Nucleon Structure Function, An Introduction of the BoNuS

Program at Hall B Jefferson Laband the G2P Program at Hall A

Jixie Zhang (Jlab)

March. 13, 2013

Outline• Thesis Work:

extract D(e,e`p)p cross section– BoNuS Project– Data Analysis– Result

• Current Work: – G2P Project– Status

• Future Work

2

3

Nucleon Structure Functions

Structure Function Definition (in the quark-parton model)

)(9

1)(

9

4)(

)(9

1)(

9

4))()(()(

12

1

22

xuxdxxF

xdxuxxqxqexxF

x

n

xq

qp

Callan-Gross Relation

4

Strong Model Dependence

SU(6) symmetry uv(x) = 2dv(x)

S = 0 dominant, one-gluon exchangeClose, Phys Lett B43 (1973)Carlitz, Phys Lett B58 (1975)Close and Thomas Phys Lett B212 (1988)Isgur, Phys Rev D59 (1999), Phys Rev Lett 41 (1978)

Sz = 0 dominant, helicity conservationFarrar and Jackson, Phys Rev Lett 35 (1975)Brodsky, Burkardt and Schmidt, Nuc Phys B441 (1995)

SLAC E139 (L. W. Whitlow, et al.), and E140 (J. Gomez, et al.)

Cross Section in the Resonance Region

• Data on the Proton: Clear resonant structure, separation from the non-resonant background is possible

• Data on the deuteron: Kinematically smeared due to binding, off-shell, final state interactions (FSI), etc.

5

Exclusive electro-production D(e,e`p)p

Detect e′, and at least ONE of the two final state protons in D(e,e`p)p to ensure exclusivity and select events where the “spectator” proton has low, backwards momentum. Conservation of energy and momentum allows to determine the initial state of the neutron.

Low momentum “spectator” proton

Novel approach by the BoNuS collaboration: detect the spectator proton directly.

e′

enp

p

ps

d

6

Q2 = -(qµ)2 = 4 sin2(e/2)

W2 = (qµ + nµ )2

= (qµ + dµ - psµ)2

= (µ + pµ )2

Production Kinematics

n - p

* = polar angle of the outgoing in C.M. frame

* = Azimuthal angle of the outgoing in C.M. frame

, q

*

*

n

p

Hadronic plane

E, k

E, k

Leptonic plane

7

Off-Shell and FSI for D(e,e′ps)X

Final State Interactions

Off-shell Effects

VIPs

Select low Ps (<120 MeV/c) and large backward pq (>100o), angle between Ps and virtual photon, to minimize FIS.

Off-shell effects are negligible for small Ps. Choose Ps<120 MeV/c as Very Important Spectator Protons (VIP)

C. Atti et al, Eur. Phys. J. A 19,133-137 (2004).

W. Melnitchouk et al, Phys. Lett. B377, 11 (1996).

8

d

p

ps

n

quasi-free (IA)

primary background

Final State Interations

dp

p

n

p

d

p

p

n

p rescattering

pp rescattering

primary background

9

No theory calculation for * n - p FSI yet. Try to estimate this from FSI ofn - p .......V. Tarasov, A. Kudryavtsev, W. Briscoe, H. Gao, IS, arXiv: 1105.0225

FSI Prediction for D(,p)p, by Laget

R = ratio of the total to the quasi-free cross sectionR = polar angle between photon and spectator protonPR = momentum of the spectator proton

underp rescattering peak region only

Strong momentum and anglular dependence

Cross Section Calculations1. Select exclusive events

2. Apply corrections: background corr., radiative corr., trigger eff., , CLAS proton and RTPC proton detection eff., and acceptance correction.

Jefferson Lab Experiment E03-012

Barely off-shell Nucleon Structure (BoNuS)

• Electron beam energies: 2.1, 4.2, 5.3 GeV• Spectator protons were detected by the newly built

Radial Time Projection Chamber (RTPC)• Scattered electrons and other final state particles were

detected by CEBAF Large Acceptance Spectrometer (CLAS)

