# Transversely Polarized Proton Spin Measurements in - Phenix - BNL

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```					 Transversely Polarized Proton
Spin Measurements in Polarized
p+p Collisions in

Mickey Chiu
Transverse Single Spin Asymmetries
  ( p)    ( p)  ( p)        where p is the 4-momentum of a
Definition:      AN                   
 ( p)   ( p)  ( p)
                     particle (hadron, jet, photon, etc...)

Experimentally, there are a variety of (~equivalent) ways this can be measured.
1. Yield difference between up/down proton in a single detector
1      N   R lumiN                                 Left
AN                               R lum i  L L-                                      Right
Pbeam    N   R lumiN 
This is susceptible to Rel. Luminosity differences
2. Or, take the left-right difference between 2 detectors
1       N   R det N    1 R det N   N 
AN               L           R
             R     L
Pbeam    N   R det N  Pbeam R det N   N 
L           R               R     L
This is susceptible to detector Relative Acceptance differences
3. Or, take the cross geometric mean (square-root formula)

1        N  N  N  N
AN                L    R    L    R

P beam     N  N  N  N
L    R    L    R
Mostly insensitive to Relative Luminosity and Detector Acceptance differences
2
Transverse Proton Spin Physics
Polarized parton distribution functions
1 1                                  q  q  q      quark helicity distribution – known
   G  Lq  Lg
2 2
Z    Z                G  g   g      gluon helicity distribution – poorly known
 T q  q  q    transversity distribution – unknown

Naïve LO, Leading Twist, pQCD Result                       pp  X at s  19 .4 GeV
E704

mq
AN         example, m q  3MeV , s  20 GeV , AN  10 4
s
Helicity violation term due to finite quark masses
3
Transverse Proton Spin Physics
•Various possible explanations have been proposed to explain these asymmetries
•Transversity x Spin-dep fragmentation (e.g., Collins effect),

                        1 N                   
Dh / q  ( z, p )  Dh / q ( z, p )   Dh / q  ( z, p ) S q  ( pq  p )
ˆ    ˆ
2

•Intrinsic-kT in proton (Transverse Momentum Dep Functions) ,
•Eg, Sivers Function

•Perturbative LO Twist-3 Calculations (Qiu-Sterman, Efremov, Koike)
•These calculations have been related to the Sivers function
A Unified picture for single transverse-spin asymmetries in hard processes,
Ji, Qiu, Vogelsang, Yuan PRL97:082002,2006
•Or some combination of the above
•Caveat: The theory is still being actively worked out                 Anim. courtesy J. Kruhwel, JLAB 4
PHENIX at RHIC Spin
•Central Arm Tracking          || < 0.35, xF ~ 0
•Drift Chamber (DC)
•momentum measurement
•pattern recognition, 3d space
point
STAR                                     •Time Expansion Chamber (TEC)
•Central Arm Calorimetry
•PbGl and PbSc
•Very Fine Granularity
•Tower x ~ 0.01x0.01
•Trigger
•Central Arm Particle Id
•RICH
•TOF
•/K/p identification
PHENIX Transversely Polarized p+p Data Set                  •Global Detectors (Luminosity,Trigger)
•BBC                     3.0 < || < 3.9
Run02       Run05               Run06                    •Quartz Cherenkov Radiators
•ZDC/SMD (Local Polarimeter)
s (GeV/c2)     200            200           200    62.4                •Forward Hadron Calorimeter
Ldt (pb-1)    0.15           0.15          2.7    0.02   •Forward Calorimetry           3.1 < || < 3.7
•MPC
<P>         0.15           0.47          0.57   0.50                •PbWO4 Crystal
•Forward Muon Arms            1.2 < || < 2.4
P2L        0.0034          0.033         0.87   0.05
5
Single Spin Asymmetries at xF=0
PRL 95, 202001 (2005)
p+p0+X at s=200 GeV/c2

