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Simulations of Single-Spin Asymmetries from SIDIS @ EIC

Simulations of Single-Spin Asymmetries from SIDIS @ EIC. TMD in SIDIS Simulation of SIDIS Projections. Xin Qian Kellogg, Caltech. Thanks to M. Huang, H. Gao and J.-P. Chen for slides/ dicussions Thanks to J. She, A. Prokudin and Z. B. Zhong for calculations.

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Simulations of Single-Spin Asymmetries from SIDIS @ EIC

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  1. Simulations of Single-Spin Asymmetries from SIDIS @ EIC TMD in SIDIS Simulation of SIDIS Projections XinQian Kellogg, Caltech Thanks to M. Huang, H. Gao and J.-P. Chen for slides/dicussions Thanks to J. She, A. Prokudin and Z. B. Zhong for calculations. EIC Meeting at CUA, July 29-31, 2010

  2. Leading Twist Transverse Momentum Dependent Parton Distributions (TMDs) Nucleon Spin Quark Spin h1= f1 = Boer-Mulder g1 = h1L= Helicity h1T = Transversity f1T= g1T= h1T= Sivers Pretzelosity

  3. SIDIS @ EIC Lab Frame π±, K±, D p, d, 3He e- e’ θe<90o (Trento convention) Ion-at-rest (collinear) frame

  4. Access TMDs through Semi-Inclusive DIS @ EIC f1 = Unpolarized Boer-Mulder h1= h1L= Transversity h1T = Polarized Ion Sivers f1T= Pretzelosity h1T= Polarized electron and ion g1 = g1T= SL, ST: Ion Polarization; le: electron Polarization Observables are function of x, Q2, z, PT Multi-dimension nature of SIDIS process

  5. f1, g1, h1 (Torino) EIC will greatly improve our knowledge here. Model Dependent EIC Meeting at CUA, July 29-31, 2010

  6. DIS (electron) Valence region, High Q2. • Electron: 2.5°< ϴe < 150°Pe > 1.0 GeV/c • Full azimuthal-angular coverage DIS cut: Q2 > 1 GeV2 W > 2.3 GeV 0.8 > y > 0.05 • Capability to detect high momentum electron • Q2 > 1 GeV2ϴe > 5° • No need to cover extreme forward angle for electron Incident electron

  7. SIDIS SIDIS cut: MX > 1.6 GeV 0.8 > z > 0.2 Incident electron • Low PT kinematics • PT < 1.0 GeV/c • High PT kinematics • PT > 1.0 GeV/c • Hadron: 5°< ϴhadron < 175° 0.7 GeV/c < Phadron < 10 GeV/c • Full azimuthal-angular coverage • Low momenta, large polar angular coverage

  8. Mapping of SSA (just phase space) 12 GeV --> approved SoLID SIDIS experiment Jlab E-10-006 Lower y cut, more overlap with 12 GeV 0.05 < y < 0.8

  9. Study both Proton and Neutron ion momentum z PNZ/A Not weighted by Cross section. Flavor separation, Combine the data the lowest achievable x limited by the effective neutron beam and the PT cut

  10. Cross Section in MC • Low PTcross section: • A. Bacchettahep-ph/0611265 JHEP 0702:093 (2003) • High PTcross section: • M. Anselminoet al. Eur. Phys. J. A31 (2007) 373 6x6 Jacobian calculation • PDF: CTEQ6M • FF: Binnewieset al. PRD 52 (1995) 4947 • <pt2> = 0.2 GeV2<kt2> = 0.25 GeV2 • NLO calculation at large PT • <pt2> = 0.25 GeV2 • <kt2> = 0.28 GeV2 • A factor K generated to interpolate between high and low PT • K assumed to be larger than 1 • K factor calculated to ensure the TMD calculation at PT = 0.8 GeV to get the same results as the large PT calculation at PT=1.2 GeV • VERY naïve interpolation between 0.8 and 1.2 GeV.