• Target: 7 atm D2 gas, 20 cm long

• Data were taken from Sep. to Dec. in 2005

N.Baillie, S. Tkachenko, J. Zhang,

K. Griffioen, S. Kuhn, Gail Dodge, C. Keppel, M.E. Christy,

W. Melnitchouk, H. Fenker, S. Bültmann

RTPC Sits in the Center of CLAS

FC

CLAS

BoNuS RTPC

stopper

13

Radial Time Projection Chamber (RTPC)

proton

Deuteron / Helium

Helium/DME at 80/20 ratio

Sensitive to protons with momenta of 67-250 Mev/c

3 layers of GEM

3200 pads (channels)

5 Tesla B field

Particles ID by dE/dx

100 µm

3-D tracking:time of drift -> rpad position -> ,

z

dE/dX

7Atm. D2 gas target, 20cm in length

Trigger Electron

14

RTPC Resolution

Trigger electrons measured by CLAS are compared to the same electrons measured in BoNuS during High Gain Calibration runs.

H. Fenker, et.al. Nucl.Instrum. Meth. A592:273-286,2008

15

Analysis Outline1. Quality Checks

2. Vertex correction and vertex z cuts

3. Particle identifications (electron, and proton )

4. Fiducial cut for trigger electron, and proton

5. Energy loss correction for electron, and proton

6. Exclusive cut (2- Missing Mass cut)

7. Acceptance cut and acceptance correction

8. Background subtraction

9. Trigger efficiency correction, CLAS proton and RTPC proton detection efficiency correction

10.Radiation correction

11.Luminosity analysis

12.Extract the cross section and structure functions

13.Systematic error estimation

Simulation Overview

RTPC(Geant4) CLAS(geant3) Reconstruction Analysis

What have been done with simulation?• Debug/optimize RTPC reconstruction packages• Generate energy loss correction tables, radiation length tables• Study Detector’s acceptance for D(e,e`pCLAS)p and D(e,e`pRTPC)p• Study particle detection efficiency • Model the background… 17

Kinematic coverage and binning, 5 GeV

cos*: 8 bins with boundaries at -1.0, -0.5, -0.1, 0.3, 0.55, 0.7, 0.8, 0.9,1.0

*: 15 bins, 24 degrees each bin, [0.0,360.0)

W: 150 MeV each bin, [1.15,2.95)

Q2 : 6 bins with boundaries at 0.1309, 0.3790, 0.7697, 1.0969, 1.5632, 2.6594, 4.5243

18

Missing Mass Cut: from Gaussian Center

5 GeV 5 GeV

background

19

Beam Energy MM Cut of D(e,e`pCLAS)p MM Cut of D(e,e`pRTPC)p

2.x 0.9436 +/- 0.0509 0.9374 +/- 0.0400

4.x 0.9401 +/- 0.0605 0.9356 +/- 0.0501

5.x 0.9389 +/- 0.0718 0.9350 +/- 0.0615

Background Subtraction

f1, f2, f3 and f4 are the fitted background fraction functions for real data. f1

sim, f2sim

, f3sim and f4

sim are the fitted background fraction functions for simulated data.

Final background correction factor:

where 0.9545 is the coverage of 2 in a gaussian distribution.

Simulated Data

average

20

Background of D(e,e`pCLAS)p, 5G Real

21

f1f2

f3f4

Background of D(e,e`pCLAS)p, 5G Sim.

22

f1sim f2

sim

f3sim

f4sim

Radiation Correction, E=5.3 GeV

23

W`=1.23

*

/

bo

rn

Leading Log approximation Calculation Based on Maid07

Using upraded “Exclurad”. Updated with MAID07 multipole model for both neutron and proton. A dedicate clas-note will be vesy soon.

CLAS trigger efficiency, 5G

24

Trigger efficiency is the fraction that the trigger particle (electron) is detected. It is obtained by scaling the simulation data to the real data, then calculating the ratio of real event counts in each p- grid to the simulated event counts in the same grid.

(deg)

P

(GeV

)

Data outside the curve will not be considered!

CLAS proton efficiency

25

RTPC proton efficiency

26

D(e,ep)p Acceptance Correction

• Binning information:

W: 150 MeV each bin, [1.15,3.10);

Q2 : 6 bins, {0.1309, 0.3790, 0.7697, 1.0969, 1.5632, 2.6594, 4.5243 };

cos*: 8 bins, 0.25 each bin, [-1.0,1.0);

*: 15 bins, 24 degrees each bin, [0.0,360.0).

• Acceptance is the ratio of the number of events detected in a given bin to the number of generated events in the same bin.

