1. Zhihong Ye Department of Physics, University of Virginia Study of Short Range Correlations at large x through Inclusive Electron-Nucleon Scattering Ph.D Defense Thesis Committee Members: Donal Day (Thesis Advisor) Douglas Higinbotham Bill Keene Simonetta Liuti Nilanga Liyanage

2. Outline  Understanding the Nuclear Structure  Short Range Correlations  E08-014 Experiment in Hall-A @JLab  Data Analysis  Preliminary Ratio  Summary

3.  We found what a nucleus looks like: Understanding the Nuclear Structure  Size  1 fm (10 -12 m) : > 10 4 times smaller in radius than an atom  Nucleons (proton and neutron)  quarks & gluons  Two-Body Potential  Long and medium range attraction and short range repulsive  Many-Body System + special potential  Impossible to directly solve A>12 nuclei Long-Rang Weak Attraction by exchanging pions Tensor Force Repulsive cores Two-Nucleon Interactions Central Force

4. Understanding the Nuclear Structure  Nucleons occupying separated energy shells  Magic Numbers – Very stable nuclei with certain A (=2, 8, 20, 28, …). Woods-Saxon Potential  But, we also found: Nuclear Shell Structure Can we simplify the problem? e.g., learn from electron orbiting the nucleus Two-nucleon normal distance  Nucleons don’t interact strongly; and move inside the nucleus nearly independently like free particles.

5.  Independent Particle Shell Model (Mean Field Theory): Understanding the Nuclear Structure  Nucleons move independently in an average field induced by the surrounding nucleons;

6.  Independent Particle Shell Model (Mean Field Theory): Understanding the Nuclear Structure  Nucleons move independently in an average field induced by the surrounding nucleons;  Solve each nucleon’s wave-function within the mean potential:  Occupying energy shells below Fermi Momentum (k F ) and Energy ( ε F ). No NN interaction Terms! The Mean Field

7.  Independent Particle Shell Model (Mean Field Theory): Understanding the Nuclear Structure  Nucleons move independently in an average field induced by the surrounding nucleons;  Solve each nucleon’s wave-function within the mean potential:  Occupying energy shells below Fermi Momentum (k F ) and Energy ( ε F ). No NN interaction Terms! Agree nicely with low energy proton-knock-out experiments With spin-orbital coupling, predicting nucleon bind-states, nuclear density, magic numbers, etc. Advanced theoretical calculations include long range interactions and solve the light nuclei systems (A<12). IPSM is a successful phenomenological theory:

8.  However, IPSM has limitations: Understanding the Nuclear Structure  Medium Energy Experiments found:  A nucleon’s occupation number is lower than the mean field prediction.  Proton knock-out experiments show that the nuclear strength is 30% -- 40% lower ;  Missing NN interaction: Medium-Range attraction, Short-Distance Repulsion.  Nuclear magnet moments.  Highly Excitation States  High Density Nuclear Matter Nucleon Occupation Number Ratio L. Lapikas, Nuclear Physics A 553, 297 (1993)

9. Nucleons can stay at closer distance (<1 fm): Strong attraction and repulsion Nucleons can carry much higher momenta: Exceed the limit of IPSM – k>k F Zero total momentum: A real ground state, not an excited state. Break-up these correlated nucleons: Detect a nucleon with much higher momentum; Short Range Correlations Mean Field Prediction The missing strength C. Ciofi degli Atti, et al, PRC 53 1689 (1996) Momentum distribution:  All possible momentum values that nucleons carry inside the nucleus.  Features of SRC: Momentum Distribution

10. Nucleons can stay at closer distance (<1 fm): Strong attraction and repulsion Nucleons can carry much higher momenta: Exceed the limit of IPSM – k>k F Zero total momentum: A real ground state, not a excited state. Break-up these correlated nucleons: Detect a nucleon with much higher momentum; Short Range Correlations SRCs MFT Nucleon Occupation Number Ratio L. Lapiks, Nuclear Physics A 553, 297 (1993)  Features of SRC:

11. p p p p n n 1.7 fm < 1.0 fm p p p p n n 2N-SRC 3N-SRC Short Range Correlations C. Ciofi degli Atti and S. Simula, Phys. Rev. C 53 (1996). SRCs MFT k fermi 2N-SRC and 3N-SRC in heavy nuclei: similar to 2 D and 3 He. Similar shape for High momentum tails: scaling behavior at k>kF Extremely high density configurations: connect to EMC effect, Neutron Stars, quark degrees of freedom, etc. Involve 2-nucleons (2N-SRC), and 3-nucleons (3N-SRC) and more; Mean Field 2N-SRC 3N-SRC … Momentum Distribution

