gure 4.7 shows the

typical 1/Eγ behavior.

Due to experimental limits one cannot measure the real number of produced η

mesons Nη(i) for every tagger channel, because one has to take into account the

detection e�ciency εdet(i) and the branching ratio. Than the photon number is

calculated with

Nη(i) =Nmeas

η (i)

Γ6γ/Γ · εdet

(4.14)

To determine the measured number of eta mesons, the signal ratio out of the

invariant mass histograms is estimated. For doing this, the invariant mass is �tted

as described above in 4.4.4 followed by the evaluation of peak �t to background

�t ratio (see appendix).

According to [13] the cross section in dependence of the photon energy is than

calculated with following equation

σ(Eγ) =Nmeas

η (Eγ)

Ne(Eγ) · εtag(Eγ) · Γ6γ/Γ · εdet ·Nd

(4.15)

The numerical values for the branching ratio Γ6γ/Γ and the target density Nd

are shown in table 4.3.

4.4. Cross section 31

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

Figure 4.6: Tagging e�ciencies of the enabled tagger channels. The second axis indicatesthe corresponding photon energies. Two tagging e�ciency runs were performed during theexperiment.

[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

γ1/E~

Figure 4.7: Total number of photons per tagger channel in dependence of the photon energy.A typical ∼ 1/Eγ bremsstrahlung curve was �tted to the data between 800 and 1400 MeV.The tagger channels in the energy range of 600 to 800 MeV were not enabled during the wholebeamtime and thus have less counts.


Tagger Channel Eγ in MeV0-9 1399-137710-19 1374-134620-29 1343-131530-39 1312-128740-49 1284-125850-59 1255-122860-69 1225-119770-79 1193-116480-89 1161-113190-99 1128-1097100-109 1093-1061110-119 1058-1025120-129 1021-988130-139 984-950140-149 946-911150-159 907-872160-169 868-832170-179 827-791180-189 787-750190-199 746-708200-209 704-666210-224 662-603

Table 4.2: Photon energy range against tagger channel. This subdivision is done for bothinvariant mass and missing mass spectra, whereas the subdivision may vary for lower energies,depending on the anlysis. The more detailed tagger energy calibration can be found in appendixB.

Quantity Symbol Valuedensity of LD2 ρLD2 0.1624 g/cm3

deuterium atomic mass A 2.0145 g/molAvogadro constant NA 6.02214x1023mol−1

η → 6γ branching ratio Γ6γ/Γ (31.35±0.27)%target length l (4.76±0.03) cmtarget density Nd (0.231± 0.00146)b−1

Table 4.3: Numerical values for calculating the cross section. [13]

5. Results and discussion

5.1. Eta identi�cation

To identify the η-meson, only hits with six photon, six photons plus one charged

particle or seven neutral hits, i.e. 6γ plus one neutron, are taken into account. The

η is then reconstructed by the 3π0 invariant mass distributions. After running the

analysis with all cuts a 3π0 invariant mass spectrum with an eta peak position

around ∼549 MeV is obtained. The spectrum is �tted by an usual combined

�t: the total �t function consists of a gaussian signal �t and a second order

polynomial background �t (�gure 5.1). The spectrum shown in �g. 5.1 is the

resulting spectrum after applying all cuts mentioned in section 4.3.3. The missing

mass cut is done from -200 MeV to 0 MeV. The spectrum is calculated over all

tagger channels, i.e. incident photon energies between 603 MeV and 1399 MeV.

Below a short summary of the analyze steps, wich were done for the following

results:

• events with six or seven neutral hits are selected

• all possible combination of photon pairs are tested

• a χ2-test is done to select the best solution for 3π0

• if the 7th neutral hit is a neutron, only events with θ < 70◦ are accepted

• cut on the π0 mass between 10 MeV and 160 MeV

• π0-mass constrain

• if the 3π0 invariant mass is between 500 MeV and 600 MeV a η-meson is

de�ned to be seen

• missing mass cut between -200 MeV and 0 MeV

33

34 Chapter 5. Results and discussion

)γ Invariant Mass [MeV] (60π3450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]0

500

1000

1500

2000

2500

3000

3500Channel 0 - 224

= 1399 - 603 MeVγE

Figure 5.1: The resulting 3π0 invariant mass spectrum after all cuts applied over all taggerchannels, i.e. incident photon energies between 603 MeV and 1399 MeV. The spectrum is �ttedby a combined �t: signal+background (solid red curve). The signal is �tted by a Gaussianfunction, while the background is �tted by a second order polynomial function (blue dashedline).

+p)γ Invariant Mass [MeV] (60π3350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500

600

700Channel 0 - 224

= 1399 - 603 MeVγE

+n)γ Invariant Mass [MeV] (60π3450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250 Channel 0 - 224

= 1399 - 603 MeVγE

Figure 5.2: The resulting quasi-free proton 3π0 invariant mass spectrum over all tagger chan-nels (left side) and the quasi-free neutron 3π0 invariant mass spectrum over all tagger channels(right side). The spectrum is �tted by a combined �t: signal+background (solid red curve).The signal is �tted by a Gaussian function, while the background is �tted by a second orderpolynomial function (blue dashed line).

