Transverse Spin Measurements at PHENIX John Koster for

Transverse Spin Measurements at PHENIX John Koster for the PHENIX collaboration University of Illinois at Urbana-Champaign DIS 2009/04/27 1

Single Transverse Spin Asymmetries in pp Collisions AN difference in cross-section between particles produced to the left and right Left Right E 704: Left-right asymmetries AN for pions: Theory Expectation: Small asymmetries at high energies π+ π0 (Kane, Pumplin, Repko, PRL 41, 1689– 1692 (1978) ) AN AN O(10 -4) Theory π- Experiment: (E 704, Fermi National Laboratory, 1991) AN O(10 -1) Measured x. F 2

Possible Origin of Large Single Spin Asymmetries h fa q FFq σ fb X’ Proton Structure Can initial and/or final state effects generate large transverse spin asymmetries? (AN ~10 -1) p. QCD small spin dependence fragmentation function 3

Transverse Spin Effects in p↑p Collisions (I) Transversity quark distributions and Collins fragmentation function E 704: Left-right asymmetries AN for pions: Correlation between proton & quark spin + spin dependant fragmentation function π+ π0 Quark transverse Collins FF spin distribution AN π- J. C. Collins, Nucl. Phys. B 396, 161 (1993) (II) Sivers quark-distribution Correlation between proton-spin and transverse quark momentum x. F Sivers distribution D. Sivers, Phys. Rev. D 41, 83 (1990) 4

RHIC Polarized Proton Collider RHIC p. C Polarimeters Absolute Polarimeter (H jet) Siberian Snakes PHOBOS BRAHMS & PP 2 PP Siberian Snakes Spin Flipper STAR PHENIX Spin Rotators Polarized Source 2009 Run: Partial Snake Strong Snake LINAC 200 Me. V Polarimeter BOOSTER Helical Partial Snake AGS Excellent performance during first 500 Ge. V run at RHIC ~10 pb-1 200 Ge. V run ongoing Rf Dipole AGS Internal Polarimeter AGS p. C Polarimeter 5

RHIC ∫L* and Polarization Run Energy Polarization [Ge. V] [%] Longitudinal L [pb-1] LP 4 [pb-1] - Transverse L [pb-1] 2002 200 15 - 2003 200 27 0. 35 1. 9 x 10 -3 - - 2004 200 40 0. 12 9 x 10 -3 - - 2005 200 49 (47) 3. 4 2 x 10 -1 0. 16 3. 5 x 10 -2 2006 200 57 (51) 7. 5 7. 9 x 10 -1 2. 7 7. 0 x 10 -1 2006 62 48 0. 08 4. 2 x 10 -3 0. 02 4. 6 x 10 -3 2008 200 46 - 5. 2 1. 1 x 100 2009 500 ~35 2009 200 - 0. 15 LP 2 [pb-1] 3. 4 x 10 -3 ~10 In progress Steadily increasing polarization and luminosity * integrated luminosity for PHENIX central arm 6

Neutral Pion Cross-Sections Experiment vs p. QCD Guzey et al, PLB 603, 173 (2004) Process Contribution to 0, η=0, s=200 Ge. V de Florian et al, PRD: 76, 094021 0 Cross-Sections at y = 0 Experiment vs Theory § √s=200 Ge. V (RHIC) Agreement § √s=19. 4 Ge. V (FNAL/E 704) Different § √s=62. 4 Ge. V (RHIC) Agreement More work needed to understand lower energies Bourrely et al, Eur. Phys. J. C 36: 371 -374, 2004 7

PHENIX Data at Mid-Rapidity Helps Constrain gluon Sivers Function Experimental Measurement at y~=0 AN PRL 95, 202001 (2005) p +p 0+X at s=200 Ge. V/c 2 Comparison of Exp. To Theory AN p. T (Ge. V/c) High statistics 2006+2008 data et coming. Anselmino al, Phys. Rev. D 74, 094011 Smaller statistical errors (factor 23 improvement for 0’s) p. T Possible • Cyan: Gluon Sivers Function at Higher 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 8 • Green: Asymmetry from Gluon Sivers for case of sea quark at positivity bound

PHENIX Detector at RHIC PHENIX strategy: Central Arms | η | < 0. 35 • Identified charged hadrons • Neutral Pions • Direct Photon • J/Psi • Heavy Flavor Measure several observables each sensitive to different transverse spin effects (i) Forward SSA Neutral Pions Muon Arms 1. 2 < | η | < 2. 4 Sivers • & Collins J/Psi • Unidentified charged hadrons • Heavy Flavor (ii) Transversity-type Asymmetries Interference Frag. Func. Analysis MPC 3. 1 < | η | < 3. 9 • Neutral Pion’s Asymmetries • Eta’s (iii) Sivers-type Heavy Flavor Back to Back Hadrons Pion AN for y~0 9