• Need to generate tables for D(e,epRTPC)p and D(e,epCLAS)p reaction separately.

• Applied event by event

• Need to have acceptance cut to ensure the reliabilities

For CLAS channel: 0.008 and less than 10% uncertainty (> 100 detected events)

For RTPC channel: 0.003 and less than 15% uncertainty (> 40 detected events) 27

Cross Section Calculations1. Select exclusive events

2. Apply corrections: background corr., radiative corr., trigger eff., , CLAS proton and RTPC proton detection eff., and acceptance correction.

Cross Section: BoNuS Vs MAID and SAID

4 GeV, W` = 1.23 GeV

0.85

Cos

0.75

0.625

0.95

MAID 07 SAID 08 D(e,epCLAS)pD(e,epRTPC)p

prel

imin

ary

GeV2

Minimizing Final State Interactions2 GeV, W` = 1.23 GeV

VIP Cut= pq>100o and 70<ps<120 MeV

prel

imin

ary

With VIP Cut

Without VIP Cut

Prediction: FSI + Binding < 20% under VIP cutData: 1)Better agreement between CLAS and RTPC channel for low Q2; 2) No obvious change other than removing data points to the results with larger Q2

Cos=0.85

Cos=0.85

Cos=0.95

Cos=0.95

30

Systematic Error 4 GeV, W` = 1.23 GeV

15% in average, mainly come from the following (values are all in average):

Cos=0.85

Cos=0.95

31

D(e,epCLAS)pD(e,epRTPC)p

Rad. corr. ~5% Background corr. 5%

Acceptance cut 10% Missing mass cut 5%

Detection eff. 8% Luminosity 2%

GeV2

FSI is estimated to be 15%, not included in the figure yet

Fit for the Structure Functions

A0 A1 Cos* A2 Cos2*= + +32

Structure Functions: BoNuS Vs MAID 5 GeV, W` = 1.525 GeV

VIP = 70<ps<120 MeV/c, and pq>100o

D(e,epRTPC)p + VIPD(e,epCLAS)p + VIP

prel

imin

ary

33FSI + Binding < 20% under VIP cut

A0: BoNuS Vs MAID, 4 GeV with VIP cut

prel

imin

ary

34

BoNuS Kinematic Correction

BoNuS

Region

VIPs

ps distribution

70, 100, 200 MeV/c

• Very Important Protons 70<ps<100 MeV/c

• Corrections make resonances stand out

• F2n/F2p can be measured at high x*

Accidental Backgrounds

• Fits to the triangular background allows us to measure backgrounds underneath the peak

• Rbg = Blue area / Pink area, Rbg is independent of kinematics

Two Analysis Methods

• The Ratio Method★ measure tagged counts divided by inclusive counts★ correct this ratio for backgrounds★ one scale factor gives F2n/F2d

• The Monte Carlo Method★ measure tagged counts★ divide by spectator model Monte Carlo results★ multiply by F2n used in the model

• The two methods have different systematic errors, but give very similar results.

Comparison of These 2 Methods

38

1, by S. Tkachenko, MC method2, by N. Baillie, Ratio method

BoNuS F2n

39

BoNuS F2n/F2

p • F2

n/F2n vs. x

• Curves are CETQ error bands

• CETQ cuts off at low x because Q2 is too low

• Lower cuts in W* imply higher x but the inclusion of resonance contributions.

• Results are consistent with CETQ trends at high x.

E12-06-113E12-06-113

BoNuS Plans for 12 GeV

Data taking:

– 35 days on D2

– 5 days on H2

– L = 2 x 1034 cm-2 sec-1

DIS region: – Q2 > 1 GeV2

– W* > 2 GeV

– ps < 100 MeV/c

– θpq > 110°

– x*max = 0.80W* > 1.8 GeV: x*max = 0.83

Summary (I) • Measured absolute cross sections for D(e,e′p)p reaction over a

wide kinematic range, 1.1<W`<2.8 GeV, 0.13<Q2<4.5 GeV2, full range of cos* and *.

• We see qualitative consistency in most bins between our results and model predictions. In most bins, the pRTPC and pCLAS channels are consistent.

• Huge increase in available data points (about 5000) for n p. Currently only ~900 points available in the world database. BoNuS data will be used to improve our understanding of neutron structure, as part of fits to world data (SAID, MAID…).