12.  Features of SRC: Short Range Correlations Back-to-Back ejection when breaking 2N-SRC R. Shneor et al, PRL 99 072501 (2007) Using A(e,e’pN)A-2 reaction in Hall-A, JLab Using A(p, p’pN)A-2 reaction at BNL A. Tang et al, PRL 90 042301 (2003) cosγ : Opening angle between the direction of two ejected nucleons

13. r  Isospin Dependence: Short Range Correlations Nucleons interact thought exchanging one pion: Parity = 1  lowest state, L= 0, S = 1/2 +1/2 =1. The attractive force at <1 fm is from the tensor component: Proton and Neutron carry different isospin (T): Proton  T= 1/2, Neutron  T= -1/2 Isospin Singlet: T = 0, n-p pairs Isospin Triplet: T = 1, p-p (T z =1), n-p (T z =0), and n-n (T z =-1) p p p p n n n n ==0  Repulsive = -3 σ 1 σ 2  Attractive Stable! due to Pauli Principle So the nature of the attractive tensor force favor the n-p pairs! = σ 1 σ 2 >0  Always repulsive

14.  Isospin Dependence: Short Range Correlations Theoretical calculation shows n-p pairs have stronger strength. Experiment discovered that np pairs are 90% in 2N-SRC R. Subedi, et al, Science 320 1476 (2008) R. Schiavilla, et al, PRL 98 132501 (2007) First JLab publication in Science!

15.  Electron-Nucleus Scattering:  An electron interacts via exchanging a virtual photon: Well known electromagnetic process (by QED).  Important quantities: Inclusive Quasielastic Scattering Benhar, Day, Sick, Rev. Mod. Phys. 80, 189 (2008) Momentum fraction of a nucleon shared by the struck quark. Four Momentum Transfer of the virtual photon.  Three processes  Three type of D.O.F. Elastic: Interact with the whole nucleus, Quaselastic: Interact with a nucleon moving inside the nucleus Inelastic: Interact with components inside a nucleon

16.  Inclusive Cross Sections:  At Quasielastic (QE) Region, the Inclusive Cross Section: Inclusive Quasielastic Scattering  Cross Sections: the probabilities of the reaction in a unit phase space (Energy & Angle).  Inclusive Measurement: Only detect the scattered electrons scattering. accounting for all electron-nucleon reactions e e’ Target (nucleus, nucleon, quark) (dE’, d Ω )  y-Scaling: y  the minimum momentum of the nucleon  Momentum Distribution of a nucleon inside a nucleus: F(y)  very small dependence on Q 2. One of two essential bulk properties of a nucleon inside the nucleus Spectral Function  Link to the nuclear structure Integral

17.  The inclusive cross section in SRC:  k>k F for x bj >1.3, so QE electron-nucleus scattering probes SRC: 2N-SRC (1.3<x bj <2) 3N-SRC (2<x bj <3)  Ratio: One nucleon:. Two nucleons:. Three nucleons: QE Scattering Study on SRC  In the definition of x bj, a quark must share the momentum from: a j (A) ---the probability of a nucleon in a jN-SRC. σ j (A) --- the cross section of an electron scattering on a nucleon in jN-SRC. a 2 and a 3 are independent of x bj and Q 2, but only depend on A  Scaling plateau

18. Frankfurt, Strikman, Day, Sargsian, PRC48, 2451 (1993) K. Egiyan et al, PRL96, 082501 (2006) CLAS & E02-019 results:  Agreement for xbj <2 region  Different onset values for 3N plateau  CLAS: Q 2 ≈ 1.6 GeV 2, E02-019: Q 2 ≈ 2.7 GeV 2  Large error bars at 3N-SRCs for E02-019 N. Fomin et al, PRL 108,092502 (2012)  Previous results: QE Scattering Study on SRC