PLB 603,173 (2004)

process contribution to
0, =0, s=200 GeV

•AN for both charged hadrons and neutral pions consistent with zero at
midrapidity.
•More statistics needed to map out pT  x  g/q dependence
•If large asymmetries at forward rapidities is from valence quark motion,
does asymmetry at mid-rapidity appear at high enough xT = 2pT/s?
•Mid-rapidity data constrains magnitude of gluon Sivers function
6
Constraints on Gluon Sivers?
Anselmino et al, PRD74:094011,2006

PHENIX 0, PRL 95, 202001 (2005)

•LO QCD Transverse Momentum Dependent parton scattering calculations
•Cyan: Gluon Sivers Function at positivity bound, no sea quark Sivers
•Thick Red: Gluon Sivers parameterized to be 1 sigma from PHENIX 0 AN
•Blue: Asymmetry from Sea quark Sivers at positivity bound
•Green: Asymmetry from Gluon Sivers for case of sea quark at positivity bound 7
0 AN at High xF
p+p0+X at s=62.4 GeV/c2

3.0<<4.0
PLB 603,173 (2004)

process contribution to
0, =3.3, s=200 GeV

•Large asymmetries at forward xF
•Valence quark effect?
•xF, pT, s, and  dependence provide quantitative tests for theories
8
RHIC Forward Pion AN at 62.4 GeV
E704, 19.4 GeV, PLB261, (1991) 201

•Brahms Spectrometer at “2.3” and “3.0” setting  <> = 3.44, comparable to PHENIX all eta
•Qualitatively similar behavior to E704 data: pi0 is positive and between pi+ and pi-, and roughly
similar magnitude: AN(pi+)/AN(pi0) ~ 25-50%
•Flavor dependence of identified pion asymmetries can help to distinguish between effects
•Kouvaris, Qiu, Vogelsang, Yuan, PRD74:114013, 2006
•Twist-3 calculation for pions for pion  exactly at 3.3
•Derived from fits to E704 data at s=19.4 GeV and then extrapolated to 62.4 and 200 GeV
•Only qualitative agreement at the moment. Must be very careful in comparisons (between expt’s
and theories) that kinematics are matched, since AN is a strong function of pT and xF.             9
Comparison to 0 at s = 200 GeV/c2

STAR

•Trend with  seems to disagree with STAR
result, but is consistent with theoretical
predictions.
•This might just be due to the different collision
energy and pT coverage
10
Kinematic Cuts and AN
pT        p
xF       cot θ  T sinh 
P          P
Phys.Rev.D74:114013,2006.

•Mean AN is measured to be lower for pT>1, even
though mean xF is higher for this pT bin, and higher xF
implies higher asymmetry
•This implies that AN is dropping with pt for a given
xF slice
•The  cut, for a given xF slice, splits that slice into high
pt and low pt, with the lower eta selecting higher pt
•This implies that AN at lower  should be smaller,
consistent with predictions of PRD74:114013
•However, at 62.4 GeV the pT are low (pQCD invalid?)
•Cross-section is being analyzed now
11
J/ AN
Quark Sivers = 0
Gluon Sivers = Max

Quark Sivers = Max
Gluon Sivers = 0

•Bkg from like-sign and sidebands
•J/ Production is gluon dominated at RHIC
•Production thought to be not well understood
•NRQCD describes data well?
•Gluon has zero transversity
•Collins Effect suppressed
•Gluon Sivers Dominant
•Anselmino et al, PRD70:074025 (hep-ph/0407100)
•Calculation for Open Charm, NOT J/
Submitted to PRL      12
Summary
•Much new data coming from transversely polarized proton interactions
•p+p (RHIC), but also e+p SIDIS (Hermes, Compass, JLab), e+e- (Belle)
•Along with new data on the helicity distribution of partons in the proton (gluon
spin), transversely polarized proton collisions could add a wealth of new
information on proton structure
•Transversity, Orbital angular momentum?                    1-dimensional
•GPD’s may be cleanest way to OAM
•However, strongest asymmetries are in p+p
•PHENIX has measured the transverse asymmetry
of 0, h, and J/, covering an xF from 0 to 0.6 (at
two different collision energies).
•There are also sizable asymmetries from                proton wave-function
forward neutrons out to xF ~ 1.*
•In the future, we expect ~25% of the polarized
p+p running will be in the transverse mode                 PHENIX preliminary

