Transverse spin physics at RHIC

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Transverse spin physics at RHIC

• Rencontres de Moriond,
• March 8 - March 15
• Ralf Seidl (RBRC)
• for the RHIC SPIN collaboration (BRAHMS, STAR,
  PHENIX)

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The RHIC ring(s) with polarized protons
RHIC pC Polarimeters
Absolute Polarimeter (H jet)
Siberian Snakes
BRAHMS PP2PP
PHOBOS
Siberian Snakes
Spin Flipper
PHENIX
STAR
Spin Rotators
Partial Snake
Helical Partial Snake
Strong Snake
2 ? 1011 Pol. Protons / Bunch e 20 p mm mrad
LINAC
AGS
BOOSTER
200 MeV Polarimeter
Rf Dipole
AGS Internal Polarimeter
AGS pC Polarimeter
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Relativistic Heavy Ion Collider

• 3 Spin Experiments
• PHENIX
• STAR
• BRAHMS
• PHOBOS (heavy-ion)

• Characteristics
• 2 counter-circulating rings
• 3.8 km in circumference
• Top Energies (each beam)
• 100GeV / Au-Au
• 250GeV / p-p
• Mixed Species (dAu)

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Local polarimetryForward Neutron Asymmetries
IP12s first asymmetry
Zero Degree Calorimeterbehind Dx magnet neutron
? shower max
AN ?0.1100.015
PLB650325-330,2007
vertical polarization
radial polarization
localasymmetriesat PHENIX
monitoring of polarization alignment when using
spin rotators
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Cross sections in (semi)inclusive DIS and pp,
Factorization
k
k
Q
fq(x1) ? fq(x2) ? s ? Dh(z)
fq(x1) ? s ? Dh(z)

• Hard scales PT and Q2
• Convolution integrals over all involved momenta
• Factorization of involved distribution and
  fragmentation functions
• (kT)-dependent distribution and fragmentation
  functions

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Cross sections well understood at vs200 GeV
PHENIXarXiv0704.3599 hep-ex
BRAHMS,PRL.98252001,2007
h 7
Transverse single spin asymmetries AN

• Look at left-right asymmetries relative to one
  transversely polarized proton beam
• To cancel acceptance effects use square root
  formula

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E704 Asymmetries
Adams et al. (E704), PLB 264, 462 (1991). Adams
et al. (E704), PRD 53, 4747 (1996).

• perturbative QCD predicted nearly vanishing
  single spin asymmetries
• Huge asymmetries seen in E704 at vs20 GeV
• Higher twist effect?

BNL-AGS vs 6.6 GeV 0.6
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Single spin asymmetries also at higher scales
Confirmed at RHIC at vs200 GeV
STARarXiv0801.2990v1 hep-ex
STAR PRL.92171801,2004
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Recently also PT dependence
STARarXiv0801.2990v1 hep-ex

• higher twist ? 1/PT dependence
• Not really seen in lower PT data,
• maybe at higher PT though

Prediction by (Sivers) DAlesio and F. Murgia,
PRD 70, 074009 (2004) and (twist-3) C.
Kouvaris, J. Qiu, W. Vogelsang, F. Yuan, PRD 74,
114013 (2006).
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Single Spin Asymmetries at mid rapidity
PHENIX, PRL. 95, 202001 (2005)
?0 (2001/02)
pt (GeV/c)
pt (GeV/c)
P15 in 2002, P47 in 2005 polarization scaling
uncertainty 30(2002), 20(2005) residual
polarization in unpolarized beam small AN

• May provide information on gluon-Sivers effect
• gg and qg processes are dominant
• Transversity Collins is suppressed

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Brahms asymmetries at vs200 GeV
J. H. Lee and F. Videbaek (BRAHMS), AIP Conf.
Proc. 915, 533 (2007)
2.3 degrees
2.3 degrees
K- and ?p asymmetries puzzling
p
4 degrees
2.3 degrees
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Asymmetries also seen at vs62 GeV
PHENIX, Chiu et al., nucl-ex/0701031
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Brahms asymmetries at vs62 GeV
BRAHMS, arXiv0801.1078 nucl-ex
p
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What creates these single spin asymmetries?