For the quasi-free proton and neutron reactions similar spectra are achieved

(�g. 5.2), but with quite low statistics due to the earlier mentioned problems

with TAPS.

All histograms in dependence of each tagger channel (see table 4.2 ) are shown

in appendix C.

Figure 5.3 shows the missing mass distribution of the three reactions for four

di�erent incident photon beam ranges.

• all tagger channels 224-0: 602 MeV ≤ Eγ ≤ 1399 MeV

• channel 220-196: 620 MeV ≤ Eγ ≤ 721 MeV



5.2. The total cross sections 35

)γ Missing Mass [MeV] (60π3-600 -400 -200 0 200 400 600

Counts

per

bin

[a.u

.]

0

500

10001500

2000

2500

30003500

4000Channel 0 - 224

= 1399 - 603 MeVγE


Counts

per

bin

[a.u

.]

0

100

200

300

400

500

600 Channel 196 - 220

= 721 - 620 MeVγE


Counts

per

bin

[a.u

.]

0

100

200

300

400

500

600

700 Channel 170 - 180

= 827 - 787 MeVγE


Counts

per

bin

[a.u

.]

0

100200300

400500600700

800 Channel 95 - 152

= 1111 - 899 MeVγE

+p)γ Missing Mass [MeV] (60π3-600 -400 -200 0 200 400 600

Counts

per

bin

[a.u

.]

0

100

200

300

400

500

600

700 Channel 0 - 224

= 1399 - 603 MeVγE


Counts

per

bin

[a.u

.]

0

5

10

15

20 Channel 196 - 220

= 721 - 620 MeVγE


Counts

per

bin

[a.u

.]

0

20

40

60

80

100

120 Channel 170 - 180

= 827 - 787 MeVγE


Counts

per

bin

[a.u

.]

0

50

100

150

200

250Channel 95 - 152

= 1111 - 899 MeVγE

+n)γ Missing Mass [MeV] (60π3-600 -400 -200 0 200 400 600

Counts

per

bin

[a.u

.]

0

50

100

150

200

250

300 Channel 0 - 224

= 1399 - 603 MeVγE


Counts

per

bin

[a.u

.]

-5

0

5

10

15

20Channel 196 - 220

= 721 - 620 MeVγE


Counts

per

bin

[a.u

.]

0

10

20

30

40

50Channel 170 - 180

= 827 - 787 MeVγE


Counts

per

bin

[a.u

.]

0

20

40

60

80

100 Channel 95 - 152

= 1111 - 899 MeVγE

Figure 5.3: The 3π0 missing mass spectrum reconstructed from 6 resp. 7 neutral hits. First

column: 6 neutral hits. Second column: quasi-free proton. Third column: quasi-free neutron.First row : Eγ = 602-1399 MeV, second row : Eγ = 620-721 MeV, third row : Eγ = 787-827 MeV,fourth row : Eγ = 899-1111 MeV.

5.2. The total cross sections

The inclusive and the quasi-free cross sections are calculated using eq. 4.13.

Because no εdet could be determined, the �rst results for the cross section are

σ× εdet. Figure 5.4 shows the inclusive and the quasi-free proton (neutron) cross

section. Both results show the signi�cant peak around Eγ= 800 MeV which

results from the S11(1535)-resonance.

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

[nb]

det

ε ×

σ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

)Xη, γinclusive cross section d(

co

he

ren

t th

resh

old

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

[nb]

det

ε ×

σ

0

0.2

0.4

0.6

0.8

1

1.2

1.4 ) x10η(pσquasi-free ) x10η(nσquasi-free

co

he

ren

t th

resh

old

Figure 5.4: Total cross section times εdet of the inclusive and the quasi-free proton (neu-tron) reaction. Left side: total cross section of d(γ, η)X as a function of the incident photonbeam energy. Right side: quasi-free proton total cross section (green squares) as a function ofthe incident photon beam energy compared to the quasi-free neutron total cross section (bluetriangles). Both are scaled by a factor of 10.


In order to optain the real cross section an approximation of the εdet was done.

Following values were chosen:

• quasi-free inclusive: εdet = 6%

• quasi-free proton: εdet = 1%

• quasi-free neutron: εdet = 0.7%

This is of course not very accurate but for a pre-result it may work. Figure

5.5 shows the resulting total cross sections in dependence of the incident photon

energy. The exact values can be found in appendix A. In general, the function

shape correspond to the Jaegle measurements [8] (see �gure 5.7), however the

quasi-free neutron cross section di�ers a lot. The inclusive cross section rises

quickly in the energy region from η production threshold up to Eγ= 800 MeV,

the S11(1535)-resonance. Furthermore, the expected bump around Eγ= 1 GeV

in the quasi-free neutron cross section could be observed. Although the bump is

hardly seen in �gure 5.5, it could clearly seen if one scales the quasi-free neutron

cross section up to the proton cross section maximum peak (see �gure 5.6). This

bump, which is only observed in the quasi-free neutron case, indicates that some

resonances couple strongly to the neutron and just weakly to the proton. In [8]

one suggests that this bump can be explained by a narrow P11(1675) resonance.

