Simulations of Single-Spin Asymmetries from SIDIS @ EIC

Xin QianKellogg, Caltech

EIC Meeting at CUA, July 29-31, 2010

1. TMD in SIDIS2. Simulation of SIDIS3. Projections

Thanks to M. Huang, H. Gao and J.-P. Chen for slides/dicussionsThanks to J. She, A. Prokudin and Z. B. Zhong for calculations.

Quark polarization

Un-Polarized Longitudinally Polarized Transversely Polarized

Nucleon Polarization

U

L

T

Leading Twist Transverse Momentum Dependent Parton

Distributions (TMDs)

f 1T =

f1 =

g1 =

g1T =

h1L =

h1 =

h1T =

h1T =

Transversity

Boer-Mulder

PretzelositySivers

Helicity

Nucleon SpinQuark Spin

SIDIS @ EIC

qP

PPz

PP

qPy

qP

Qx

p

hp

iep

p

p

2

2

q

qpP hh

S

h

Ion-at-rest (collinear) frame

(Trento convention)

sPPyx

Q iep

2

2

syxQ 2

e’ θe<90o

e-

Lab Frame

p, d, 3He

π±, K ±, D

Access TMDs through Semi-Inclusive DIS @ EIC

...]})cos(1[

...]1[

...])3sin(

...)()sin(

)sin([

...])2sin([

...)2cos(

...{

)1(2

)cos(2

2

)3sin(

)sin(

)sin(

)2sin(

)2cos(

,

2

2

2

2

Sh

Sh

Sh

Sh

h

h

LTSheT

LLeL

UTSh

ULSh

UTShT

ULhL

UUh

TUU

hhS

FS

FS

F

F

FS

FS

F

F

y

xyQdPdzddxdyd

d

Unpolarized

PolarizedIon

Polarizedelectron andion

Boer-Mulder

Sivers

Transversity

Pretzelosity

f1 =

f 1T =

g1 =

g1T =

h1 =

h1L =

h1T =

h1T =

SL, ST: Ion Polarization; le: electron Polarization

Observables are function of x, Q2, z, PT

Multi-dimension nature of SIDIS process

EIC Meeting at CUA, July 29-31, 2010

f1, g1, h1(Torino)

Model Dependent

EIC will greatly

improve our

knowledge here.

DIS (electron)Electron: 2.5°< ϴe < 150°Pe > 1.0 GeV/cFull azimuthal-angular coverage

DIS cut: Q2 > 1 GeV2

W > 2.3 GeV

0.8 > y > 0.05

Capability to detect high momentum electronQ2 > 1 GeV2 ϴe > 5°No need to cover extreme forward angle for electron

Incident electron

Valence region, High Q2.

SIDIS

Hadron: 5°< ϴhadron < 175° 0.7 GeV/c < P hadron < 10 GeV/cFull azimuthal-angular coverageLow momenta, large polar angular coverage

SIDIS cut: MX > 1.6 GeV 0.8 > z > 0.2

Low PT kinematics PT < 1.0 GeV/c

High PT kinematics PT > 1.0 GeV/c

Incident electron

))1

1(2

tan1(

2tan

1 2

yyP

P

x

x fe

fe

fe

fe

fe

Mapping of SSA (just phase space)

Lower y cut, more overlap with 12 GeV

0.05 < y < 0.8

12 GeV --> approved SoLID SIDIS experimentJlab E-10-006

Study both Proton and Neutron

ion momentum

z

PN Z/A

Not weighted by Cross section.

Flavor separation, Combine the datathe lowest achievable x limited by the effective neutron beam and the PT cut

Cross Section in MC

• Low PT cross section:– A. Bacchetta hep-ph/0611265 JHEP 0702:093 (2003)

• High PT cross section:– M. Anselmino et al. Eur. Phys. J. A31 (2007) 373

2 hH dPdddzdydx

d

hhhfe

fe

fe dddpdddp

d

cos cos • PDF: CTEQ6M• FF: Binnewies et al. PRD 52 (1995) 4947

• <pt2> = 0.2 GeV2 <kt

2> = 0.25 GeV2

• NLO calculation at large PT– <pt

2> = 0.25 GeV2

– <kt2> = 0.28 GeV2

– A factor K generated to interpolate between high and low PT

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• 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 - 0.8PT: 5 bins 0-1 GeV