• Systematic error is estimated to be ~15% (not include FSI).

• Plan to repeat this analysis using other deuteron data, i.e. CLAS E6 data. Will also use BoNuS 12GeV data to increase statistics.

42

Summary (II)

43

• We have measured F2n on a “free” neutron target

• No effects from Fermi motion and final-state interactions

• No evidence for off-shell structure for ps<100 MeV/c• F2

n/F2p behaves at high x much like CETQ high-x fits

• F2n resonance data will significantly improve the

world data set, which up to now came from d with nuclear corrections

Backup Slices

44

Motivation• Purpose: In order to understand the structure of the

nucleon (neutron and proton) we need to study the excited states (resonances).

• We have a lot of data on the proton but almost nothing on the neutron – both are needed for a complete understanding.

• Strategy is to use pion production: * + n p

• We have some real photon data, almost no electroproduction (virtual photon)

• Difficulty: No free neutron target, need to use deuteron instead.

45

46

Deep Inelastic Electron Scattering

Need to know this ratio to extract structure function information from inclusive processes (Rosenbluth separation)

•Provided first experimental evidence for the “partonic” structure of the nucleon

•As we increase the momentum transferred to the target, the resolving power increases

Deep Inelastic ScatteringDeep Inelastic Scattering

MQ

x2

2

e- e-

*

Nq

q

Q2 > 1 GeV2, W > 2 GeV

2cos

'4 24

22 Q

EMott

Resonances predicted by Quark Model vs. experimental measurements

From http://pdg.lbl.gov/2009/reviews/rpp2009-rev-quark-model.pdf

Full lines: tentative assignment to

observed states

Dashed lines: so far no observed

counterparts.

47

Resonances6 families, depending on quark content (Isospin):

N*(1/2), (3/2),(0), (1), (1/2), (0)

N*, Resonance, combination of u and d only

Notation: L2I2J

L: orbital angular momentum

I: Isospin

J: total angular momentum J = L+S

S,P,D,F,G,H L= 0,1,2,3,4,5

+N + N

Possible for N not

Heisenberg Uncertainty Principle:

short life time wide energy

Measured from the decay products

I=1 I=1/2

+N + NI=0 I=1/2

Possible for both N and

48

Resonances examples

49

Exclusive Cross Section

Unpolarized virtual photon cross-section of *+n +p

Degree of transverse polarization:

,

50

d

p

ps

n

quasi-free (IA)

primary background

Final State Interations

d

p

0

p

p

dp

p

n

p

d

p

p

n

p rescattering

pp rescattering ep scattering

primary background

51

52

Continuous Electron Beam Accelerator Facility (CEBAF)

53

Jefferson Lab

A B C

Continuous Electron Beam Accelerator Facility

E: 0.75 –6 GeV Imax: 200A RF: 1499 MHz Duty Cycle: 100% (E)/E: 10-4

Polarization: 85% Simultaneous

distribution to 3 experimental Halls

Injector

LIN

AC L

INA

CExperimental Halls

54

CLAS in Jefferson Lab, Hall B

55

Radial Time Projection Chamber (RTPC)

56

Analysis Procedure1. Quality Checks

2. Vertex correction and cuts

3. Particle identification (electron, and proton )

4. Fiducial cut for trigger electron, and protons

5. Energy loss correction

6. Exclusive cut (Missing Mass cut)

7. Acceptance correction

8. Background subtraction

9. Radiation correction

10.Particle detection efficiency for e, proton and RTPC proton

11.Extract cross section and structure functions

Run Selection: Quality Checks

4 GeV 5 GeV

Without Stopper

Bad Runs

58

Zel-Z2

(mm)

Sector 2

Sector 6

Sector 4

Sector 1

Sector 3

Sector 5

Zel-Z2

(mm)

Before and After Vertex Correction

Using real data, find the best beam position to minimize the vertex difference among coincident particles

59

Vertex Cut

60

Electron Identification

• rtr

1. Negative charge.

2. Number of photo electrons (Nphe) > 1.5

3. E_inner > 0.06 and 0.016*P+0.15 < E_total/P < 0.34

4. Pass Osipenko cut (geometry matching between SC and CC)61

CLAS Particle IdentificationsNegative non-trigger particles:

(1) above purple curve

(2) Among the rest, between purple and light blue curve K

(3) Among the rest, below light blue curve anti-proton

Positive particles:

(1) between light blue and green curve proton

() below green curve Deuteron

(3) Among the rest, above purple curve

(4) Among the rest, between purple and light blue curve K

62

RTPC Proton Identification

proton

Deuteron Helium

dQ/dx

calcdxdQ

dxdQ

/

/log exp

10

protons

NucleiReal data

63

The Drift Path of An Ionized Electron

•The red lines show the drift path of each ionization electron that would appear on a given channel.