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

b]

µ [

σ

0

2

4

6

8

10

12

14

16

18

20

22

24

)Xη, γinclusive d(

cohere

nt th

resh

old

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

b]

µ [

σ

0

2

4

6

8

10

12

14)η(pσquasi-free

)η(nσquasi-free

cohere

nt th

resh

old

Figure 5.5: Total cross section of the inclusive and the quasi-free proton (neutron) reaction.Left side: total cross section of d(γ, η)X as a function of the incident photon beam energy.Right side: quasi-free proton total cross section (green squares) as a function of the incidentphoton beam energy compared to the quasi-free neutron total cross section (blue triangles).

5.2. The total cross sections 37

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

b]µ [σ

0

2

4

6

8

10

12

14)η(pσquasi-free

) x1.6η(nσquasi-free

cohe

rent

thre

shol

d

Figure 5.6: quasi-free proton total cross section (green squares) as a function of the incidentphoton beam energy compared to the scaled quasi-free neutron total cross section (blue trian-gles). In energy region around Eγ = 1000 GeV, the bump in the neutron cross section is clearlyseen.

Figure 5.7: Total cross section taken from I. Jaegle [8] measurement. Left side: Results forthe fully inclusive (open blue circles) and for the quasi-free inclusive (�lled red circles) reactions.Right side: Results for the quasi-free proton (blue triangles) and the quasi-free neutron (redtriangles).


[MeV]γE700 800 900 1000 1100 1200 1300 1400

pσ/

nσ

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pσ/nσ

Figure 5.8: The neutron-proton cross section ratio as a function of the incident photon beamernergy. Left: This work, right: I. Jaegle's [8] measurements.

In �gure 5.8 the neutron-proton cross section ratio as a function of the incident

photon beam is shown. Again, this result is compared to I. Jaegle's measure-

ments. Two regions can be distinguish: the S11(1535) energy region (around Eγ

= 800 MeV) and the energy region around Eγ = 1 GeV. As one can see, both

measurements show the same enhancement around Eγ = 1 GeV. Due to the fact,

that no detection e�ency was calculated and used in the analysis, the result for

the proton-neutron cross section ratio is not very accurate. For lower energies the

σn/σp-ratio should be approximately constant and equal to 2/3. This area corre-

spond to the S11(1535) energy region. Above Eγ = 800 MeV the ratio starts to

increase due to higher lying resonances, like the S11(1650), P11(1710), P13(1720)

and D15(1675). There are di�erent theories and models that predict, that some

resonances couple strongly to the neutron like and weakly to the proton and vice

versa [8] or and interference of resonances may occur. But as the optained results

for the neutron cross section and the neutron-proton cross section ratio do not

correspond to the expected results of other experiments, the study of the reso-

nances is quite di�cult. Furthermore a better analysis, where for example the

Fermi smearing is reduced, has to be performed and the angular distributions

have to be measured.

5.3. Conclusion and outlook 39

5.3. Conclusion and outlook

In the �rst test measurements of the MAMI C accelerator, some analysis according

to the η-meson could be done. The total cross sections of the quasi-free inclusive,

quasi-free proton and quasi-free neutron reactions as well as the neutron-proton

cross section ratio could be determined. But due to the short beamtime and

the limited time frame of a project thesis, just a standard analysis is made and

the results are just approximations. Nevertheless it shows that much more data

statistics as in previous experiments could be achieved and the obtained results

correspond to the expected ones. In future projects, longer beamtimes and mea-

surements (hopefully with TAPS-data) a more precise and high statistics data

should be available. Furthermore a more sophisticated analysis and properly

calibrated detectors should resolve the open questions of resonance coupling.

A. Cross section data

inclusive cross section

Eγ σ ∆σ

[MeV] [µb] [µb]

615.9 0.151 0.014

637.1 0.606 0.029

658.1 2.250 0.062

677.0 5.152 0.114

695.7 10.242 0.164

716.5 15.936 0.225

737.5 20.159 0.289

756.0 21.405 0.335

774.5 21.964 0.312

794.9 20.505 0.300

815.5 17.154 0.247

835.5 15.364 0.231

855.5 14.547 0.229

877.5 12.973 0.235

893.5 11.993 0.236

913.0 10.389 0.161

934.5 9.875 0.178

953.7 8.708 0.159

972.7 8.183 0.159

991.7 7.630 0.153

Eγ σ ∆σ

[MeV] [µb] [µb]

