1. Carl Gagliardi – WWND – Trans Spin at RHIC 1 Transverse Spin Physics in pp Collisions at RHIC Carl A. Gagliardi Texas A&M University Outline Introduction Forward rapidity measurements Mid-rapidity measurements Looking ahead

2. Carl Gagliardi – WWND – Trans Spin at RHIC 2 RHIC: the Relativistic Heavy Ion Collider Search for and study the Quark-Gluon Plasma Explore the partonic structure of the proton Determine the partonic structure of nuclei

3. Carl Gagliardi – WWND – Trans Spin at RHIC 3 From PDFs to polarized PDFs There are really three different sets of PDFs for the proton q(x) g(x) Δq(x) Δg(x) δ q(x) Proton spin    + Proton spin    Unpolarized PDF “Polarized” distribution “Transversity” distribution Consider a proton moving toward the right

4. Carl Gagliardi – WWND – Trans Spin at RHIC 4 Current knowledge of the polarized distributions Quarks and antiquarks only carry ~30% of total proton spin Proton “spin crisis” Know very little about orbital motion Gluon and anti-quark polarizations have large uncertainties RHIC transverse spin program DSSV, PRL 101, 072001 Anselmino et al, arXiv:0807.0173 Transversity also has large uncertainties

5. Carl Gagliardi – WWND – Trans Spin at RHIC 5 RHIC: the world’s first polarized hadron collider Spin varies from rf bucket to rf bucket (9.4 MHz) Spin pattern changes from fill to fill Spin rotators provide choice of spin orientation “Billions” of spin reversals during a fill with little if any depolarization

6. Carl Gagliardi – WWND – Trans Spin at RHIC 6 Transverse single-spin asymmetries Definition: dσ ↑(↓) – cross section for scattering to the left when incoming proton has spin up(down) Two methods of measurements: Single arm calorimeter: R – relative luminosity P beam – beam polarization Two arm (left-right) calorimeter: Less sensitive to instrumental effects π 0, x F <0 π 0, x F >0 Left Right p p Positive A N : more  0 going to left of the polarized beam

7. Carl Gagliardi – WWND – Trans Spin at RHIC 7 Transverse single-spin asymmetries at forward rapidity Large single-spin asymmetries at CM energy of 19.4 GeV Weren’t supposed to be there in naïve pQCD FNAL E704

8. Carl Gagliardi – WWND – Trans Spin at RHIC 8 Forward π 0 production at ISR energies Bourrely and Soffer, EPJ C36, 371: NLO pQCD calculations underpredict the data at ISR energies Maybe the E704 results arise from soft physics? √s=23.3GeV√s=52.8GeV xFxF xFxF           Ed 3  dp 3 [  b/GeV 3 ] NLO calculations with different scales: p T and p T /2 Data-pQCD differences at p T =1.5GeV

9. Carl Gagliardi – WWND – Trans Spin at RHIC 9 First A N measurement at RHIC PRL 92, 171801 (2004) Sivers: spin and k T correlation in parton distribution functions (initial state) Collins: spin and k T correlation in fragmentation function (final state) Qiu and Sterman (initial state) / Koike (final state): twist-3 pQCD calculations, multi-parton correlations Can be described by several models: Similar to result from E704 experiment (√s=19.4 GeV, 0.5 < p T < 2.0 GeV/c) √s=200 GeV, = 3.8 STAR

10. Carl Gagliardi – WWND – Trans Spin at RHIC 10 Forward pp  π 0 + X cross sections at 200 GeV NLO pQCD calculations by Vogelsang, et al. PRL 97, 152302 STAR The error bars are statistical plus point-to-point systematic Consistent with NLO pQCD calculations at 3.3 < η < 4.0 Data at low p T trend from KKP fragmentation functions toward Kretzer.

11. Carl Gagliardi – WWND – Trans Spin at RHIC 11 Sivers and Collins effects in pp collisions Collins mechanism: final-state asymmetry in the forward jet fragmentation Sivers mechanism: initial-state k T dependence in the parton distribution SPSP k T,q p p SPSP p p SqSq k T, π Sensitive to proton spin – parton transverse motion correlations Sensitive to transversity Observed transverse single-spin asymmetries could arise from the Sivers effect or Collins effect, or from a linear combination of the two

12. Carl Gagliardi – WWND – Trans Spin at RHIC 12 Collins Sivers Sivers and Collins effects in deep-inelastic scattering Semi-inclusive DIS can distinguish the Sivers and Collins effects HERMES finds both are non-zero

13. Carl Gagliardi – WWND – Trans Spin at RHIC 13 Recent π 0 results at 200 GeV from STAR Sivers fit to HERMES SIDIS describes η = 3.3; overpredicts η = 3.7 Twist-3 fit to E704 plus preliminary STAR Runs 3 and 5 data describes η = 3.7; underpredicts η = 3.3 STAR PRL 101, 222001

14. Carl Gagliardi – WWND – Trans Spin at RHIC 14 Charged pion measurements at 200 GeV from BRAHMS Sign dependence of charged pion asymmetries seen in FNAL E704 persists to 200 GeV BRAHMS 2.3 deg (  ~3.4)4 deg (  ~3)

15. Carl Gagliardi – WWND – Trans Spin at RHIC 15 3.0<  <4.0 p  +p  0 +X at  s=62.4 GeV/c 2  0 results at 62.4 GeV from PHENIX Asymmetries are comparable or larger at 62.4 GeV than they are at 200 GeV

16. Carl Gagliardi – WWND – Trans Spin at RHIC 16 Charged-hadron results at 62.4 GeV from BRAHMS BRAHMS Limitation of the BRAHMS measurements: Very strong correlation between x F and p T from small acceptance PRL 101, 042001 Very large asymmetries! K - (= su ) asymmetry is a surprise. Sea-quark Sivers effect or disfavored fragmentation?