19.  Final State Interactions:  Re-scattering of the struck nucleon: The final state is modified by the A-1 system.  Alter the inclusive cross section. y-Scaling violates in FSI.  Proportional to 1/Q 2 (fast reaction): small effect at larger Q 2 (>1 GeV 2 ) but not vanish!  FSI in SRC:  Still have significant effect when scattering on a nucleon in SRC.  However, FSI is dominated by that with the SRC pairs  Small effects outside the SRC.  FSI is expected to be cancelled in the ratio.  Still need more careful experimental studies. QE Scattering Study on SRC

20.  Connection? SRC vs. EMC EMC Effect:  A nucleon has different structures placed in different nuclei. “slope” in EMC:  how difference a nucleon in a nucleus compared with one in the Deuterium. J.Seely, et al., PRL 103, 202301 (2009) D. Gaskel, E03103 Hall-C a 2 in SRC:  Probability of two nucleons to be correlated. slope a2

21.  Linear correlation! L. Weinstein et al, PRL 106, 052301 (2011) J. Arrington et al., PRC 86, 065204 (2012) O. Hen et al, PRC 85, 047301 (2012) D.O.F: Nucleus  Nucleon  Quarks & Gluons ? Data contributed by JLab: Egiyan, et al. (2006 PRL, Hall B) J. Seely, et al. (2009, Hall C) N. Fomin, et al. (2012, Hall C) And SLAC data SRC vs. EMC slope EMC: 0.3<xbj<0.7  How quarks&gluons form nucleons. SRC: xbj > 1.3  How nucleons form nuclei. Understanding how EMC connects to SRCs will be one of the major studies in 12 GeV.

22.  Hall-A: (Tritium experiments)  Hall-C: E12-11-112: Precision Measurement of the Isospin Dependence in the 2N- and 3N-SRC region. Spokespersons: J. Arrington, D. Day, D. Higinbotham, P. Solvignon E12-10-103: Measurement of the F2n/F2p, d/u Ratios and A=3 EMC effect in Deep Inelastic Scattering off the Tritium and Helium Mirror Nuclei. Spokespersons: J. Annand, G. Petratos, J. Holt, J. Gomez, R. Ransome E12-06-105: Inclusive Scattering for Nuclei at x>1 in the Quasielastic and deeply inelastic regimes. Spokespersons: J. Arrington, D. Day,.N. Fomin, P. Solviginon E12-10-008: Detailed studies of the nuclear dependence of F2 in light nuclei. Spokespersons: J. Arrington, A. Daniel, D. Gaskell E12-11-107: In Medium Nucleon Structure Functions, SRC, and the EMC Effect. Spokespersons: O. Hen, L. Weinstein, S. Gilad, S. Woods E12-10-003: W. Boeglin, M. Jones; E12-06-107: D. Dutta. R. Ent. etc… SRC vs. EMC  New SRC & EMC Experiments at JLab:

23.  Measuring inclusive cross sections (y-Scaling, momentum distribution, FSI etc).  Studying the onset of 3N-SRC scaling plateau at x>2;  Isospin effect at SRCs (Ca40 & Ca48)  Theory assumes Isospin-Independent in inclusive measurement: 25% difference E08-014 Experiment in Hall-A@JLab  From recent theoretical calculation: M. Vanhalst, et. al., PRC 84, 031302 (2011), PRC 86, 044619 (2012)  New experiment  E12-11-112 using H3/He3: 40% difference  For 2N-SRC, n-p (T=0) pairs dominate: 8.7% difference

24. E08-014 Experiment in Hall-A@JLab HRS-L HRS-R Beam Line Target Detector Huts Hall-A

25. E08-014 Experiment in Hall-A@JLab HRS-L HRS-R Beam Line Target Detector Huts Hall-A e (3.356 GeV) e’ We choose a portion of scattered electrons by setting HRS’s accepted angle and momentum range. e’

26. E08-014 Experiment in Hall-A@JLab HRS-L HRS-R Beam Line Target Detector Huts Hall-A e (3.356 GeV) e’ We choose a portion of scattered electrons by setting HRS’s accepted angle and momentum range. e’ Angle & Position Energy Time & Speed

27. E08-014 Experiment in Hall-A@JLab  Configurations: Un-polarized Electron Beam; Two HRSs taking data Simultaneously; Standard Setup.  Modified Triggers: T1&T3: S1.and. S2m.and. GC, main production triggers.  Targets: Cryo-Targets: LH2, He3, He4 Solid Targets : C12, Ca40, Ca48, and other calibration targets. Kin3.1 Kin3.2 Kin4.1 Kin4.2 Kin5.1 Kin5.2 Kin5.0 Kin6.5 Kin5.05 E0 = 3.356GeV  Kinematic Coverage: E0: 3.356 GeV Ep: 2. 505 – 3.055 GeV/c Central Angle: 21 0, 23 0, 25 0 and 28 0  Data taken in Spring 2011.