(i) Forward SSA AN 0 in MPC • η > 3. 5 < η < 3. 7 • • η 3. 1 < 3. 5 Forward asymmetries contain mixture of contributions from § Sivers § Transversity x Collins § Twist-3 PHENIX 0 results available for √s=62 Ge. V Coming soon from 2008 √s=200 Ge. V dataset – 0 and 5. 2 pb-1, 46% Polarization Process contribution to 0, =3. 3, s=200 Ge. V Asymmetries could enter a global analysis on transverse spin asymmetries 10 Guzey et al, PLB 603, 173 (2004)

(ii) Constraints on Transversity: Dihadron IFF Analysis IFF _ + + _ Interference Fragmentation Function Analysis Measure di-hadron asymmetry with hadron pairs in central arm ( 0, h+) ( 0, h-), (h+, h-) § Measures δq(x) x H 1 Transversity extraction will become possible with Interference Fragmentation Function (H 1 ) 11 measurement in progress at BELLE

Models for Interference Fragmentation Function § § Use partial wave analysis of phase shift data to model IFF Sign change around r mass Jaffe, Jin and Tang, PRL 80 (1998) 1166 § § Breit-Wigner shape for p wave No sign change around r mass Trend consistent with HERMES results Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006) Analysis done in mass bins above and below the ρ mass 12

vs mass of the pair Added statistics from 2008 running NEW No significant asymmetries seen at mid-rapidity. 13

vs invariant mass of the pair Added statistics from 2008 running NEW No significant asymmetries seen at mid-rapidity. 14

(iii) Constraints on Sivers Function: Heavy Flavor D meson AN • Production dominated by gluon-gluon fusion at RHIC energy • Gluon transversity zero Asymmetry cannot originate from Transversity x Collins • Sensitive to gluon Sivers effect Theoretical prediction: p↑p DX Anselmino et al, Phys. Rev. D 70, 074025 (2004) Gluon Sivers=Max Quark Sivers=0 Gluon Sivers=0 Quark Sivers=Max 15

(iii) Constraints on Sivers Function: Heavy Flavor PHENIX: no reconstruction of D meson Exploratory measurements of AN for single muons Dominated by charm production in current kinematic range Predicted asymmetry smeared by decay kinematics 16

(iii) Constraints on Sivers Function: J/Psi Exploratory measurement of AN J/Psi §J/Psi production mechanism not well understood §Single spin asymmetries may shed light on production mechanism Constraints on gluon Sivers function Yuan, PRD 78: 014024, 2008 17

(iii) Constraints on Sivers Function: Di. Jet Production Azimuthal distribution of Di-Jet production in pp Suggested in: Boer, Vogelsang, Phys. Rev. D 69, 094025 Counts Proton Spin k. T δφ Beam is in and out of page Look at back-to-back jet opening angles δφ Sensitive to Sivers function only! No Collins-type effects 18

(iii) Constraints on Sivers Function: Di. Hadron Production pi 0 h+/- PHENIX Result from 2006 data: § Done with di-hadrons at y 1=y 2~=0 § Asymmetry consistent with zero Large 2008 data set available! Similar analysis possible in different combinations of rapidity ηmin ηmax -3. 7 -3. 1 -2. 0 -1. 4 -0. 35 +0. 35 1. 4 2. 0 3. 1 3. 9 Works in progress… 19

Summary § § Initial constraints on gluon Sivers function Dedicated transversity channels: – IFF Analysis – Future analysis with Collins asymmetry (See next slide) § Sivers function constraints possible with more data – Connection to orbital angular momentum? Near Term Outlook -- Large 2008 Dataset (i) Forward SSA AN 0 at √s=200 Ge. V soon. Exploring η, K 0 short, Direct γ (ii) Transversity-type measurements IFF results already preliminary Exploration Forward IFF (iii) Sivers-type measurements AN for y~0 smaller errors and higher p. T AN Heavy Flavor -- Forward open heavy flavor, J/Psi -- Mid-rapidity open heavy flavor Di-Jet analyses will expand to rapidity-separated hadron pairs 20

Long Term Outlook -- Upgrades § Vertex Detectors (2011 -2012) Large acceptance precision tracking – Heavy flavor tagging – Jets – Drell-Yan – Electrons from charm decays and beauty decays separately – c, b-Jet Correlations § Forward Calorimetery (2012 -2013) Proposed PHENIX Upgrade ( 1 < eta < 3 ) – AN 0, Direct γ, γ-Jet – Collins-type analyses 21

Backup 22

IFF: Definition of Vectors and Angles Bacchetta and Radici, PRD 70, 094032 (2004) 23

IFF: Transversity from di-hadron SSA Physics asymmetry Unpolarized quark distribution Known from DIS Transversity to be extracted Hard scattering cross section from p. QCD IFF + Di-hadron FF to be measured in e+e- 24

Ongoing IFF measurement at BELLE (RBRC/Illinois) j 2 - IFF sensitivity projection from data e- -j 1 e+ thrust axis Artru and Collins, Z. Phys. C 69, 277 (1996) Boer, Jakob, and Radici, PRD 67, 094003 (2003) 25

Models for IFF § § Use partial wave analysis of phase shift data to model IFF Sign change around r mass Jaffe, Jin and Tang, PRL 80 (1998) 1166 § § Breit-Wigner shape for p wave No sign change around r mass Trend consistent with HERMES results Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006) 26