1012.0 6.810 0.132

1032.5 6.592 0.153

1050.5 6.258 0.145

1070.3 5.628 0.122

1091.1 5.157 0.137

1114.2 4.262 0.142

1129.3 4.232 0.104

1149.5 4.302 0.105

1169.3 4.030 0.103

1188.7 3.748 0.102

1209.2 3.949 0.098

1229.0 3.581 0.107

1248.5 3.236 0.090

1268.0 2.962 0.090

1286.8 3.078 0.096

1308.0 2.967 0.087

1330.5 3.369 0.111

1367.0 2.278 0.083

1386.1 2.060 0.075

1396.5 1.781 0.233

41

42 Chapter A. Cross section data

quasi-free proton cross section

Eγ σ ∆σ

[MeV] [µb] [µb]

618.0 0.104 0.045

643.5 0.130 0.055

660.0 0.413 0.093

679.1 0.473 0.065

699.9 2.984 0.170

718.5 4.424 0.231

737.5 7.133 0.288

758.1 9.483 0.332

778.5 11.493 0.384

799.1 13.151 0.397

817.5 12.616 0.394

835.5 12.309 0.353

855.5 12.452 0.369

877.5 11.265 0.387

895.5 9.870 0.343

914.9 8.245 0.291

934.5 8.143 0.301

953.7 6.598 0.264

972.7 6.161 0.265

993.5 5.654 0.237

Eγ σ ∆σ

[MeV] [µb] [µb]

1013.9 4.796 0.238

1032.5 4.985 0.267

1052.3 4.671 0.233

1073.8 3.969 0.210

1093.2 4.156 0.278

1115.8 3.439 0.235

1131.1 3.192 0.210

1149.5 3.166 0.188

1170.9 2.921 0.172

1191.8 3.042 0.197

1210.8 2.914 0.193

1230.5 2.430 0.174

1250.0 2.465 0.185

1269.5 2.053 0.153

1288.2 1.700 0.171

1308.0 1.934 0.152

1330.5 1.604 0.246

1347.0 1.790 0.202

1367.0 1.418 0.146

1387.3 1.031 0.113

43

quasi-free neutron cross section

Eγ σ ∆σ

[MeV] [µb] [µb]

624.5 0.077 0.046

649.5 0.353 0.144

672.5 0.210 0.080

687.5 2.159 0.169

708.3 4.415 0.248

727.0 6.687 0.348

745.5 8.043 0.371

766.5 8.151 0.353

786.5 8.532 0.392

805.5 8.005 0.376

823.5 7.800 0.321

843.5 7.174 0.308

862.5 6.243 0.335

883.5 5.732 0.289

901.5 6.254 0.338

920.7 4.945 0.242

942.3 5.166 0.275

961.3 4.824 0.265

980.3 4.657 0.277

999.1 4.457 0.271

Eγ σ ∆σ

[MeV] [µb] [µb]

1017.7 4.265 0.275

1037.8 3.660 0.240

1057.7 3.636 0.260

1075.7 3.510 0.258

1093.2 3.162 0.285

1117.5 2.689 0.220

1134.5 2.923 0.238

1152.8 2.323 0.192

1172.5 2.140 0.188

1193.4 2.204 0.184

1214.0 2.301 0.208

1232.0 1.969 0.197

1251.5 1.843 0.174

1271.0 1.517 0.170

1289.6 2.282 0.215

1309.4 1.565 0.175

1330.5 1.968 0.326

1347.0 1.644 0.229

1367.0 1.205 0.160

1387.3 1.064 0.137

44 Chapter A. Cross section data

neutron-proton cross section ratio

Eγ σ ∆σ

[MeV] [µb] [µb]

727.0 0.812 0.057

743.5 0.637 0.044

758.2 0.582 0.043

772.5 0.513 0.033

786.5 0.485 0.034

801.2 0.420 0.025

815.5 0.432 0.027

829.5 0.430 0.025

845.5 0.390 0.023

859.5 0.377 0.027

875.5 0.342 0.026

889.5 0.361 0.026

903.5 0.481 0.036

916.8 0.420 0.030

932.5 0.457 0.033

948.0 0.475 0.036

963.2 0.495 0.038

976.5 0.567 0.055

989.8 0.583 0.049

1004.8 0.543 0.049

1019.5 0.587 0.055

1034.2 0.510 0.050

1048.8 0.557 0.056

Eγ σ ∆σ

[MeV] [µb] [µb]

