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Measuring the Sivers Effect via Back-to-Back Di-Hadron Correlations in the PHENIX Experiment at RHIC. Feng Wei PHENIX Collaboration Iowa State University. Sivers effect. It is sensitive to proton spin and related to parton orbital angular momentum. Sivers Function. - PowerPoint PPT Presentation
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DNP 2008 - Sivers Effect Feng Wei 1
Measuring the Sivers Effect via Back-to-Back Di-Hadron Correlations in the PHENIX
Experiment at RHIC Feng WeiPHENIX CollaborationIowa State University
Feng Wei 2DNP 2008 - Sivers Effect
Sivers effect
||||||
)(),(),(),,( 2
10
TpT
TpTT
NTTT
kPS
kPSkxfkxfSkxf
It is sensitive to proton spin and related to parton orbital angular momentum
Sivers Function
D.W. Sivers, Phys. Rev D41, 83 (1990), Phys. Rev. D 43, 261 (1991)
In arbitrary scale, schematic to show shape
kT ┴kT ┴
Perturbative LO Twist-3 Calculations (Qiu-Sterman, Efremov, Koike) is related
Feng Wei 3DNP 2008 - Sivers Effect
Physics Observable
||||||
)(),(),(),,( 2
10
TpT
TpTT
NTTT
kPS
kPSkxfkxfSkxf
TkPS
kPS
N kATpT
TpT
||||||
)(
Sivers Function
X
Y
pT
(h)
pT (π0)
qTqT┴
qT||ST
Pp
PHENIX central arms cover only half of the azimuthal angle Measure the vector sum of trigger π0 and away-side leading hadrons' transverse momentum as qT
The Sivers di-jet measurement was proposed by Boer-Vogelsang in Phys.Rev.D69:094025 (2004)
Feng Wei 4DNP 2008 - Sivers Effect
RHIC as polarized proton collider
BRAHMS & PP2PP (p)
STAR (p)
PHENIX (p)
AGS
LINACBOOSTER
Pol. Proton Source500 A, 300 s
1-2
-1
nb607L)FOM(P
onPolarizati Average%53
pb 2.7 Luminosity ,200
GeVs
Spin Rotators
Partial Siberian Snake
Siberian Snakes
200 MeV Polarimeter AGS Internal PolarimeterRf Dipoles
RHIC pC PolarimetersAbsolute Polarimeter (H jet)
2 1011 Pol. Protons / Bunch120 Bunches / Fill
Feng Wei 5DNP 2008 - Sivers Effect
PHENIX Detector - Central Arm
h-
0
EMCAL — measure energy deposit of particles — e,γ, h
DC — obtain momentum of charged particles
PC — measure hit position of charged particles
Tracking and Matching (DC, PC)
charged hadrons
Central Arm: |η| < 0.35
EMCAL (PbSc + PbGl)
0
Feng Wei 6DNP 2008 - Sivers Effect
AN Measurements
NNNN
NNNN
PA
L
LR
RNN
RNN
PA
N
N
1
,1
N: Di-Hadron Yield
↑(↓): Spin Up (Down)
+ (-) : qT┴>0 (<0)
R: Relative Luminosity (BBC)
P: Beam Polarization
Bunch spin configuration alternates every crossing
Possibility for false asymmetries are greatly reduced
Feng Wei 7DNP 2008 - Sivers Effect
Acceptance Correction
Toy MC simulation: A simple “Gaussian” model
kT┴ and kT|| are Gaussian distributions
PRD 74, 072002 (2006) The kT┴ distribution “shift” due to
the Sivers effect Parametrizes the pythia output to
inject an asymmetry Calculate the output asymmetry in
acceptance Asymmetry of kT┴ is diluted Asymmetry of kT|| is enhanced
kT┴ kT||
Factor 0.83 1.24
Full 2π Acceptance
PHENIX Acceptance
Input Asymmetry
Output
Asym
metry
)acceptance 2 Full(
)acceptance PHENIX(
DHN
DHN
A
Af
Fragmentation is not included, kT┴, kT|| were studied
cGeVkk TT /5.12//
2
Feng Wei 8DNP 2008 - Sivers Effect
Fragmentation DilutionToy MC simulation: A recent global analysis of
fragmentation functions for charged hadrons was Included
The parameterization for light quarks only
The transverse momentum of each “hadron” is smeared using a Gaussian jT,
PRD 74, 072002 (2006) Use the same cuts for real data
analysis to select the hadron pair Calculate output asymmetry
respect to input asymmetry to extract dilution factor
Input Asymmetry
Output
Asym
metry
PHENIX Acceptance
Full 2π Acceptance
]1,2[]1,2[])1(1[)1(
0 ),(
iiiiii
ii
iiai
BBzzzNH
i zD
PRD 76, 074033 (2007)
Where DiH for quarks and anti-quarks of
all flavors i as well as for gluons
cGeVjT /587.02
Feng Wei 9DNP 2008 - Sivers Effect
Preliminary Result from PHENIX in run-6
qT┴ should show an asymmetry due to Sivers function. qT|| should show no asymmetry, only for cross check.
