Nucleon Structure Functions: An Introduction of the BoNuS Program at Hall B Jefferson Lab and the G2P Project at Hall A Jixie Zhang (Jlab) March. 13, 2013

Outline Thesis Work –BoNuS Project –Data Analysis: Exclusive: Extract D(e,e` p)p cross section Inclusive: F 2 n structure function –Results Current Work –G2P Project –Status Future Work 2

3 Nucleon Structure Functions Structure Function Definition (in the quark-parton model) Dominated by the valence quarks contribution at large x

4 Very Strong Model Dependence SU(6) symmetry u v (x) = 2d v (x) S = 0 dominant, one-gluon exchange Close, 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) S z = 0 dominant, helicity conservation Farrar and Jackson, Phys Rev Lett 35 (1975) Brodsky, Burkardt and Schmidt, Nuc Phys B441 (1995) SLAC E139 (J. Gomez et al.) and E140 (L. W. Whitlow et al.)

Cross Section in the Resonance Region Goal: to understand neutron as well as proton, understand u and d quark structure function... 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 e npnp p psps d 6

Off-Shell and FSI for D(e,ep s )X Final State Interactions Off-shell Effects VIP s Select low P s ( 100 o ), angle between Ps and virtual photon, to minimize FIS. Off-shell effects are negligible for small P s. Choose P s <120 MeV/c as Very Important Spectator Protons (VIP) C. Atti et al, Eur. Phys. J. A 19, (2004). W. Melnitchouk et al, Phys. Lett. B377, 11 (1996). 7

d p psps n quasi-free (IA) primary background FSI for D(e,e ` p)p d p p n p d p p n p rescattering pp rescattering primary background 8 No theory calculation for * n - p FSI yet. Try to estimate this from FSI of n - p V. Tarasov, A. Kudryavtsev, W. Briscoe, H. Gao, IS, arXiv:

FSI Prediction for D(, p)p, by Laget R = ratio of the total to the quasi-free cross section R = polar angle between photon and spectator proton P R = momentum of the spectator proton under p rescattering peak region only Strong momentum and anglular dependence

Jefferson Lab Experiment E 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 D 2 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, P. Bosted and......

RTPC Sits in the Center of CLAS FC CLAS BoNuS RTPC stopper 11

Radial Time Projection Chamber (RTPC) proton Deuteron / Helium Helium/DME at 80/20 ratio Sensitive to protons with momenta of 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 -> r pad position ->, z dE/dX 7Atm. D2 gas target, 20cm in length Trigger Electron 12

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: ,

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 Detectors acceptance for D(e,e` p CLAS )p and D(e,e` p RTPC )p Study particle detection efficiency Model the background… 14

Q 2 = -(q µ ) 2 = 4 sin 2 ( e /2) W 2 = (q µ + n µ ) 2 = (q µ + d µ - p s µ ) 2 = ( µ + p µ ) 2 Exclusive Electro-Production Analysis 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 Leptonic plane 15

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 , , , , , ,

Cross Section Calculations 1.Select exclusive events 2.Apply corrections: background corr., radiative corr., trigger eff.,, CLAS proton and RTPC proton detection eff., and acceptance correction.

Missing Mass Cut: from Gaussian Center 5 GeV background 18 Beam Energy MM Cut of D(e,e` p CLAS )p MM Cut of D(e,e` p RTPC )p / / / / / /

Background Subtraction f 1, f 2, f 3 and f 4 are the fitted background fraction functions for real data. f 1 sim, f 2 sim, f 3 sim and f 4 sim are the fitted background fraction functions for simulated data. Final background correction factor: where is the coverage of 2 in a gaussian distribution. Simulated Data average 19

Radiation Correction, E=5.3 GeV 20 W`=1.23 * / born Leading Log approximationCalculation Based on Maid07 Using upraded Exclurad. Updated with MAID07 multipole model for both neutron and proton. A dedicate clas-note will be vesy soon.

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) CLAS trigger efficiency, 5G 21 Data outside the curve will not be considered!