•Lots more data coming
enhance physics reach
•Nose Cone Calorimeter
•Silicon Detectors (SVTX and FVTX)           * See Poster by M. Togawa 13
University of São Paulo, São Paulo, Brazil
Collaboration, 2006
China Institute of Atomic Energy (CIAE), Beijing, P. R. China
Peking University, Beijing, P. R. China
Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 12116 Prague,
Czech Republic
Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering,
Brehova 7, 11519 Prague, Czech Republic
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21
Prague, Czech Republic
Laboratoire de Physique Corpusculaire (LPC), Universite de Clermont-Ferrand, F-63170
Aubiere, Clermont-Ferrand, France
Dapnia, CEA Saclay, Bat. 703, F-91191 Gif-sur-Yvette, France
IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406 Orsay, France
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-
91128 Palaiseau, France
SUBATECH, Ecòle des Mines at Nantes, F-44307 Nantes, France
14 Countries; 68 Institutions; 550 Participants*
University of Muenster, Muenster, Germany
KFKI Research Institute for Particle and Nuclear Physics at the Hungarian Academy of
Sciences (MTA KFKI RMKI), Budapest, Hungary
Debrecen University, Debrecen, Hungary
Eövös Loránd University (ELTE), Budapest, Hungary
Banaras Hindu University, Banaras, India                                                  Abilene Christian University, Abilene, Texas, USA
Bhabha Atomic Research Centre (BARC), Bombay, India                                       Brookhaven National Laboratory (BNL), Chemistry Dept., Upton, NY 11973, USA
Weizmann Institute, Rehovot 76100, Israel                                                 Brookhaven National Laboratory (BNL), Collider Accelerator Dept., Upton, NY 11973, USA
Center for Nuclear Study (CNS-Tokyo), University of Tokyo, Tanashi, Tokyo 188, Japan      Brookhaven National Laboratory (BNL), Physics Dept., Upton, NY 11973, USA
Hiroshima University, Higashi-Hiroshima 739, Japan                                        University of California - Riverside (UCR), Riverside, CA 92521, USA
KEK - High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-       University of Colorado, Boulder, CO, USA
0801, Japan                                                                               Columbia University, Nevis Laboratories, Irvington, NY 10533, USA
Kyoto University, Kyoto, Japan                                                            Florida Institute of Technology, Melbourne, FL 32901, USA
Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki, Japan                      Florida State University (FSU), Tallahassee, FL 32306, USA
RIKEN, The Institute of Physical and Chemical Research, Wako, Saitama 351-0198, Japan     Georgia State University (GSU), Atlanta, GA 30303, USA
RIKEN – BNL Research Center, Japan, located at BNL                                        University of Illinois Urbana-Champaign, Urbana-Champaign, IL, USA
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501,   Iowa State University (ISU) and Ames Laboratory, Ames, IA 50011, USA
Japan                                                                                     Los Alamos National Laboratory (LANL), Los Alamos, NM 87545, USA
Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan                  Lawrence Livermore National Laboratory (LLNL), Livermore, CA 94550, USA
University of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi Ibaraki-ken 305-8577, Japan            University of Maryland, College Park, MD 20742, USA
Waseda University, Tokyo, Japan                                                           Department of Physics, University of Massachusetts, Amherst, MA 01003-9337, USA
Cyclotron Application Laboratory, KAERI, Seoul, South Korea                               Old Dominion University, Norfolk, VA 23529, USA
Ewha Womans University, Seoul, Korea                                                      University of New Mexico, Albuquerque, New Mexico, USA
Kangnung National University, Kangnung 210-702, South Korea                               New Mexico State University, Las Cruces, New Mexico, USA
Korea University, Seoul 136-701, Korea                                                    Department of Chemistry, State University of New York at Stony Brook (USB), Stony Brook,
Myong Ji University, Yongin City 449-728, Korea                                           NY 11794, USA
System Electronics Laboratory, Seoul National University, Seoul, South Korea              Department of Physics and Astronomy, State University of New York at Stony Brook (USB),
Yonsei University, Seoul 120-749, Korea                                                   Stony Brook, NY 11794, USA                                  *as of July 2006
IHEP (Protvino), State Research Center of Russian Federation , Protvino 142281, Russia    Oak Ridge National Laboratory (ORNL), Oak Ridge, TN 37831, USA
Joint Institute for Nuclear Research (JINR-Dubna), Dubna, Russia                          University of Tennessee (UT), Knoxville, TN 37996, USA and growing
Kurchatov Institute, Moscow, Russia                                                       Vanderbilt University, Nashville, TN 37235, USA
PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region 188300, Russia                                                                                          14
15
Run02 Inclusive AN Systematic Errors
In addition to calculating the asymmetry using more than one
method, potential systematic errors have been investigated in the
following ways:
• Measured asymmetry of background
– Immediately outside the 0 mass peak
– In the mass region between the 0 and the 
•    Compared independent measurements for two polarized beams
•    Compared results for left and right sides of detector
•    Compared minimum bias and triggered data samples
•    Examined fill-by-fill consistency of asymmetry values
•    Used the “bunch shuffling” technique to check for systematic errors
– Randomly reassign the spin direction to each bunch in the beam
– Recalculate the asymmetry
– Repeat many times (1000) to produce a “shuffled” asymmetry
distribution centered around zero
– Compare width of shuffled distribution to statistical error on physics
asymmetry