1063.0 0.542 0.055

1079.3 0.602 0.057

1095.5 0.560 0.074

1112.5 0.430 0.071

1122.5 0.674 0.077

1137.9 0.603 0.063

1152.8 0.460 0.059

1166.0 0.508 0.065

1180.7 0.556 0.066

1196.5 0.443 0.057

1211.0 0.499 0.070

1224.5 0.527 0.076

1239.5 0.598 0.078

1254.5 0.463 0.068

1269.5 0.558 0.082

1283.9 0.684 0.132

1298.1 0.730 0.107

1312.3 0.468 0.077

1330.5 0.591 0.137

1345.2 0.513 0.105

1358.2 0.760 0.170

1371.5 0.535 0.104

1379.5 0.710 0.296

46 Chapter B. Tagger energy calibration

B. Tagger energy calibration

∗broken channels

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 3.07

1 1396.60 2.08 31 1309.29 2.83 61 1221.61 3.08

2 1394.48 2.16 32 1306.48 2.80 62 1218.52 3.09

3 1392.27 2.25 33 1303.69 2.78 63 1215.42 3.10

4 1389.98 2.33 34 1300.91 2.78 64 1212.32 3.11

5 1387.60 2.42 35 1298.12 2.79 65 1209.20 3.12

6 1385.14 2.51 36 1295.32 2.81 66 1206.07 3.14

7 1382.58 2.60 37 1292.50 2.83 67 1202.93 3.15

8 1379.93 2.69 38 1289.66 2.84 68 1199.77 3.16

9 1377.20 2.77 39 1286.81 2.85 69 1196.61 3.17

10 1374.39 2.85 40 1283.95 2.86 70 1193.44 3.18

11 1371.51 2.92 41 1281.09 2.87 71 1190.25 3.19

12 1368.55 2.99 42 1278.21 2.88 72 1187.06 3.20

13 1365.53 3.06 43 1275.33 2.89 73 1183.85 3.21

14 1362.45 3.11 44 1272.43 2.90 74 1180.63 3.22

15 1359.31 3.16 45 1269.52 2.91 75 1177.40 3.23

16∗ 1356.13 3.20 46 1266.61 2.92 76 1174.17 3.25

17 1352.92 3.23 47 1263.68 2.93 77 1170.92 3.25

18 1349.68 3.25 48 1260.75 2.94 78 1167.65 3.27

19 1346.42 3.26 49 1257.80 2.95 79 1164.38 3.28

20∗ 1343.15 3.26 50 1254.84 2.96 80 1161.10 3.29

21 1339.89 3.26 51 1251.87 2.97 81 1157.81 3.30

22∗ 1336.65 3.23 52 1248.90 2.98 82 1154.50 3.31

23 1333.43 3.21 53 1245.91 3.00 83 1151.19 3.32

24 1330.24 3.17 54 1242.91 3.00 84 1147.86 3.33

25 1327.10 3.12 55 1239.90 3.02 85 1144.53 3.34

26∗ 1324.00 3.07 56 1236.88 3.03 86 1141.18 3.35

27∗ 1320.96 3.02 57 1233.84 3.04 87 1137.82 3.36

28 1317.97 2.96 58 1230.80 3.05 88 1134.46 3.37

29 1315.03 2.91 59 1227.75 3.06 89 1131.08 3.38

90 1127.69 3.39 135 965.15 3.81 180 786.79 4.09

91 1124.29 3.40 136 961.34 3.82 181 782.70 4.10

92 1120.88 3.41 137 957.52 3.83 182 778.60 4.10

47

Ch Eγ ∆Eγ Ch Eγ ∆Eγ Ch Eγ ∆Eγ

[MeV] [MeV] [MeV] [MeV] [MeV] [MeV]