28. The flow-chart to extract inclusive cross sections: Initial Raw Data Reply Beam Calibration (BCM, BPM, Raster) Beam Calibration (BCM, BPM, Raster) Detector Calibration (VDC, Scin, GC, Calo) Detector Calibration (VDC, Scin, GC, Calo) Optics Calibration PID Cuts Study Detectors’ Efficiencies Detectors’ Efficiencies Final Raw Data Reply Several Raw Data Reply Target Density (Boiling, Thickness) Target Density (Boiling, Thickness) Live Time Kinematics Settings Electron Charge Cuts Binning Yield_EX Monte Carlo Simulation (SAMC) Wider Acceptance than HRSs Non Uniform Cryo-Target Correction Reconstructed DeltaP Correction Reconstructed DeltaP Correction Cross Section Model (XEMC) σ DIS F1F2IN09 σ QE F(y) Radiation Correction Cuts Binning σ Born σ Radiated Target Luminosity Yield_MC Other Corrections Iterating Cross Section Models Efficiencies E08-014 Data Analysis Experimental Data Analysis Ratio

29. The flow-chart to extract inclusive cross sections: Initial Raw Data Reply Beam Calibration (BCM, BPM, Raster) Beam Calibration (BCM, BPM, Raster) Detector Calibration (VDC, Scin, GC, Calo) Detector Calibration (VDC, Scin, GC, Calo) Optics Calibration PID Cuts Study Detectors’ Efficiencies Detectors’ Efficiencies Final Raw Data Reply Several Raw Data Reply Target Density (Boiling, Thickness) Target Density (Boiling, Thickness) Live Time Kinematics Settings Electron Charge Cuts Binning Yield_EX Monte Carlo Simulation (SAMC) Wider Acceptance than HRSs Non Uniform Cryo-Target Correction Reconstructed DeltaP Correction Reconstructed DeltaP Correction Cross Section Model (XEMC) σ DIS F1F2IN09 σ QE F(y) Radiation Correction Cuts Binning σ Born σ Radiated Target Luminosity Yield_MC Other Corrections Iterating Cross Section Models Efficiencies E08-014 Data Analysis Experimental Data Analysis Ratio

30. The flow-chart to extract inclusive cross sections: (in few words) E08-014 Data Analysis 1, What do we need?  Inclusive Cross Section (XS) with <5% errors (hint): XS in Unit Angle and Unit Momentum = # Events happened in Unit Angle and Unit Momentum at the target. / # electrons we shoot / # nuclei we shoot at;

31. The flow-chart to extract inclusive cross sections: (in few words) E08-014 Data Analysis 1, What do we need?  Inclusive Cross Section (XS) with <5% errors (hint): XS in Unit Angle and Unit Momentum = # Events happened in Unit Angle and Unit Momentum at the target. / # electrons we shoot / # nuclei we shoot at; 2, (a) How many electrons we shoot?  The electron charge from beam (easy) (b) How many nuclei we shoot at?  Target density and their boiling effects. (tough) (c) How many events happened at the reaction point? (hard)

32. The flow-chart to extract inclusive cross sections: (in few words) E08-014 Data Analysis 1, What do we need?  Inclusive Cross Section (XS) with <5% errors (hint): XS in Unit Angle and Unit Momentum = # Events happened in Unit Angle and Unit Momentum at the target. / # electrons we shoot / # nuclei we shoot at; 2, (a) How many electrons we shoot?  The electron charge from beam (easy) (b) How many nuclei we shoot at?  Target density and their boiling effects. (tough) (c) How many events happened at the reaction point? (hard) (c1) What is the percentage of events our detectors can measure? Efficiencies (c2) How to know what happens in the target? HRS Optics Reconstruction (c3) Are these events are all electrons? Particle Identification. (c4) Do we group and count the events in the right way? We can not do the “unit” ones Cross Section Models and Monte Carlo Simulation

