Transverse spin physics at RHIC Rencontres de Moriond, March 8 - March 15 Ralf Seidl (RBRC) for the RHIC SPIN collaboration (BRAHMS, STAR, PHENIX) La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

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

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

Local polarimetry: Forward Neutron Asymmetries IP12’s first asymmetry Zero Degree Calorimeter behind Dx magnet neutron  shower max AN = 0.110±0.015 PLB650:325-330,2007 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

Cross sections in (semi)inclusive DIS and pp, Factorization k’ 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

Cross sections well understood at √s=200 GeV PHENIX:arXiv:0704.3599 [hep-ex] BRAHMS,PRL.98:252001,2007 |h| < 0.35 La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

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

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

Single spin asymmetries also at higher scales: Confirmed at RHIC at √s=200 GeV STAR:arXiv:0801.2990v1 [hep-ex] STAR: PRL.92:171801,2004 La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

Recently also PT dependence STAR:arXiv:0801.2990v1 [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, 074009 (2004) and (twist-3): C. Kouvaris, J. Qiu, W. Vogelsang, F. Yuan, PRD 74, 114013 (2006). La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

Single Spin Asymmetries at mid rapidity PHENIX, PRL. 95, 202001 (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

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

Asymmetries also seen at √s=62 GeV PHENIX, Chiu et al., nucl-ex/0701031 La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

Brahms asymmetries at √s=62 GeV BRAHMS, arXiv:0801.1078 [nucl-ex] p La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

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

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 Trento’04 > La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

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:0712.4240 [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

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

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:0801.4357 [hep-ph] La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

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

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) 074019 La Thuile, March 10th R.Seidl: Transverse spin measurements at RHIC

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 0.1 0.2 0.3 x R.Seidl: Transverse spin measurements at RHIC La Thuile, March 10th

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

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

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

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

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

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