CLAS proton efficiency 22

RTPC proton efficiency 23

D(e,e p)p Acceptance Correction Binning information: W : 150 MeV each bin, [1.15,3.10); Q 2 : 6 bins, {0.1309, , , , , , }; 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,e p RTPC )p and D(e,e p CLAS )p reaction separately. Applied event by event Need to have acceptance cut to ensure the reliabilities For CLAS channel: and less than 10% uncertainty (> 100 detected events) For RTPC channel: and less than 15% uncertainty (> 40 detected events) 24

Cross Section: BoNuS Vs MAID and SAID 4 GeV, W` = 1.23 GeV 0.85 Cos MAID 07SAID 08 D(e,e p CLAS )pD(e,e p RTPC )p preliminary GeV 2

Minimizing Final State Interactions 2 GeV, W` = 1.23 GeV VIP Cut= pq >100 o and 70<p s <120 MeV preliminary With VIP Cut Without VIP Cut Prediction: FSI + Binding < 20% under VIP cut Data: 1)Better agreement between CLAS and RTPC channel for low Q 2 ; 2) No obvious change other than removing data points to the results with larger Q 2 Cos =0.85 Cos =

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 = D(e,e p CLAS )pD(e,e p RTPC )p Rad. corr.~5%Background corr.5% Acceptance cut10%Missing mass cut5% Detection eff.8%Luminosity2% GeV 2 FSI is estimated to be 15%, not included in the figure yet

Fit for the Structure Functions A0 A1 Cos *A2 Cos2 * = ++ 28

Structure Functions: BoNuS Vs MAID 5 GeV, W` = GeV VIP = o D(e,e p RTPC )p + VIPD(e,e p CLAS )p + VIP preliminary 29 FSI + Binding < 20% under VIP cut

Summary of Exclusive Analysis Measured absolute cross sections for D(e,e p)p reaction over a wide kinematic range, 1.1<W`<2.8 GeV, 0.13<Q 2 <4.5 GeV 2, full range of cos * and *. We see qualitative consistency in most bins between our results and model predictions. In most bins, the p RTPC and p CLAS 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. 30

Inclusive Analysis The Ratio Method measure tagged counts divided by inclusive counts correct this ratio for backgrounds one scale factor gives F 2 n /F 2 d The Monte Carlo Method measure tagged counts divide by spectator model Monte Carlo results multiply by F 2 n used in the model The two methods have different systematic errors, but give very similar results.

BoNuS Kinematic Correction BoNuS Region VIPs p s distribution 70, 100, 200 MeV/c Very Important Protons 70<ps<100 MeV/c Corrections make resonances stand out F 2 n /F 2 p can be measured at high x*

Accidental Backgrounds Fits to the triangular background allows us to measure backgrounds underneath the peak R bg = Blue area / Pink area, R bg is independent of kinematics

Comparison of These 2 Methods 34 1, by S. Tkachenko, MC method 2, by N. Baillie, Ratio method

BoNuS F 2 n 35

BoNuS F 2 n /F 2 p F 2 n /F 2 n vs. x Curves are CETQ error bands CETQ cuts off at low x because Q 2 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.

E BoNuS Plans for 12 GeV Data taking: – 35 days on D 2 – 5 days on H 2 – L = 2 x cm -2 sec -1 DIS region: – Q 2 > 1 GeV 2 – W* > 2 GeV – p s < 100 MeV/c – θ pq > 110° – x* max = 0.80 W* > 1.8 GeV: x* max = 0.83

Summary of Inclusive Analysis 38 We have measured F 2 n on a free neutron target No effects from Fermi motion and final-state interactions No evidence for off-shell structure for p s <100 MeV/c F 2 n/ F 2 p behaves at high x much like CETQ high-x fits F 2 n resonance data will significantly improve the world data set, which up to now came from d with nuclear corrections

The G2P Project at Hall A 39 My Contributions: Simulation Helped to optimize run plan Optimized the local dump and its shielding Estimate the radiation damage Concept design for the 3 rd arm Field mapping Made the optics run plan Managed the shift schedule, helped to organize meetings Measured the beam polarization with Moller Event reconstruction (Optics)

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The Geant4 Simulation Program, HRSMC 48 Designed to support all Hall HRS experiment BitBite geometry and detector included Use SANKE transport packages. HRS QQDQ field not include Used by G2P, GEP, CREX

Adjust Simulation to Match Data Working on a new SNAKE model. Courtesy to Chao Gu and Min Huang no raster

Isolate Target Field from SNAKE Model Optics models could be simplied and well known for no target field Can we isolate the target filed behavious in g2p|gep optics? 5.0 Tesla target field, the integrated BdL_y from 800 mm to beyond is only 0.01 Tesla.m, about 1.46% of the total. 50