17. Carl Gagliardi – WWND – Trans Spin at RHIC 17 Inclusive π 0 A N (p T ) in x F bins Combined data from three runs at =3.3, 3.7 and 4.0 Measured A N is not a smooth decreasing function of p T as predicted by theoretical models Kouvaris et al, PRD 74, 114013 STAR PRL 101, 222001

18. Carl Gagliardi – WWND – Trans Spin at RHIC 18 A potential fly in the ointment? To date, the η meson has looked like a “high-mass, low-yield π 0 ” in all measurements at RHIC A N for the η mass region is much larger at high x F STAR 2006 PRELIMINARY η ~ 3.66 STAR

19. Carl Gagliardi – WWND – Trans Spin at RHIC 19 Mid-rapidity inclusive pion A N Mid-rapidity pion yields are gluon-dominated at these p T No Collins effect for gluons May help to constrain the gluon Sivers function PRL 95, 202001

20. Carl Gagliardi – WWND – Trans Spin at RHIC 20 Mid-rapidity inclusive jet A N Gluon-dominated at low p T Dominated by qg scattering at higher p T Within uncertainties, A N is consistent with zero STAR Preliminary P T (GeV/c) -0.5<  <0.0 -0.9<  <-0.5 0.0<  <0.5 0.5<  <0.9 STAR

21. Carl Gagliardi – WWND – Trans Spin at RHIC 21 Sivers effect in di-jet production 11 22 spin di-jet bisector kTxkTx  > 180  for k T x > 0 Sivers effect: Left/right asymmetry in the k T of the partons in a polarized proton Spin dependent sideways boost to di-jets Measure the di-jet opening angle as a function of proton spin Requires parton orbital angular momentum

22. Carl Gagliardi – WWND – Trans Spin at RHIC 22 Mid-rapidity di-jet Sivers effect measurement PRL 99, 142003 Observed asymmetries are an order of magnitude smaller than seen in semi-inclusive DIS by HERMES Detailed cancellations of initial vs. final state effects and u vs. d quark effects, coupled with very small gluon Sivers effect? STAR

23. Carl Gagliardi – WWND – Trans Spin at RHIC 23 Mid-rapidity di-hadron Sivers effect measurement PHENIX is performing a similar measurement Back-to-back correlations between a trigger π 0 and an away-side charged hadron

24. Carl Gagliardi – WWND – Trans Spin at RHIC 24 Separating Sivers and Collins effects in pp collisions Collins mechanism: asymmetry in the forward jet fragmentation Sivers mechanism: asymmetry in the forward jet or γ production SPSP k T,q p p SPSP p p SqSq k T, π Sensitive to proton spin – parton transverse motion correlations Sensitive to transversity Need to go beyond inclusive hadrons to measurements of jets or direct γ

25. Carl Gagliardi – WWND – Trans Spin at RHIC 25 Large-acceptance forward detectors Both PHENIX and STAR have installed large-acceptance electromagnetic calorimeters in the forward direction PHENIX Muon Piston Calorimeters 3.1 < |η| < 3.7 STAR Forward Meson Spectrometer 2.5 < η < 4.0

26. Carl Gagliardi – WWND – Trans Spin at RHIC 26 First look at jet-like events with the STAR FMS Comparisons of the jet profile and effective mass in data vs. PYTHIA + GEANT simulations

27. Carl Gagliardi – WWND – Trans Spin at RHIC 27 Transverse spin forward  + mid-rapidity jet Bacchetta et al., PRL 99, 212002 Conventional calculations predict the asymmetry to have the same sign in SIDIS and  +jet Calculations that account for the repulsive interactions between like color charges predict opposite sign Critical test of our basic theoretical understanding

28. Carl Gagliardi – WWND – Trans Spin at RHIC 28 In the further future: Drell-Yan In SIDIS, final-state interaction of outgoing quark with proton remnant involves opposite color charges – attractive In Drell-Yan, initial-state interaction of the incoming quark with the spectator components of the proton involves like color charges – repulsive Sign of A N should reverse

29. Carl Gagliardi – WWND – Trans Spin at RHIC 29 Conclusions RHIC has observed large transverse single-spin asymmetries for forward particle production These asymmetries may provide evidence for parton orbital angular momentum and/or quark transversity Measurements to identify the underlying cause(s) are underway Future measurements will provide a direct illustration of attractive vs. repulsive color-charge interactions RHIC, the world’s first polarized hadron collider, is generating a wealth of new data regarding the spin structure of the proton Stay tuned!

30. Carl Gagliardi – WWND – Trans Spin at RHIC 30

31. Carl Gagliardi – WWND – Trans Spin at RHIC 31 Low-p T forward transverse single-spin asymmetries Rotator tuning for longitudinal polarization requires local polarimetry STAR BBCs PHENIX ZDCs