Simulations of Single-Spin Asymmetries from EIC Xin Qian Kellogg, Caltech EIC Meeting at CUA, July 29-31, TMD in SIDIS 2.Simulation of SIDIS 3.Projections 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.

Leading Twist Transverse Momentum Dependent Parton Distributions (TMDs) f 1T  = f 1 = g 1 = g 1T  = h 1L  = h1 =h1 = h 1T = h 1T  = Transversity Boer-Mulder Pretzelosity Sivers Helicity Nucleon Spin Quark Spin

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

Access TMDs through Semi-Inclusive EIC Unpolarized Polarized Ion Polarized electron and ion Boer-Mulder Sivers Transversity Pretzelosity f 1 = f 1T  = g 1 = g 1T  = h1 =h1 = h 1L  = h 1T  = h 1T = S L, S T : Ion Polarization; e : electron Polarization Observables are function of x, Q 2, z, P T Multi-dimension nature of SIDIS process

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

DIS (electron)  Electron: 2.5° 1.0 GeV/c  Full azimuthal-angular coverage DIS cut: Q 2 > 1 GeV 2 W > 2.3 GeV 0.8 > y > 0.05 Capability to detect high momentum electron Q 2 > 1 GeV 2 ϴ e > 5° No need to cover extreme forward angle for electron Incident electron Valence region, High Q 2.

SIDIS  Hadron: 5°< ϴ hadron < 175° 0.7 GeV/c < P hadron < 10 GeV/c  Full azimuthal-angular coverage  Low momenta, large polar angular coverage SIDIS cut: M X > 1.6 GeV 0.8 > z > 0.2 Low P T kinematics P T < 1.0 GeV/c High P T kinematics P T > 1.0 GeV/c Incident electron

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

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

Cross Section in MC Low P T cross section: – A. Bacchetta hep-ph/ JHEP 0702:093 (2003) High P T cross section: – M. Anselmino et al. Eur. Phys. J. A31 (2007) 373 PDF: CTEQ6M FF: Binnewies et al. PRD 52 (1995) 4947 = 0.2 GeV 2 = 0.25 GeV 2 NLO calculation at large PT – = 0.25 GeV 2 – = 0.28 GeV 2 – A factor K generated to interpolate between high and low P T 6x6 Jacobian calculation 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.

Comparison with LEPTO/PEPSI (H. Avagyan)

Projections with Proton GeV 36 days L = 3x10 34 /cm 2 /s 2x10 -3, Q 2 <10 GeV 2 4x10 -3, Q 2 >10 GeV GeV 36 days L = 1x10 34 /cm 2 /s 3x10 -3, Q 2 <10 GeV 2 7x10 -3, Q 2 >10 GeV 2 Polarization 80% Overall efficiency 70% z: 12 bins P T : 5 bins 0-1 GeV φ h angular coverage considered Show the average of Collins/Sivers/Pretzlosity projections Still with θ h <40 cut, needs to be updated for all projections. Also π -

Proton π + (z = )

Proton K + (z = )

Projections with 3 He (neutron) GeV 72 days GeV 72 days 12 GeV SoLid 3 He : 86.5% effective polarization Dilution factor: 3 Equal stat. for proton and neutron (combine 3 He and D) Similar for D GeV GeV P36 d (3x10 34 /cm 2 /s)36 d (1x10 34 /cm 2 /s) D72 d 3 He72 d

3 He π + (z = )

Summary of Low P T SIDIS ( P T < 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 s defines the Q 2 and x coverage (Q 2 =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 P T physics and D- meson.

High P T Physics TMD: P T << Q Twist-3 formulism: Λ QCD << P T Unified picture in Λ QCD << P T << Q – Ji et al. PRL (2006) Asymmetries depend on the convoluted integral Simplified in the Gaussian Ansatz. P T weighted asymmetry EIC Meeting at CUA, July 29-31, 2010

High P T kinematics High P T : hadron momenta dramatically increase require high momentum PID, large polar angular coverage Essential to P T weighted moments. TMD vs Twist-3

P T dependence (High P T ) on p of π + 10 bins GeV in log(P T )

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

Event Generator Q 2 : y: 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: %

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

Z>0.4 Q 2 >2.0 Need more forward angle coverage and ability for PID (selecting π and K at a wide momentum coverage)

D meson SSA (Proton) 144 Days L=3e deg; 10 > hadron P > 0.8 GeV; Q 2 >1.0 GeV 2 ; Proton Polarization 80%; efficiency 70%; angular separation ~ sqrt(2) (Sivers only); Dilution due to GVMD; Projection for Dbar meson is slightly better.

Summary Detector Requirement (SIDIS): – Not absolute essential to cover extreme angles. – Wide polar angular coverage – Wide momentum coverage with PID ability (π, K) High P T 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

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

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) P T dependence: Anselmino et al. arXiv: – Sivers TMD: Anselmino et al. arXiv: – Collins Fragmentation function: Anselmino et al. arXiv: Pretzlosity: – Measurement of relativistic effect (H. Avakian et al. Phys. Rev. D 78, ) – Direct measurement of obital angular momentum (Ma et al. PRD ) Q 2 =10 GeV 2 s: 11 GeV + 60 GeV

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

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

Projections with Proton GeV 36 days L = 3x10 34 /cm 2 /s GeV 36 days L = 3x10 34 /cm 2 /s For both 2x10 -3, Q 2 <10 GeV 2 4x10 -3, Q 2 >10 GeV 2 Polarization 80% Overall efficiency 70% z: 12 bins P T : 5 bins 0-1 GeV φ h angular coverage considered Show the average of Collins/Sivers/Pretzlosity projections Also π -

Projections with 3 He (neutron) GeV 72 days GeV 72 days 12 GeV SoLid 3 He : 86.5% effective polarization Dilution factor: 3 Equal stat. for proton and neutron (combine 3 He and D) Similar for D GeV GeV P36 d (3x10 34 /cm 2 /s) D72 d 3 He72 d

Q 2 & x coverage Q 2 =x y s s defines how low x and how high Q 2 we can achieve Electron Forward angle, lose high-Q 2 coverage Lower momentum, lose high-x coverage

Cross Section in MC Low PT cross-section: – A. Bacchetta hep-ph/ JHEP 0702:093 (2007) High PT cross-section: – M. Anselmino et al. Eur. Phys. K. A (2007) 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. 6x6 Jacobian calculation

Comparison with H. Avagyan (JLab) We choose the e + p --> e' + π + + X channel as an example Electron: 4 GeV + proton: 60 GeV The phase space and kinematics cuts: Electron: 14°<θ e <90° 0.7 GeV/c < P e < 5 GeV/c Hadron: 40°< θ hadron < 175° 0.7 GeV/c < P hadron < 10 GeV/c Full azimuthal angular coverage 10 GeV 2 >Q 2 >1 GeV 2, W>2.3 GeV, 0.2<z<0.8, 0.05<y<0.8 P T < 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

Projections with D (neutron) GeV 72 days GeV 72 days D : 88% effective polarization Effective dilution

D π + (z = )

All the following plots are based on 4x 50 energy configuration. Simulate in P hadron 0.1—50 GeV/c, θ hadron 0—180 degrees Q 2 >1 GeV 2, 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