Optics: No Target Field Vertex to Sieve: propagated by Geant4 with a physics model (i.e. MSC, Decay, Ionization, EM physics...) Sieve to Focal: project sieve to target then using SNAKE forward model, 8-10 software collimator cuts are applied along the trajectory to make sure particle is really hitting the focal plane. Focal to target: using SNAKE backward model or real optics matrix. Target to Vertex: linear projection. Jixie ZhangHRS Optics51 Target plane Vertex plane Sieve plane Virtual boundary Focal plane Snake forward Snake backward Propagated by Geant4

Optics: With Target Field Vertex to Sieve: propagated by Geant4 with a physics model Sieve to Focal: project sieve to target then using SNAKE forward model, 8-10 software collimator cuts are applied along the trajectory to make sure particle is really hitting the focal plane. Focal to Sieve: using SNAKE backward model or real optics matrix from focal to target, then project from target to sieve. Sieve to Target: using Drift-In-Field model. Target to Vertex: using Drift-In-Field model. Jixie ZhangHRS Optics52 Target plane Vertex plane Sieve plane Virtual boundary Focal plane Snake forward Snake backward Propagated by Geant4 Drift-In-Field

Resolution of HRSMC Using SNAKE Model shim, No Target Field 53 Raster=2.4cm, BPM resolution: 1 mm in vertical, No target field

Resolution of HRSMC Using SNAKE Model shim, Stop at Exact Z0,5T 54 Raster=2.4cm, BPM resolution: 1 mm in vertical, 5.0T target field Reconstruct to thrown vertex z (perfect Ytg_tr resolution)

Resolution of HRSMC Using SNAKE Model shim, Stop at Target Plane,5T 55 Raster=2.4cm, BPM resolution: 1 mm in vertical, 5.0 T target field Reconstructed to the target center

How well can we determine the central value? 56

Summary for the G2P Project We managed to accompolish most of the proposed physics goal. Detector calibration is almost done. Only BPM calibration is left over. The strategy of the reconstruction with target field is: No-Target-Filed-HRS + Drift-in-Taget-Field. This strategy works well. Geant4 simulation program for HRS is ready to use. This program can also be used for any other HRS experiements with minimum modification (just add the target geometry). There is huge difficulty to find the vertex plane (interaction plane). We can only reconstruct events back onto the target plane. That said we will not have good event by event resolution for the scattering angle. But we will be able to determine the XS central value up to 1%. 57

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Resonances predicted by Quark Model vs. experimental measurements From Full lines: tentative assignment to observed states Dashed lines: so far no observed counterparts. 59

Resonances 6 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: L 2I2J 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 + N I=0 I=1/2 Possible for both N and 60

Resonances examples 61

Jefferson Lab A B C Continuous Electron Beam Accelerator Facility E: 0.75 –6 GeV I max : 200A RF: 1499 MHz Duty Cycle: 100% (E)/E: Polarization: 85% Simultaneous distribution to 3 experimental Halls Injector LINAC Experimental Halls 62

CLAS in Jefferson Lab, Hall B 63

Radial Time Projection Chamber (RTPC) 64

Analysis Outline 1.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

Vertex Cut 66

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. 67

RTPC Gain Calibration Channel by Channel gain multipliers can be determined for each run by comparing the tracks 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 68

Energy Loss Correction for CLAS Particles Binned by measured,, z, p; Based on simulation, fit P 0 -P vs P with an integral Bethe-Bloch function for all particles Pr e P 0 -P measured (Gev/c) P measured (Gev/c) 69

Energy Loss Correction for RTPC Proton 70

Exclusive Events Selection 1.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 corrections 6.Apply 2- missing mass cut 71

Background of D(e,e` p CLAS )p, 5G Real 72 f1f1 f2f2 f3f3 f4f4

Background of D(e,e` p CLAS )p, 5G Sim. 73 f 1 sim f 2 sim f 3 sim f 4 sim

D(e,e p)p Acceptance Correction Binning information: W : 150 MeV each bin, [1.15,3.10); Q 2 : 6 bins, {0.1309, , , , , , }; 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,e p RTPC )p and D(e,e p CLAS )p reaction separately. Applied event by event Need to have acceptance cut to ensure the reliabilities For CLAS channel: and less than 10% uncertainty (> 100 detected events) For RTPC channel: and less than 15% uncertainty (> 40 detected events) 74

Acceptance Correction, E=5.3 GeV 75

Acceptance Correction, E=5.3 GeV 76

Target Thickness Calculate the effective target pressure, P eff, for a data set by weighting the pressure of each run with the number of good electrons in that run. 77

Time integrated Luminosity 78

Sim Vs Real Real 5G Simulation 5G 79

A 0 : BoNuS Vs MAID, 4 GeV with VIP cut preliminary 80

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