33. The flow-chart to extract inclusive cross sections: (in few words) E08-014 Data Analysis 1, What do we need?  Inclusive Cross Section (XS) with <5% errors (hint): XS in Unit Angle and Unit Momentum = # Events happened in Unit Angle and Unit Momentum at the target. / # electrons we shoot / # nuclei we shoot at; 2, (a) How many electrons we shoot?  The electron charge from beam (easy) (b) How many nuclei we shoot at?  Target density and their boiling effects. (tough) (c) How many events happened at the reaction point? (hard) (c1) What is the percentage of events our detectors can measure? Efficiencies (c2) How to know what happens in the target? HRS Optics Reconstruction (c3) Are these events are all electrons? Particle Identification. (c4) Do we group and count the events in the right way? We can not do the “unit” ones Cross Section Models and Monte Carlo Simulation #1 #2 #3 Talked next …

34. E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Focal Plane Target Plane Q1 Q2 Dipole Q3  Optics Calibration: Detectors Magnetic “Optics” Target Plane  Object Focal Plane  Image (see by VDC) Quadruple  Lens Dipole  Prism Detectors  Are you a candle? Optics reconstruction  predict where the object is and how it looks like The “image” is different from the “object”.  Like digital camera record “current” instead of “color”. Need reconstruction!

35. E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Ideally Focal Plane Target Plane Practically Dipole  Optics Calibration: An optics calibration procedure is to obtain the parameters in the polynomial functions. Detectors Q1 Q2 Q3 Dipole

36. E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Ideally Focal Plane Target Plane Sieve Slit Practically  Optics Calibration: An optics calibration procedure is to obtain the parameters in the polynomial functions. Calibration Data: Unrastered Beam, QE region, 7-foil carbon targets, Sieve Slit Plate; & Survey reports. Detectors 7-foil target  y tg is known in each foil. Sieve slit plate  The angle ( θ tg & φ tg ) from the target to each hole is known. Elastic peak  Changing δ p and see how the peak moves (should be at xbj=1). Q1 Q2 Dipole Q3

37. E08-014 Data Analysis - Optics Old optics matrix on HRS-R doesn’t work anymore. Need a complete new matrix! Reconstructed with original optics: RQ3 is not focused  blur “pictures”! Target Vertex Sieve Slit Pattern  Optics Calibration - RHRS: Scaled down Q3 field by 87.72% for each HRS central momentum setting.

38. E08-014 Data Analysis - Optics Old optics matrix on HRS-R doesn’t work anymore. Need a complete new matrix! Target Vertex Sieve Slit Pattern  Optics Calibration - RHRS: Scaled down Q3 field by 87.72% for each HRS central momentum setting. Reconstructed with new optics: RQ3 is not focused  shape “pictures”!

39.  Why need a cross section model?  A Cross Section Model = Theory + Experiment Data Fitting + Corrections  Should produce roughly close results to the new data, but not predict anything!  Useful for Acceptance Study, Bin-Centering Correction and Radiative Correction, etc. E08-014 Data Analysis - XEMC E’ (or θ 0 ) Bin-Centering Effect:  We bin the data along E’ (and/or θ 0 ), calculate the average cross section over this bin, but assign the value to the center of the bin but not the “mean” center. Event Distribution E min E max E’ 1 E’ 2 E’ 3 Bin CenterStatistical Center Correction: B = σ 2 /σ 1 σ 1  Average σ 2  True Note: For electron, E’ ≈ P

40.  Cross Section Package - XEMC: Quasi-Elastic Cross Section: (1), XEM -- F(y) Function, from Hall-C EMC&X>1 collaboration (from D. Gaskell, N. Fomin, etc.). Converted into C++. Parameters are updated by fitting data from E02-019 (2), QFS -- From Temple Univ. group (K. Slifer, D. Flay, H. Yao, etc.); (3), F1F2QE09 -- P. Bosted and V. Mamyan In FORTRAN – f1f209.f (arXiv:1203.2262v2). Inelastic Cross Section: (a), XEM - F1F2IN06 (P. Bosted & E. Christy) + special corrections in different regions (b), QFS - DIS + Delta + Resonances + DIP (c), F1F2IN09 - P. Bosted and V. Mamyan – f1f209.f Born Cross Section Models: Several Born Cross Section Models coded; Radiative Correction Subroutines; Stand-alone subroutines in C++, easily called by other codes; (Tech note is available). E08-014 Data Analysis - XEMC In E08-014 analysis, XEM + F1F2IN09 was used

41.  Comparing with E02-019 data from Hall-C: He3 Red dots -> Exp. Blue dots -> XEMC C12 E08-014 Data Analysis - XEMC D2 He4

42.  Radiative Correction: E08-014 Data Analysis - XEMC What we measure is not what it really should be, since: 1, Incoming electrons lose energies before hitting on the nuclei. Bremsstrahlung Radiation, Ionization, etc. 2, Scattered electrons lose energies before getting out from the target. The measured value is called the radiated cross section, needed corrections to get the Born cross section before compared with theory.