93 1117.46 3.42 138 953.69 3.83 183 774.50 4.11

94 1114.03 3.44 139 949.85 3.84 184 770.39 4.11

95 1110.59 3.45 140 946.00 3.85 185 766.28 4.12

96∗ 1107.14 3.46 141 942.15 3.86 186 762.16 4.12

97∗ 1103.68 3.47 142 938.29 3.86 187 758.04 4.12

98 1100.21 3.48 143 934.42 3.87 188 753.92 4.13

99 1096.73 3.49 144 930.55 3.88 189 749.79 4.13

100∗ 1093.24 3.50 145 926.66 3.89 190 745.66 4.13

101 1089.73 3.51 146 922.77 3.89 191 741.52 4.14

102 1086.22 3.52 147 918.88 3.90 192 737.38 4.14

103 1082.70 3.53 148 914.98 3.91 193 733.24 4.15

104 1079.17 3.54 149 911.06 3.91 194 729.09 4.15

105 1075.63 3.54 150 907.15 3.92 195 724.94 4.15

106 1072.08 3.56 151 903.22 3.93 196 720.78 4.16

107 1068.52 3.57 152 899.29 3.93 197 716.62 4.16

108 1064.95 3.57 153 895.36 3.94 198 712.46 4.16

109 1061.37 3.58 154 891.41 3.95 199 708.30 4.17

110 1057.78 3.59 155 887.46 3.95 200 704.13 4.17

111 1054.19 3.60 156 883.50 3.96 201 699.96 4.17

112 1050.58 3.61 157 879.54 3.97 202 695.79 4.18

113 1046.96 3.62 158 875.57 3.97 203 691.61 4.18

114 1043.34 3.63 159 871.59 3.98 204 687.43 4.18

115 1039.70 3.64 160∗ 867.61 3.99 205 683.25 4.18

116 1036.06 3.65 161 863.62 3.99 206 679.06 4.19

117 1032.40 3.66 162 859.63 4.00 207 674.87 4.19

118 1028.74 3.67 163 855.63 4.00 208 670.68 4.19

119 1025.07 3.68 164 851.62 4.01 209 666.49 4.20

120 1021.39 3.68 165 847.61 4.02 210 662.29 4.20

121 1017.70 3.69 166 843.59 4.02 211 658.09 4.20

122 1014.00 3.70 167 839.57 4.03 212 653.89 4.20

123 1010.29 3.71 168 835.54 4.03 213 649.69 4.20

124 1006.58 3.72 169 831.51 4.04 214 645.48 4.21

125 1002.85 3.73 170 827.47 4.04 215 641.27 4.21

126 999.12 3.74 171 823.42 4.05 216 637.06 4.21

127 995.38 3.75 172 819.37 4.05 217 632.85 4.21

128 991.63 3.75 173 815.32 4.06 218 628.64 4.22

129 987.87 3.76 174 811.26 4.06 219 624.42 4.22

130 984.10 3.77 175 807.19 4.07 220 620.20 4.22

131 980.33 3.78 176 803.12 4.07 221 615.98 4.22

132 976.55 3.79 177 799.05 4.08 222 611.76 4.22

133 972.76 3.80 178 794.97 4.08 223 607.54 4.22

134 968.96 3.80 179 790.88 4.09

48 Chapter B. Tagger energy calibration

C. Invariant Mass Spectra

)γ Invariant Mass [MeV] (60π3

450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

012

34

567

8 Channel 0 - 9

= 1399 - 1377 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12Channel 10 - 19

= 1374 - 1346 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10 Channel 20 - 29

= 1343 - 1315 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

02

4

6

8

1012

14

16Channel 30 - 39

= 1312 - 1287 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25 Channel 40 - 49

= 1284 - 1258 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25Channel 50 - 59

= 1255 - 1228 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30 Channel 60 - 69

= 1225 - 1197 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30 Channel 70 - 79

= 1193 - 1164 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40Channel 80 - 89

= 1161 - 1131 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

05

101520

2530354045

Channel 90 - 99

= 1128 - 1097 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60 Channel 100 - 109

= 1093 - 1061 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

70

80Channel 110 - 119

= 1058 - 1025 MeVγE


Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100

120Channel 120 - 129

= 1021 - 988 MeVγE


Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100

120

140 Channel 130 - 139

= 984 - 950 MeVγE


Cou

nts

per

bin

[a.u

.]

0

50

100

150

200Channel 140 - 149

= 946 - 911 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250Channel 150 - 159

= 907 - 872 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250

300 Channel 160 - 169

= 868 - 832 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400Channel 170 - 179

= 827 - 791 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500 Channel 180 - 189

= 787 - 750 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500

600 Channel 190 - 199

= 746 - 708 MeVγE


Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250

300

350Channel 200 - 209

= 704 - 666 MeVγE


Cou

nts

per

bin

[a.u

.]

010

2030405060708090

Channel 210 - 224

= 662 - 603 MeVγE

Figure C.1: The resulting 3π0 invariant mass spectrum after all cuts applied in dependenceof the tagger channels. The spectrum is �tted by a combined �t: signal+background (solid redcurve). The signal is �tted by a Gaussian function, while the background is �tted by a secondorder polynomial function (blue dashed line).

49

+p)γ Invariant Mass [MeV] (60π3

350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

0.51

1.52

2.5

3

3.54

Channel 0 - 9

= 1399 - 1377 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4Channel 10 - 19

= 1374 - 1346 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

0.51

1.52

2.5

3

3.54 Channel 20 - 29

= 1343 - 1315 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5 Channel 30 - 39

= 1312 - 1287 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10 Channel 40 - 49

= 1284 - 1258 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10 Channel 50 - 59

= 1255 - 1228 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12 Channel 60 - 69

= 1225 - 1197 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12

14Channel 70 - 79

= 1193 - 1164 MeVγE


Cou

nts

per

bin

[a.u

.]

02

4

6

8

1012

14

16Channel 80 - 89

= 1161 - 1131 MeVγE


Cou

nts

per

bin

[a.u

.]

02

4

6

8

10

12

14

16Channel 90 - 99

= 1128 - 1097 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20Channel 100 - 109

= 1093 - 1061 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25 Channel 110 - 119

= 1058 - 1025 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35 Channel 120 - 129

= 1021 - 988 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

510

1520

2530

3540 Channel 130 - 139

= 984 - 950 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60 Channel 140 - 149

= 946 - 911 MeVγE


350 400 450 500 550 600 650 700 750 800

Cou

nts

per

bin

[a.u

.]