16
Muon Piston Calorimeter Performance

•Shower Reconstruction Using Shower Shape Fits   •Energy Scale Set by MIP
•In Noisy Towers, Used
All Pairs          Background
Mixed Events            subtracted
Tower Spectrum

MIP Peak

•Photon Pair Cuts
•Pair Energy > 8 GeV
•Asymmetry |E1-E2|/|E1+E2| < 0.6             •Confirmed with 0,  peaks
•Noisy Towers (up to 25% of MPC) Excluded
•Width ~ 20 MeV

17
MPC N Fit Examples, Fill 8015

N ( )  N ( )
•Black: Fit of R   N sin( ) to polarization raw asymmetry               N ( )  
N ( )  N ( )
•R is consistent with the Relative Luminosity determined from
scalers (where possible)
R               N  ( )  N  ( )  N  ( )  N  ( )
•Red: Fit of  N cos( ) to square root raw asymm  N ( )    L          R          L          R

N  ( )  N ( )  N  ( )  N ( )
L          R          L          R

•Both polarization and sqrt asymmetries were calculated
•Polarization asymmetries were used for the final
numbers
•The RMS difference between different plot/fit
techniques was considered to be a systematic error.
•Other systematic errors (residual relative luminosity in
unpolarized beam, background subtraction of pi0) were
small.

18
Future PHENIX Acceptance
2                      NCC                                   NCC
HBD

EMCAL
 coverage

EMCAL
MPC

MPC
VTX & FVTX
0

-3         -2   -1           0   1        2          3 
•History – PHENIX is a small acceptance, high rate, rare probes (photons, J/Psi, etc.) detector
•Muon Piston Calorimeter (2006-end): PbWO4 Electromagnetic Calorimeter
•Hadron Blind Detector (2007-2009): CsI Triple GEM Cerenkov Detector
•Nose Cone Calorimeter (2010-end): Tungsten-Silicon Electromagnetic Calorimeter with
limited Jet Capabilities (1 arm, possibly 2 with funding)
•SVTX (2009-end): Central Arm Silicon Tracker
•FVTX (2010-end): Muon Arm Silicon Tracker                                                   19

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