  11. Comparison with LEPTO/PEPSI (H. Avagyan)

  12. Projections with Proton • 11 + 60 GeV • 36 days • L = 3x1034 /cm2/s • 2x10-3 , Q2<10 GeV2 • 4x10-3 , Q2>10 GeV2 • 3 + 20 GeV • 36 days • L = 1x1034/cm2/s • 3x10-3 , Q2<10 GeV2 • 7x10-3 , Q2>10 GeV2 • Polarization 80% • Overall efficiency • 70% • z: 12 bins 0.2 - 0.8 • PT: 5 bins 0-1 GeV φh angular coverage considered Show the average of Collins/Sivers/Pretzlosity projections Still with θh <40 cut, needs to be updated for all projections. • Alsoπ-

  13. Proton π+ (z = 0.3-0.7)

  14. Proton K+ (z = 0.3-0.7)

  15. Projections with 3He (neutron) • 11 + 60 GeV • 72 days • 3 + 20 GeV • 72 days • 12 GeVSoLid • 3He: 86.5% effective polarization • Dilution factor: 3 • Equal stat. for proton and neutron (combine 3He and D) • Similar for D

  16. 3He π+ (z = 0.3-0.7)

  17. Summary of Low PT SIDIS ( PT < 1.0 GeV/c) • No need the extreme “forward” /“backward” angular coverage for electrons/hadrons • Scattered electron ~ initial electron energy • Resolution and PID at high momentum • Leading hadron momentum < 6-7 GeV/c • Good PID: kaons/pions • Large polar angular coverage • sdefines the Q2andxcoverage (Q2=x y s) • High Luminosity (large and small s) essential to achieve precise mapping of SSAs in 4-D projection • Even more demanding for high PT physics and D-meson.

  18. High PT Physics • TMD: PT << Q • Twist-3 formulism: ΛQCD << PT • Unified picture in ΛQCD << PT << Q • Ji et al. PRL 97 082002 (2006) • Asymmetries depend on the convoluted integral • Simplified in the Gaussian Ansatz. • PT weighted asymmetry EIC Meeting at CUA, July 29-31, 2010

  19. High PT kinematics High PT : hadronmomenta dramatically increase require high momentum PID, large polar angular coverage Essential to PT weighted moments. TMD vs Twist-3

  20. 10 bins 1 -- 10 GeV in log(PT) PT dependence (High PT) on p of π+

  21. Simulation • Use HERMES Tuned Pythia (From H. Avagyan, E. Aschenauer) • First try 11+60 configuration. • Physics includes: • VMD • Direct • GVMD • DIS (intrinsic charm) • Pythia is used, since lack of Dmeson fragmentation This is what we want!!

  22. Event Generator • Q2: 0.8-1500 • y: 0.2-0.8 • LUND Fragmentation. • Major decay channel of D meson are • Major contamination channel is from GVMD • 10-30% contamination, can be reduced with more sophisticated cuts. Branching ratio: 3.8+-0.07%

  23. Forward angle detection of hadrons. Wide hadron polar angular coverage Need low momentum coverage of hadrons Backgrounds?

  24. Z>0.4 Q2>2.0 Need more forward angle coverage and ability for PID (selecting π and K at a wide momentum coverage)

  25. D meson SSA (Proton) 144 Days L=3e34 1 < PT < 5 GeV; 0.05 < z < 0.8; hadronθ > 10 deg; 10 > hadron P > 0.8 GeV; Q2>1.0 GeV2; Proton Polarization 80%; efficiency 70%; angular separation ~ sqrt(2) (Sivers only); Dilution due to GVMD; Projection for Dbar meson is slightly better.