0

10203040506070

8090

Channel 150 - 159

= 907 - 872 MeVγE


Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100Channel 160 - 169

= 868 - 832 MeVγE


Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100

120Channel 170 - 179

= 827 - 791 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

70 Channel 180 - 189

= 787 - 750 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50 Channel 190 - 205

= 746 - 683 MeVγE

Figure C.2: The resulting quasi-free proton 3π0 invariant mass spectrum after all cutsapplied in dependence of the tagger channels. The spectrum is �tted as before.

51

+n)γ Invariant Mass [MeV] (60π3

450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

0.2

0.4

0.6

0.8

1

1.2Channel 0 - 9

= 1399 - 1377 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

0.5

1

1.5

2

2.5 Channel 10 - 19

= 1374 - 1346 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

0.5

1

1.5

2

2.5Channel 20 - 29

= 1343 - 1315 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

0.5

1

1.5

2

2.5

3 Channel 30 - 39

= 1312 - 1287 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

0.51

1.52

2.5

3

3.54 Channel 40 - 49

= 1284 - 1258 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5Channel 50 - 59

= 1255 - 1228 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5Channel 60 - 69

= 1225 - 1197 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6Channel 70 - 79

= 1193 - 1164 MeVγE


Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6Channel 80 - 89

= 1161 - 1131 MeVγE


Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6

7Channel 90 - 99

= 1128 - 1097 MeVγE


Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10Channel 100 - 109

= 1093 - 1061 MeVγE


Cou

nts

per

bin

[a.u

.]0

2

4

6

8

10

12 Channel 110 - 119

= 1058 - 1025 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

024

6

8101214

1618

Channel 120 - 129

= 1021 - 988 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20Channel 130 - 139

= 984 - 950 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20Channel 140 - 149

= 946 - 911 MeVγE


450 500 550 600 650 700 750

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25 Channel 150 - 159

= 907 - 872 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35 Channel 160 - 169

= 868 - 832 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35

40Channel 170 - 179

= 827 - 791 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35Channel 180 - 189

= 787 - 750 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35 Channel 190 - 205

= 746 - 683 MeVγE

Figure C.3: The resulting quasi-free neutron 3π0 invariant mass spectrum after all cutsapplied in dependence of the tagger channels. The spectrum is �tted as before.

52 Chapter C. Invariant Mass Spectra

D. Missing Mass Spectra

)γ Missing Mass [MeV] (60π3

-600-400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8Channel 0 - 9

= 1399 - 1377 MeVγE


-600 -400-200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12 Channel 10 - 19

= 1374 - 1346 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10Channel 20 - 29

= 1343 - 1315 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20 Channel 30 - 39

= 1312 - 1287 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25 Channel 40 - 49

= 1284 - 1258 MeVγE


-600-400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25Channel 50 - 59

= 1255 - 1228 MeVγE


-600 -400-200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30 Channel 60 - 69

= 1225 - 1197 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

05

1015

2025

30

3540 Channel 70 - 79

= 1193 - 1164 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50 Channel 80 - 89

= 1161 - 1131 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40Channel 90 - 99

= 1128 - 1097 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

70 Channel 100 - 109

= 1093 - 1061 MeVγE

)γ Missing Mass [MeV] (60π3-600-400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100Channel 110 - 119

= 1058 - 1025 MeVγE

)γ Missing Mass [MeV] (60π3-600 -400-200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100

120 Channel 120 - 129

= 1021 - 988 MeVγE


Cou

nts

per

bin

[a.u

.]

020406080

100120140160180 Channel 130 - 139

= 984 - 950 MeVγE


Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250 Channel 140 - 149

= 946 - 911 MeVγE


-600-400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250

300

350Channel 150 - 159

= 907 - 872 MeVγE


-600 -400-200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500Channel 160 - 169

= 868 - 832 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500

600 Channel 170 - 179

= 827 - 791 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500

600

700 Channel 180 - 189

= 787 - 750 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

100

200

300

400

500

600

700 Channel 190 - 199

= 746 - 708 MeVγE

)γ Missing Mass [MeV] (60π3-600-400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

50

100

150

200

250

300

350 Channel 200 - 209

= 704 - 666 MeVγE

)γ Missing Mass [MeV] (60π3-600 -400-200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

102030405060708090

Channel 210 - 224

= 662 - 603 MeVγE

Figure D.1: The resulting 3π0 missing mass spectrum in dependence of the tagger channels.The spectrum is �tted by a combined �t: signal+background (solid red curve). The signal andfor Eγ ≥ 1 GeV also the background are �tted by a Gaussian function, while for lower energiesthe background is �tted by a second order polynomial function (blue dashed line).

