1. Transverse spin physics at RHIC
Rencontres de Moriond,
March March 15
Ralf Seidl (RBRC)
for the RHIC SPIN collaboration (BRAHMS, STAR, PHENIX)
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

2. The RHIC ring(s) with polarized protons
Absolute Polarimeter (H jet)
RHIC pC Polarimeters
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
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

3. 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 (d+Au)
The experiment is taking place at Brookhaven National Laboratory at RHIC. RHIC is composed by 2 counter circulating rings - blue and yellow- of 3.8 Km in circumference. RHIC has the ability to accelerate ions at speeds close to the speed of light, and particularly Au Au at 100GeV, pp at 250 Gev or even mixed species, and collide them at 4 different crossing points. STAR is located at 6 o’clock. STAR stands for Solenoidal Tracker at RHIC and it is composed by several detectors that have the ability to track particles produced by collisions and measure their energy.
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

4. Local polarimetry: Forward Neutron Asymmetries
IP12’s first asymmetry
Zero Degree Calorimeter behind Dx magnet
neutron  shower max
AN = 0.110±0.015
PLB650: ,2007
local asymmetries at PHENIX
vertical polarization
radial polarization
monitoring of polarization alignment when using spin rotators
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

5. Cross sections in (semi)inclusive DIS and pp, Factorizationk’ k Q
fq(x1)  fq(x2)  s̃  Dh(z)
fq(x1)  s̃  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
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

6. Cross sections well understood at √s=200 GeV
PHENIX:arXiv: [hep-ex]
BRAHMS,PRL.98:252001,2007
|h| < 0.35
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

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
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

8. 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 √s=20 GeV
Higher twist effect?
BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

9. Single spin asymmetries also at higher scales: Confirmed at RHIC at √s=200 GeV
STAR:arXiv: v1 [hep-ex]
STAR: PRL.92:171801,2004
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

10. Recently also PT dependence
STAR:arXiv: v1 [hep-ex]
higher twist  1/PT dependence
Not really seen in lower PT data,
maybe at higher PT though
Prediction by:
(Sivers): D’Alesio and F. Murgia, PRD 70, (2004)
and (twist-3): C. Kouvaris, J. Qiu, W. Vogelsang, F. Yuan, PRD 74, (2006).
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

11. Single Spin Asymmetries at mid rapidity
PHENIX, PRL. 95, (2005)
0 (2001/02)
pt (GeV/c)
pt (GeV/c)
May provide information on gluon-Sivers effect
gg and qg processes are dominant
Transversity+ Collins is suppressed
P=15% in 2002, P=47% in 2005
polarization scaling uncertainty: 30%(2002), ≈ 20%(2005)
residual polarization in unpolarized beam: < 10% and small AN
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

12. Brahms asymmetries at √s=200 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
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

13. Asymmetries also seen at √s=62 GeV
PHENIX, Chiu et al., nucl-ex/
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

14. Brahms asymmetries at √s=62 GeV
BRAHMS, arXiv:  [nucl-ex] p
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

15. 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
Transversity
Collins function
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

16. Naïve Sivers interpretation
Attractive rescattering of hit quark by gluon creates transverse momentum
M.Burkardt [hep-ph ] – impact parameter formalism
Orbital angular momentum at finite impact parameter
observed and true x differ
Observable left/right asymmetry
Taken from H. Tanaka in Trento’04
>
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

17. 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, D’Alesia, Murgia
e-Print: arXiv:  [hep-ph]
Reasonable well agreement vs xF
Not so well agreement at lower PT
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

18. Brahms asymmetries Pion asymmetries fairly well described
J. H. Lee and F. Videbaek (BRAHMS), AIP Conf. Proc. 915, 533 (2007)
√s=200 GeV
Pion asymmetries fairly well described
At least same sign for both K asymmetries as in data
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

19. Heavy flavor related single spin asymmetries
Open charm single spin
asymmetrie s most sensitive to gluon Sivers function (d’Alesio et al,….)
J/y slightly more involved due to questions concerning production
new calculations for charmonium from F.Yuan, arXiv: [hep-ph]
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

20. 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, (2004)
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

21. Sivers back-to-back jet measurements
STAR,PRL,99(2007)142003
Emphasizes (50%+ )
quark Sivers
AN consistent with zero in central region
Partial cancellation of SIDIS –like and DY –like
contributions from Sivers function
VY 1, VY 2 are
calculations by
Vogelsang & Yuan,
PRD 72 (2005)
054028
-Bomhof et al PRD
75, (2007)
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

22. Experiment SIDIS vs Drell Yan:
Sivers|DIS= − Sivers|DY
*** Test QCD Prediction of Non-Universality ***
HERMES Sivers Results
RHIC II Drell Yan Projections
Sivers Amplitude
Markus Diefenthaler
DIS Workshop
Műnchen, April 2007
Feng Yuan
Werner Vogelsang x
R.Seidl: Transverse spin measurements at RHIC
La Thuile, March 10th

23. 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
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

24. Summary Single spin asymmetries confirmed at higher √s
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
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

25. Backup slides La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC

26. 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
R.Seidl: Transverse spin measurements at RHIC
La Thuile, March 10th

27. 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)
R.Seidl: Transverse spin measurements at RHIC
La Thuile, March 10th

28. Transversity and friends
q(x)
Unpolarized DF
helicity DF
Transversity DF
Dq(x)
dq(x)
Sivers function
Boer-Mulders function
La Thuile, March 10th
R.Seidl: Transverse spin measurements at RHIC