43.  Radiative Correction:  Basic Idea: Mo&Tsai Rev. Mod. Phys. 41. 205 (1969), S. Stein et al, Phy. Rev. D 12 1884 (1975)  Old XEM code has a Radiative Correction subroutine with full radiation tail integrals (but in FORTRAN, specified for x<1, and runs very slow).  Peaking-Approximation method based on subroutines from RadCor package (from Temple Univ.). NEED Plots here!!! E08-014 Data Analysis - XEMC Comparing with E02-019 Radiated Cross Sections He3C12

44.  Well organized packages in C++.  Standard HRS configurations. HRS Acceptance is simulated by Transportation functions generated by SNAKE.  Updated HRS-R Transportation Functions for RQ3 with mistuning field.  Cross Section Model embedded (QFS, XEMC etc).  Special correction on cryo-target bumps has been added: Embed the non-uniform target density distributions. E08-014 Data Analysis - SAMC  Monte Carlo Simulation-SAMC (Courtesy to A. Deur and H. Yao)  Hall-A Single-Arm Monte Carlo simulation tool:  A similar “experiment” running on a computer  Directly compare with real data. An experiment is so complicated, and we may not understand (or measure) everything!

45. E08-014 Data Analysis - SAMC  Acceptance Effect:  Particles going in the HRS may not come out and be detected by the detectors:  Need MC simulation to evaluate the percentage, a.k.a., the Acceptance Correction. Spectrometer Acceptance Effect: Edge Smearing The effect can be reduced by applying tight cuts but can not be removed completely.

46. HRS-L Blue -> Simulation Data Red -> E08-014 Data C12 Target Plane Quantities: HRS-R  Monte Carlo Simulation-SAMC E08-014 Data Analysis - SAMC Histograms are weighted by Cross Sections from XEMC Small y tg offset for foil-target  no big deal!

47. Blue -> Simulation Data Red -> E08-014 Data Cryogenic Target “Bump” is simulated. Histograms are weighted by Cross Sections from XEMC He3 Target Plane Quantities:  Monte Carlo Simulation-SAMC E08-014 Data Analysis - SAMC

48.  Cryo-Target Density Uniformity Cryogenic coolant distributes along 20 cm cells; Non-uniform target density on H2, He3 and He4 targets; Higher current, bigger effect (bumps!). Problems: Hard to evaluate target luminosity; Complicated boiling effect correction; Complicated radiative corrections. 20 cm Cryogenic flow Beam E08-014 Data Analysis - Target Warmer! For LH2 (20 K), He3 (22 K), and He4 (19 K)

49. E08-014 Data Analysis - Target Running a simulation of the cryogenic target system for LH2, He3 and He4. Courtesy to Silviu Covrig in Jlab Target Group LD2 Density in the cell  Cryo-Target Density Uniformity – Proved by simulation

50.  Boiling Effect Study:  Taking data with different currents.  Calculating yields and correlating them with currents. Fitting the slops and constants for both arm.  Distribution of Y 0 denotes the relative density distribution.  Binning VZ into 60 bin and fitting the boiling factors in each bin. E08-014 Data Analysis - Target

51.  Boiling Effect Study: E08-014 Data Analysis - Target Relative Target Density Distribution Boiling Factors  Taking data with different currents.  Calculating yields and correlating them with currents. Fitting the slops and constants for both arm.  Distribution of Y 0 denotes the relative density distribution.  Binning VZ into 60 bin and fitting the boiling factors in each bin.