53

+p)γ Missing Mass [MeV] (60π3

-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

0.51

1.52

2.5

3

3.54

Channel 0 - 9

= 1399 - 1377 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

0.51

1.52

2.5

33.5

4

4.5Channel 10 - 19

= 1374 - 1346 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

-0.50

0.51

1.52

2.5

3

3.5 Channel 20 - 29

= 1343 - 1315 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6 Channel 30 - 39

= 1312 - 1287 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8Channel 40 - 49

= 1284 - 1258 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8Channel 50 - 59

= 1255 - 1228 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12 Channel 60 - 69

= 1225 - 1197 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

02

4

6

8

1012

14

16 Channel 70 - 79

= 1193 - 1164 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20 Channel 80 - 89

= 1161 - 1131 MeVγE


Cou

nts

per

bin

[a.u

.]

024

68

101214

1618 Channel 90 - 99

= 1128 - 1097 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20 Channel 100 - 109

= 1093 - 1061 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30Channel 110 - 119

= 1058 - 1025 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35

40Channel 120 - 129

= 1021 - 988 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50 Channel 130 - 139

= 984 - 950 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

70

80Channel 140 - 149

= 946 - 911 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100 Channel 150 - 159

= 907 - 872 MeVγE


Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100

120 Channel 160 - 169

= 868 - 832 MeVγE


Cou

nts

per

bin

[a.u

.]

0

20

40

60

80

100

120Channel 170 - 179

= 827 - 791 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50

60

70 Channel 180 - 189

= 787 - 750 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40 Channel 190 - 206

= 746 - 679 MeVγE

Figure D.2: The resulting 3π0 missing mass spectrum for the quasi-free proton in depen-dence of the tagger channels. The spectrum is �tted as before.

55

+n)γ Missing Mass [MeV] (60π3

-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4Channel 0 - 9

= 1399 - 1377 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4Channel 10 - 19

= 1374 - 1346 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

0.51

1.52

2.5

3

3.54 Channel 20 - 29

= 1343 - 1315 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6 Channel 30 - 39

= 1312 - 1287 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6

7 Channel 40 - 49

= 1284 - 1258 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

1

2

3

4

5

6 Channel 50 - 59

= 1255 - 1228 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

01

2

34

5

6

7 Channel 60 - 69

= 1225 - 1197 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

012

34

567

89

Channel 70 - 79

= 1193 - 1164 MeVγE


Cou

nts

per

bin

[a.u

.]

012

34

5

67

89

Channel 80 - 89

= 1161 - 1131 MeVγE


Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10 Channel 90 - 99

= 1128 - 1097 MeVγE


Cou

nts

per

bin

[a.u

.]

0

2

4

6

8

10

12Channel 100 - 109

= 1093 - 1061 MeVγE


Cou

nts

per

bin

[a.u

.]024

68

1012141618 Channel 110 - 119

= 1058 - 1025 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20 Channel 120 - 129

= 1021 - 988 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25 Channel 130 - 139

= 984 - 950 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35 Channel 140 - 149

= 946 - 911 MeVγE


-600 -400 -200 0 200 400 600

Cou

nts

per

bin

[a.u

.]

0

5

1015

20

2530

3540 Channel 150 - 159

= 907 - 872 MeVγE


Cou

nts

per

bin

[a.u

.]

0

510

15

2025

3035

40 Channel 160 - 169

= 868 - 832 MeVγE


Cou

nts

per

bin

[a.u

.]

0

10

20

30

40

50Channel 170 - 179

= 827 - 791 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30

35Channel 180 - 189

= 787 - 750 MeVγE


Cou

nts

per

bin

[a.u

.]

0

5

10

15

20

25

30 Channel 190 - 199

= 746 - 708 MeVγE

Figure D.3: The resulting 3π0 missing mass spectrum for the quasi-free neutron in depen-dence of the tagger channels. The spectrum is �tted as before.

56 Chapter D. Missing Mass Spectra

Bibliography

[1] A. Fix, L. Tiator, M. V. Poyakov: Photoproduction of η-mesons on the

deuteron above S11(1535) in presence of a narrow P11(1670) resonance. 2007.

[2] Annand, J. R. M.: Data analysis within an AcquRoot Framework. Univer-

sity of Glasgow, 2005.

[3] B. Krusche, S. Schadmand: Study of Non-Strange Baryon Resonances

with Meson Photoproduction. Progress in Particle and Nuclear Physics,

51:399, 2003.

[4] Bianchi, N. et al.: Total hadronic photoabsorption cross section on nuclei

in the nucleon resonance region. Phys. Rev. C, 54(4):1688�1699, Oct 1996.

[5] Collaboration, The CB-ELSA: Photoproduction of η-mesons o� pro-

tons. Eur. Phys. J. A, 33:133�146, 2007.

[6] Contemporary Physics Education Project:

http://www.cpepweb.org.

[7] Griffiths, David: Einführung in die Elementarteilchenphysik. Akademie

Verlag, 1996.

[8] Jaegle, Igal: ππ , η and η′ photoproduction o� the deuteron or the search

for missing resonances. 2007.

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