• Transverse momentum dependent distribution
  function Sivers effect
• Transversity with transverse momentum dependent
  fragmenation function Collins effect
• Higher twist effect on the distribution function
  or fragmentation function side Description
  found to be equivalent to TMDs at intermediate PT
  

Sivers function
unpol FF
Collins function
Transversity
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Naïve Sivers 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

Taken from H. Tanaka in Trento04

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Recent theoretical progress in understanding the
ANs

• Fitting HERMES and COMPASS Sivers data,
• Take Collins contribution into account and
• Calculate phases to describe RHIC AN results

STAR asymmetries
Boglione, DAlesia, Murgia e-Print
arXiv0712.4240 hep-ph
Reasonable well agreement vs xF Not so well
agreement at lower PT
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Brahms asymmetries
J. H. Lee and F. Videbaek (BRAHMS), AIP Conf.
Proc. 915, 533 (2007)
vs200 GeV

• Pion asymmetries fairly well described
• At least same sign for both K asymmetries as in
  data

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Heavy flavor related single spin asymmetries

• Open charm single spin
• asymmetrie s most sensitive to gluon Sivers
  function (dAlesio et al,.)
• J/y slightly more involved due to questions
  concerning production
• new calculations for charmonium from F.Yuan,
  arXiv0801.4357 hep-ph

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Sivers Back-to-back jets

• Idea Jets should be sensitive to initial kt of
  quarks and gluons
• No sensitivity to final kt of hadrons
• Possibility to pin down Sivers effect in pp
  collisions
• Measure spin depentent deviation of dijets

D. Boer and W. Vogelsang, Phys. Rev. D 69, 094025
(2004)
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Sivers back-to-back jet measurements
STAR,PRL,99(2007)142003
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Experiment SIDIS vs Drell Yan SiversDIS -
SiversDY Test QCD Prediction of
Non-Universality
RHIC II Drell Yan Projections
HERMES Sivers Results
0
Sivers Amplitude
Markus Diefenthaler DIS Workshop Munchen, April
2007
0
Feng Yuan Werner Vogelsang
0.1 0.2 0.3 x
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Other future measurements

• Direct access to transversity via Interference
  Fragmentation function
• No Sivers like contributions
• kT integrated, evolution understood
• Open charm single spin asymmetries
• Direct photon jet Sivers asymmetries
• Drell Yan for Sivers function and
• Boer-Mulders function

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Summary

• Single spin asymmetries confirmed at higher vs
• Increasing with xF for pions and kaons
• Compatible to zero for small and negative xF
• PT dependence only falling for higher PT ,lower
  not well understood
• First heavy quark single spin asymmetries
  compatible with zero
• Sivers Back-to-back measurements compatible with
  zero due to partial cancellations of DY type and
  SIDIS type contributions
• More exciting results in the future

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Backup slides
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Transversity

• In helicity basis helicity distribution and
  momentum difference and sum of diagonal
  amplitudes
• Transversity contains helicity flip and is not
  diagonal
• Helicity is conserved quantity for (nearly)
  massless quarks
• All interactions conserve helicity/chirality
• ? Transversity cannot be observed in DIS

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Quark distributions in spin bases

• Sum of quarks with parallel and antiparallel
  polarization relative to proton spin
• (well known from Collider DIS experiments)

q(x),G(x)
Unpolarized distribution function q(x)
Difference of quarks with parallel and
antiparallel polarization relative to
longitudinally polarized proton (known from
fixed target (SI)DIS experiments)
Dq(x), DG(x)
Helicity distribution function Dq(x)
Difference of quarks with parallel and
antiparallel polarization relative to
transversely polarized proton (first results
from HERMES and COMPASS with the help of Belle)

dq(x)
Transversity distribution function dq(x)
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Transversity and friends
Unpolarized DF helicity DF Transversity DF
q(x)
Dq(x)
dq(x)
Sivers function
Boer-Mulders function