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
qPPP
z
PPqP
y
qPQx
p
hp
iep
p
p
2
2
qqp
P 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
yxyQdPdzddxdyd
d
Unpolarized
PolarizedIon
Polarizedelectron andion
Boer-Mulder
Sivers
Transversity
Pretzelosity
f1 =
f 1T =
g1 =
g1T =
h1 =
h1L =
h1T =
h1T =
SL, ST: Ion Polarization; e: 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
))11(2
tan1(
2tan
1 2
yyPP
xx f
efe
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 Neutronion 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 dPdddzdydxd
hhhfe
fe
fe dddpdddp
d
cos cos
• PDF: CTEQ6M• FF: Binnewies et al. PRD 52 (1995) 4947• <pt
2> = 0.2 GeV2 <kt2> = 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 dPdddzdydxd
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
zPdPdddzdydx
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
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