52. Extracting Cross Sections  Experimental differential cross section:  Typical Formula to extract experimental (radiated) cross section: A  Acceptance Correction, B  Bin-Centering Correction, RC  Radiative Correction. (binning in E’)

53.  Experimental Yield: -- Total events in ith bin; -- Total electron charge; -- Total Detectors’ efficiencies.  Monte Carlo Yield: -- Total target luminosity; -- Total generated MC events; - Entire phase space in MC (slight larger than HRS) - Radiated Cross Section Sum of all events in each bin Extracting Cross Sections  Experimental differential cross section:  Typical Formula to extract experimental (radiated) cross section:  We re-arrange the terms: A  Acceptance Correction, B  Bin-Centering Correction, RC  Radiative Correction. (binning in E’)

54.  Advantages of Yield Ratio: Studying the acceptance effect; Checking the differences of data between two HRSs before combining them; Experimental Yields remain untouched, but only to apply correction to MC Yield and iterate the XEMC model until the ratio gets close to one; Reducing model dependence. Extracting Cross Sections  Experimental differential cross section:

55. Extracting Cross Sections 21 0 23 0 25 0 Yield Ratio  Y EX /Y MC Preliminary  Preliminary Cross Section Results: (He3)

56. Extracting Cross Sections 21 0 23 0 25 0 Preliminary  Preliminary Cross Section Results: (He4) Yield Ratio  Y EX /Y MC

57. Extracting Cross Sections  Preliminary Cross Section Results: (C12) 21 0 23 0 25 0 Yield Ratio  Y EX /Y MC Preliminary

58. Extracting Cross Sections  Preliminary Cross Section Results: (Ca40 & Ca48)  First High-Q2 cross section for Ca40&Ca48; Need more work on the cross section model. Preliminary

59. Preliminary Ratio  C12/H2 Ratio : Preliminary Statistical Errors only

60. Preliminary Ratio E08-014 agrees with E02-019 but shows more FSI effects.  C12/He3 Ratio (Comparing with E02-019 ): Preliminary Statistical Errors only

61. Preliminary Ratio  He4/He3 Ratio (Compared with CLAS E02-019 ): No 3N-SRC Plateau?  Can’t conclude yet! Need to check radiative corrections and the He3 Cross Section Model. Preliminary Statistical Errors only

62. Preliminary Ratio Preliminary  Ca48/Ca40 Ratio: Need more work on iterating the cross section models and radiative corrections. Simply Isospin dependence prediction Theory prediction Isospin Independent assumption Statistical Errors only

63. Summary  Nuclear Structure can be well modeled by Shell Model, but not 100%.  SRCs attribute to the 30% - 40% missing strength in nuclei, predicted by Mean Field Theory  Studies of SRC and EMC help us to understand the nucleus  nucleon  quarks D.O.F..  Inclusive QE electron scattering provides a clean tool to probe 2N-SRC, 3N-SRC.  E08014 aims to verify the onset of 3N-SRC at x>2 and study isospin dependence with Ca40 and Ca48.  Data analysis is nearly completed and preliminary results are available.  SRC and EMC are important topics in the next decade.

64. Summary  Nuclear Structure can be well modeled by Shell Model, but not 100%.  SRCs attribute to the 30% - 40% missing strength in nuclei, predicted by Mean Field Theory  Studies of SRC and EMC help us to understand the nucleus  nucleon  quarks D.O.F..  Inclusive QE electron scattering provides a clean tool to probe 2N-SRC, 3N-SRC.  E08014 aims to verify the onset of 3N-SRC at x>2 and study isospin dependence with Ca40 and Ca48.  Data analysis is nearly completed and preliminary results are available.  SRC and EMC are important topics in the next decade. Thank you for your time!

65. Backup Slides

66.  How to cleanly probe SRC:  Isolate QES:  above the broad QE peak (x bj >1.3 )  Suppress FSI and MEC:  Q 2 >1 GeV 2  Remove Mean Field contributions  only detect struck nucleon with large momentum (k>k Fermi ).  Isolate SRC:  large momentum transfer (q 0 >>V NN, q>>m N /c ) to instantly remove SRCs from intact nucleus;  Sufficiently high x bj and Q 2 to detect nucleons with minimum momenta. QE Scattering Study on SRC

67. e/π>10 4 Total Pion Suppression after Calo & Cer: 99.85% Electrons Survive after Calo & Cer: 99.58% HRS-L d),PID Study Cuts: L.prl2.e>=100. && E/P >=0.5&& L.cer.asum_c>=50.