•In green is the spatial reconstruction of where the ionization took place.

•In reconstruction, hits which are close to each other in space are linked together and fit to a helical trajectory.

•This resulting helix tells us the vertex position and the initial three momentum of the particle.

A MAGBOLTZ simulation of the crossed E and B fields, together with the drift gas mixture, determines the drift path and the drift velocity of the electrons.

64

RTPC Gain CalibrationChannel by Channel gain multipliers can be determined for each run by comparing the track’s expected energy loss to the measured value.

After applying the gain corrections, a clear separation of protons and heavier particles through dE/dx has been achieved.

Gain constants (vs phi and z) determined independently for two different runs.Before and After Gain Calibration

65

Energy Loss Correction for CLAS Particles

Binned by measured , , z, p;

Based on simulation, fit ‘P0-P vs P’ with an integral Bethe-Bloch function for all particles

Pr

e

P0-P

me

asu

red (

Ge

v/c

)

Pmeasured (Gev/c)66

Energy Loss Correction for RTPC Proton

67

Fiducial Cut Fitting Function

Fiducial cut is the geometry cut which is used to remove inefficiency part of the detector.

Momentum dependent

Electron: = 0.35,

Pion: = 1.0

Ptoton : = 3.0

Fitting function:

New Fiducial cut for e

69

Fiducial cut for

70

Fiducial cut for proton

71

Exclusive Events Selection1. Select good trigger (scattered electron)

q<0 , CC + Osipenko (CC geometry match cut)EC (Ein>0.06, without Etot/p Cut)Theta_Z_Cut

2. Vertex Z correlation cut|z_el –Z_i| < 2.71 cm, i could be , fast proton or RTPC proton.

3. Identify the , if not found, use a negative non-trigger particle as

4. Identify protons, if not found, use a positive particle as proton

5. Apply vertex and energy loss corrections6. Apply 2- missing mass cut

72

D(e,ep)p Acceptance Correction

• Binning information:

W: 150 MeV each bin, [1.15,3.10);

Q2 : 6 bins, {0.1309, 0.3790, 0.7697, 1.0969, 1.5632, 2.6594, 4.5243 };

cos*: 8 bins, 0.25 each bin, [-1.0,1.0);

*: 15 bins, 24 degrees each bin, [0.0,360.0).

• Acceptance is the ratio of the number of events detected in a given bin to the number of generated events in the same bin.

• Need to generate tables for D(e,epRTPC)p and D(e,epCLAS)p reaction separately.

• Applied event by event

• Need to have acceptance cut to ensure the reliabilities

For CLAS channel: 0.008 and less than 10% uncertainty (> 100 detected events)

For RTPC channel: 0.003 and less than 15% uncertainty (> 40 detected events) 73

Acceptance Correction, E=5.3 GeV

74

Acceptance Correction, E=5.3 GeV

75

Target Thickness

Calculate the effective target pressure, Peff , for a data set by weighting the pressure of each run with the number of good electrons in that run.

76

Time integrated Luminosity

77

Sim Vs Real

Real 5G

Simula

tion 5

G

78

A0: BoNuS VIP Vs MAID, 2 GeV

prel

imin

ary

79

Cross Section: BoNuS Vs MAID and SAID

2 GeV, W` = 1.23

0.85

Cos

0.75

0.625

0.95

MAID 07 SAID 08 D(e,epCLAS)pD(e,epRTPC)p

prel

imin

ary

80

Cross Section: BoNuS Vs MAID and SAID

5 GeV, W` = 1.23

0.85

Cos

0.75

0.625

0.95

MAID 07 SAID 08 D(e,epCLAS)pD(e,epRTPC)p

prel

imin

ary

81

A0: BoNuS VIP Vs MAID, 4 GeV

prel

imin

ary

82

A0: BoNuS VIP Vs MAID, 5 GeV

prel

imin

ary

83