  26. Summary • Detector Requirement (SIDIS): • Not absolute essential to cover extreme angles. • Wide polar angular coverage • Wide momentum coverage with PID ability (π, K) • High PT physics • PID at high momentum • D-meson physics • Hadron PID at forward angle (initial electron direction) • Multi-dimension nature of SIDIS • High luminosity is essential for π, K and D • Large kinematics coverage (low s, and high s settings) EIC Meeting at CUA, July 29-31, 2010

  27. Backup Slides EIC Meeting at CUA, July 29-31, 2010

  28. Calculation Used • Calculation code is from Ma et al. (Peking University) • PDF: MRST 2004 • FF: Kretzer’s fit EPJC 52 (2001) 269 • Collins/Pretzelosity: She et al. PRD 79 (2009) 054008 • PT dependence: Anselminoet al. arXiv: 0807.0173 • Sivers TMD: Anselmino et al. arXiv: 0807.0166 • Collins Fragmentation function: Anselminoet al. arXiv: 0807.0173 • Pretzlosity: • Measurement of relativisticeffect (H. Avakian et al. Phys. Rev. D 78, 114024) • Direct measurement of obitalangularmomentum (Ma et al. PRD 58 09608) • Q2=10 GeV2 • s: 11 GeV + 60 GeV

  29. Here, for comparison, the angle is defined with incident ion direction at 0 deg. Compare with DIS_pions.pdf from BNL Expand hadron acceptance in the simulation to Phadron 0.1—50 GeV/c Release z, PT cut we can see similar trend

  30. D meson Asymmetry X-dependence EIC Meeting at CUA, July 29-31, 2010

  31. Projections with Proton • 11 + 60 GeV • 36 days • L = 3x1034 /cm2/s • 11 + 100 GeV • 36 days • L = 3x1034/cm2/s • For both • 2x10-3 , Q2<10 GeV2 • 4x10-3 , Q2>10 GeV2 • Polarization 80% • Overall efficiency • 70% • z: 12 bins 0.2 - 0.8 • PT: 5 bins 0-1 GeV φh angular coverage considered Show the average of Collins/Sivers/Pretzlosity projections • Alsoπ-

  32. Projections with 3He (neutron) • 11 + 60 GeV • 72 days • 11 + 100 GeV • 72 days • 12 GeVSoLid • 3He: 86.5% effective polarization • Dilution factor: 3 • Equal stat. for proton and neutron (combine 3He and D) • Similar for D

  33. Q2 & x coverage Q2=x y s sdefines how low xand how high Q2we can achieve • Electron • Forward angle, lose high-Q2 coverage • Lower momentum, lose high-x coverage

  34. Cross Section in MC • Low PT cross-section: • A. Bacchettahep-ph/0611265 JHEP 0702:093 (2007) • High PT cross-section: • M. Anselminoet al. Eur. Phys. K. A31 373 (2007) 6x6 Jacobian calculation • K factor is assumed to be larger than 1 • K factor is calculated to ensure the TMD calculation at PT = 0.8 GeV get the same results as the large PT calculation at PT=1.2 GeV • VERY naïve interpolation between 0.8 and 1.2 GeV.

  35. Comparison with H. Avagyan (JLab) • We choose thee + p --> e' + π+ + X channel as an example • Electron: 4 GeV + proton: 60 GeV • The phase space and kinematics cuts: Electron: 14°<θe<90° 0.7 GeV/c < Pe< 5 GeV/c Hadron: 40°< θhadron < 175° 0.7 GeV/c < Phadron < 10 GeV/c Full azimuthal angular coverage 10 GeV2>Q2>1 GeV2, W>2.3 GeV, 0.2<z<0.8, 0.05<y<0.8 PT < 1 GeV/c • x axis: log(x)/log(10) • y axis: the integrated cross section over the phase space of one bin, then divided by the width of the x bin • Match nicely

  36. Projections with D (neutron) • 11 + 60 GeV • 72 days • 3 + 20 GeV • 72 days • D: 88% effective polarization • Effective dilution

  37. D π+ (z = 0.3-0.7)

  38. All the following plots are based on 4x 50 energy configuration. Simulate in Phadron 0.1—50 GeV/c, θhadron 0—180 degrees Q2>1 GeV2, W>2.3 GeV, Mx>1.6 GeV, 0.05<y<0.8, 0.2<z<0.8 To study the high hadron momentum (>10 GeV/c) effects

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