Measurement result: the asymmetry for qT┴
due to Sivers effect is consistent with zero.
Fragmentation dilution factor is not included.
TzNzNTpTN qPAPAkPSA for )()( )(If an asymmetry is
measured
Feng Wei 10DNP 2008 - Sivers Effect
Extension work in run-8
Central arms: ||<0.35, =290o
Muon arms: 1.2<||<2.4, =360o
New muon arm hadron trigger was used
MPC: 3.1<||<3.7, =360o
Higher luminosity — more than twice recorded luminosity in run6
hadron
π0Phys. Rev. D 75, 074019 (2007)
By C.J. Bomhof et al.
Feng Wei 11DNP 2008 - Sivers Effect
Summary PHENIX measured the asymmetry due to the Sivers
effect consistent with zero in di-hadron correlation at mid-rapidity. More data would produce a better constraint.
Theory suggests that the asymmetry may be larger at forward rapidity than that at mid-rapidity
Exciting results can be expected from run8 at forward rapidityCentral-Muon arm di-hadron correlationDi-hadron measurement with the MPC
Feng Wei 12DNP 2008 - Sivers Effect
Back Up
Feng Wei 13DNP 2008 - Sivers Effect 13
Interpretation
Attractive rescattering of hit quark by gluon creates transverse momentum M.Burkardt [hep-ph0309269] – impact parameter formalism Orbital angular momentum at finite impact parameter Observed and true x differ Observable left/right asymmetry
P1 P2
1. Nuclear Shadowing (angular momentum)
2. Impact Parameter Space Changes with polarization
Two Possibilities:
Feng Wei 14DNP 2008 - Sivers Effect
PHENIX Spin Program
Prompt Photon LLA (gq X)
Transverse Spinu u d d , , ,
u u d d
Flavor decomposition
GGluon Polarization
L lA (u d W ) T
,
A p p ( , ) X
I nterference fragmentation:
:Transversity q
NSingle Asymmetries A
Production LLA (gg,gq X) W Production
L lA (u d W )
Heavy Flavors LLA (gg cc,bb X)
TTDrell Yan A
Utilizing high energy polarized proton beams of RHIC
Sivers Effect et al.
Feng Wei 15DNP 2008 - Sivers Effect
Di-hadronΔφ distribution
Red: Spin ↑
Blue: Spin ↓
Red: Spin ↑
Blue: Spin ↓
Feng Wei 16DNP 2008 - Sivers Effect
Result from STAR at RHIC
PRL 99, 142003 (2007)
- VY 1, VY 2 are calculations by Vogelsang & Yuan, PRD 72 054028 (2005)- Bomhof et al PRD 074019 75, (2007)
Feng Wei 17DNP 2008 - Sivers Effect
Hermes Measurement
Yan-Drell2
1SIDIS2
1 |),(|),( TTTT kxfkxf
PRL. 94, 012002 (2005)
Collins Effect
Sivers Effect