φh angular coverage consideredShow the average of Collins/Sivers/Pretzlosity projections

Still with θh <40 cut, needs to be updated for all projections. Also π-

Proton π+ (z = 0.3-0.7)

Proton K+ (z = 0.3-0.7)

Projections with 3He (neutron)• 11 + 60 GeV 72 days• 3 + 20 GeV 72 days • 12 GeV SoLid

3He: 86.5% effective polarization Dilution factor: 3

Equal stat. for proton and neutron (combine 3He and D)

Similar for D

11 + 60 GeV 3 + 20 GeV

P 36 d (3x1034/cm2/s) 36 d (1x1034/cm2/s)

D 72 d 72 d3He 72 d 72 d

3He π+ (z = 0.3-0.7)

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

• s defines the Q2 and x coverage (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.

EIC Meeting at CUA, July 29-31, 2010

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

High PT kinematics

High PT : hadron momenta dramatically increase require high momentum PID, large polar angular coverageEssential to PT weighted moments. TMD vs Twist-3

PT dependence (High PT) on p of π+10 bins 1 -- 10

GeV in log(PT)

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!!

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.

)()()(

)()()(0

0

suKduucD

usKduucD

Branching ratio: 3.8+-0.07%

Forward angle detection of hadrons.

Wide hadron polar angular coverage

Need low momentum coverage of hadronsBackgrounds?

Z>0.4Q2>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=3e34

1 < PT < 5 GeV; 0.05 < z < 0.8; hadron θ > 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.

EIC Meeting at CUA, July 29-31, 2010

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

Backup Slides

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: Anselmino et al. arXiv: 0807.0173– Sivers TMD: Anselmino et al. arXiv: 0807.0166– Collins Fragmentation function: Anselmino et al. arXiv: 0807.0173

• Pretzlosity:– Measurement of relativistic effect (H. Avakian et al. Phys.

Rev. D 78, 114024)– Direct measurement of obital angular momentum (Ma et

al. PRD 58 09608)• Q2 =10 GeV2

• s: 11 GeV + 60 GeV

Compare with DIS_pions.pdf from BNL

Expand hadron acceptance in the simulation to Phadron 0.1—50 GeV/cRelease z, PT cut

we can see similar trend

Here, for comparison, the angle is defined with incident ion direction at 0 deg.

EIC Meeting at CUA, July 29-31, 2010

D meson Asymmetry X-dependence

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 - 0.8PT: 5 bins 0-1 GeV

φh angular coverage consideredShow the average of Collins/Sivers/Pretzlosity projections

Also π-

Projections with 3He (neutron)• 11 + 60 GeV 72 days• 11 + 100 GeV 72 days • 12 GeV SoLid

3He: 86.5% effective polarization Dilution factor: 3

Equal stat. for proton and neutron (combine 3He and D)

Similar for D

11 + 60 GeV 11 + 100 GeV

P 36 d (3x1034/cm2/s) 36 d (3x1034/cm2/s)

D 72 d 72 d3He 72 d 72 d

Q2 & x coverage

Q2=x y ss defines how low x and how high Q2 we can achieve

Electron• Forward angle, lose

high-Q2 coverage• Lower momentum,

lose high-x coverage

Cross Section in MC• Low PT cross-section:

– A. Bacchetta hep-ph/0611265 JHEP 0702:093 (2007)

• High PT cross-section:– M. Anselmino et al. Eur. Phys. K. A31 373 (2007)

2 hH dPdddzdydx

d

hhhfe

fe

fe dddpdddp

d

cos cos

• 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

22

22

2

)/exp(

zxyQ

zP

dPdddzdydx

d T

hH

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°<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

Projections with D (neutron)

• 11 + 60 GeV 72 days• 3 + 20 GeV 72 days

D: 88% effective polarization Effective dilution

8

D π+ (z = 0.3-0.7)

All the following plots are based on 4x 50 energy configuration.Simulate in Phadron 0.1—50 GeV/c, θhadron 0—180 degreesQ2>1 GeV2, W>2.3 GeV, Mx>1.6 GeV, 0.05<y<0.8, 0.2<z<0.8To study the high hadron momentum (>10 GeV/c) effects