68. Total Pion Suppression after Calo & Cer: 99.62% Electrons Survive after Calo & Cer: 99.86% HRS-R d),PID Study Cuts: R.sh.e>=200. && E/P >=0.5 && R.cer.asum_c>=50. e/π>10 4

69.  DeltaP Correction for HRS-R Data: (with SAMC data) E08-014 Data Analysis -DeltaP Q1+Q2+D+Q3 HRS SNAKE Target Plane  Focal Plane: Magnet Field Forward Transportation Polynomials (F) Target Plane  Focal Plane: Optics Matrix Backward Transportation Polynomials (B) F(Q1) F(Q2) F(D) F(Q3) B(Q1) B(Q2) B(D) B(Q3) Case #1: DeltaP is reconstructed incorrectly, ( δ p wrong ), similar to real data if D-matrix is not calibrated. Target PlaneFocal Plane F(Q3) B(Q3) F(Q3) B(Q3) 100% 87.72% F(Q1) F(Q2) F(D) F(Q3) B(Q1) B(Q2) B(D) B(Q3) Case #2: DeltaP is reconstructed correctly, ( δ p right ), similar to the real data if D-matrix is calibrated DeltaP in SAMC: Field Setting

70. higher order residuals  Same event seeds at the target, Correcting data by defining the polynomial correction function: E08-014 Data Analysis -DeltaP 70  DeltaP Correction for HRS-R Data: (with SAMC data)

71. E08-014 Data Analysis -DeltaP 71  DeltaP Correction for HRS-R Data: (with SAMC data)  Fitting the correction function by correlating with focal plane variables:.vs. x fp.vs. θ fp δp right - δp wrong 2-D Profile-Y Residual.vs. y fp.vs. ϕ fp.vs. δp old δp right - δp wrong 2-D Profile-Y Residual  From MC data, the correction function can recover DeltaP reconstruction as good as near 0.03%. higher order residuals  Same event seeds at the target, Correcting data by defining the polynomial correction function:

72.  DeltaP Correction for HRS-R Data: (with real data) E08-014 Data Analysis -DeltaP  Applying the correction function to experimental data 72  Conclusions: 1, HRS optics with distorted Q3 field still can be extracted (need a good optics run plan); 2, Gaining additional Yields due to Q3 enlarging the acceptances (Q3 -13%  +5% Yield); 3, Pay attention to the acceptance effect.

73. He3 Red dots -> Exp. Blue dots -> XEMC C12 E08-014 Data Analysis - XEMC D2 He4  Comparing with data from QE-Archive: (D. Day, Rev. Mod. Phys. 80, 189-224, 2008)

74. In Real Data: Z react (Vertex Z) distribution includes the density distribution and the acceptance effects. In MC Data: Assuming the target density is uniform, Z react (Vertex Z) distribution includes only the acceptance effects.  Extracting the density distribution from data: E08-014 Data Analysis - Target

75. In Real Data: Z react (Vertex Z) distribution includes the density distribution and the acceptance effects. In MC Data: Assuming the target density is uniform, Z react (Vertex Z) distribution includes only the acceptance effects.  Extracting the density distribution from data: E08-014 Data Analysis - Target Relative density distribution can be correctly extracted. However, need to know the absolute density at the entrance using the temperature and pressure reading. May have to normalize the deviation using 2N-SRC ratio of C12 and Cryo-targets.

76. 1, Radiation Length is calculated at the center of the target with uniform density. 2, For non-uniform targets, Radiative Correction (RC) is different from different reaction locations and paths. 3, Binning on VZ, calculating RC in each location and weighting the total RC by the density profile). RC depends on the location of reactions.  Radiative Correction with Non-Uniform Target: E08-014 Data Analysis - Target

77. Extracting Cross Sections  Event Selection & Efficiencies  VDC One-Track-Only Cuts (> 99%);  Trigger Cuts (>99% since GC included);  PID Cuts (very loose cuts, 99% for GC, 99% for Calo);  Focal Plane Variables Cuts (removing big-angle events);  20cm Cryo-Target End-Cup Cuts: No end-cup subtraction since using long 20cm target cell and good optics reconstruction.  Target Plane Acceptance Cuts: (using very tight cuts, will open up when other effects are cleaned);  Beam Trip Cuts: Removing events taken during beam trip.  Errors  Statistic Errors and Systematic Errors from Detectors are included;  Final evaluation of Total Errors will be proceeded.