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Transverse Spin Asymmetries at RHIC Access to transverse momentum dependent distributions

Discover the significance of transverse single-spin asymmetries in high-energy particle collisions at RHIC, with insights from theory and experiments, including PHENIX, STAR, and more. Learn about the Sivers mechanism, Collins/Hepplemann mechanism, and the intriguing results observed in hadron collider experiments. The text delves into the challenges and advancements in understanding forward p0 production, QCD theories, and data-pQCD comparisons at RHIC.

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Transverse Spin Asymmetries at RHIC Access to transverse momentum dependent distributions

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  1. Transverse Spin Asymmetries at RHICAccess to transverse momentum dependent distributions L.C. Bland Brookhaven National Laboratory 11 June 2007

  2. Relativistic Heavy Ion Collider 3Spin 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)

  3. RHIC Polarized Collider RHIC pC Polarimeters Absolute Polarimeter (H jet) BRAHMS & PP2PP PHOBOS Siberian Snakes Siberian Snakes PHENIX STAR Spin Rotators (longitudinal polarization) Spin Rotators (longitudinal polarization) Pol. H- Source LINAC BOOSTER Helical Partial Siberian Snake AGS 200 MeV Polarimeter AGS pC Polarimeter Strong AGS Snake 2006: 1 MHz collision rate; Polarization=0.6

  4. Definition: dσ↑(↓) – differential cross section of p0 when incoming proton has spin up(down) One way to measure: Single arm detector: R – relative luminosity PBeam – beam polarization Left p0,xF<0 p0 , xF>0 pT,p p  p pL,p=xFp Transverse Single Spin Asymmetry (SSA)Definitions: how and what to measure in an experiment • positive AN: more p0 from spin up() than from spin down() • Accuracy,dAN  1/(N+N)½ many events required for good accuracy In general, AN is a function of both xF and pT

  5. Expectations from Theory What would we see from this gedanken experiment? F0 as mq0 in vector gauge theories, so AN ~ mq/pT or,AN ~ 0.001 for pT ~ 2 GeV/c Kane, Pumplin and Repko PRL 41 (1978) 1689

  6. A Brief and Incomplete History… s=20 GeV, pT=0.5-2.0 GeV/c • QCD theory expects very small (AN~10-3) transverse SSA for particles produced by hard scattering. • The FermiLab E-704 experiment found strikingly large transverse single-spin effects in p+p fixed-target collisions with 200 GeV polarized proton beam (s = 20 GeV). • 0 – E704, PLB261 (1991) 201. • +/- - E704, PLB264 (1991) 462.

  7. Sivers mechanism requires spin-correlated transverse momentum in the proton (orbital motion). SSA is present for jet or g Collins/Hepplemann mechanism requires transverse quark polarization and spin-dependent fragmentation Two of the Explanations for Large Transverse SSA Require experimental separation of Collins and Sivers contributions

  8. Transverse Single-Spin AsymmetriesWorld-wide experimental and theoretical efforts • Transverse single-spin asymmetries are observed in semi-inclusive deep inelastic scattering with transversely polarized proton targets •  HERMES (e-); COMPASS (m); and planned at JLab • Transverse single spin asymmetries are observed in hadron-pair production in e+e- collisions (BELLE) • Intense theory activity underway

  9. Hard ScatteringHard scattering hadroproduction p Factorization theorems state that the inclusive cross section for p+p  p +X can be computed in perturbative QCD using universal PDF and fragmentation functions, and perturbatively calculated hard-scattering cross sections, , for partonic process a+bc. All such processes are summed over to yield the inclusive p production cross section.

  10. Ed3s/dp3[mb/GeV3] q=6o q=10o q=53o xF Do we understand forward p0 production in p + p?At s < 200 GeV, not really… √s=23.3GeV √s=52.8GeV Data-pQCD difference at pT=1.5GeV 2 NLO collinear calculations with different scale: pT and pT/2 Bourrely and Soffer [Eur. Phys. J C36 (2004) 371], data references therein to ISR and fixed target results Ed3s/dp3[mb/GeV3] q=15o q=22o xF sdata/spQCD appears to be function of q, √s in addition to pT Collinear NLO pQCD underpredicts the data at s < 200 GeV

  11. Does pQCD describe particle production at RHIC?Compare cross sections measured for p+pp0 +X at s=200 GeV to next-to-leading order pQCD calculations S.S. Adler et al. (PHENIX), PRL 91 (2003) 241803 J. Adams et al. (STAR), PRL 92 (2004) 171801; and PRL 97 (2006) 152302 Cross sections agree with NLO pQCD down to pT~2 GeV/c over a wide range, 0 < h< 3.8, of pseudorapidity (h = -ln tan /2) at s = 200 GeV.

  12. Accepted for publication in Phys. Rev. Lett. hep-ex/0701041 K+  0 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 pT GeV/c pp collision at s=200GeV (3) Cross sections at forward rapidity y=2.95 are consistent with NLO pQCD.

  13. Expect QCD scaling of form:  Require s dependence to disentangle pT and xT dependence STAR-FPD Cross Sections Similar to ISR analysis J. Singh, et al Nucl. Phys. B140 (1978) 189.

  14. <z> <xq> <xg> Forwardp0production in hadron collider Ep p0 p d EN qq qp p Au xgp xqp qg EN (collinear approx.) • Large rapidity p production (hp>4) probes asymmetric partonic collisions • Mostly high-x valence quark + low-x gluon • 0.3 < xq< 0.7 • 0.001< xg < 0.1 • <z> nearly constant and high 0.7 ~ 0.8 • Large-x quark polarization is known to be large from DIS • Directly couple to gluons  probe of low x gluons NLO pQCD Jaeger,Stratmann,Vogelsang,Kretzer

  15. First Transverse SSA at RHICprior to RHIC run 6 p+p collisions , s = 200 GeV S.S. Adler et al. Phys. Rev Lett. 95 (2005) 202001 Particle production at ~90 (midrapidity) relative to the colliding beams have zero tranverse single spin asymmetry.

  16. Spin Effects in the Forward Direction √s=200 GeV, <η> = 3.8 Spin effects initially observed in RHIC run 2 confirmed by measurements in runs 3,5. STAR collaboration Phys. Rev. Lett. 92 (2004) 171801 D. Morozov, for STAR [hep-ex/0512013] Can be described by several models available as predictions: • Sivers: spin correlated k in the proton (orbital angular momentum) • Collins/Heppelmann: spin and k correlation in quark  p fragmentation • Qiu/Sterman (initial state) / Koike (final state): twist-3 pQCD  multi-parton correlations  Transverse SSA persist at large xF at RHIC energies

  17. Particle Identification using RICH e   K p,K identification < 30 GeV/c pbar > 17 GeV/c with efficiency ~ 97%

  18.  SSAs at 2.3 and 4 deg. at s = 200 GeV SSA 0.1 + 0  4 2.3 0.1 • SSA(+): positive SSA(): negative 4-6% in 0.15 <xF< 0.3. • SSA () survive.

  19. SSAs at 2.3 deg. at √s = 200 GeV SSA 0.1 0 0.1 K p • SSA(K+), SSA(K-): positive 2-5% for 0.15 <xF <0.3. • SSA(pbar), SSA(K-) > 0: Contribution from sea-quarks. • SSA(p) ~ 0: Significant fraction of proton can be mostly from polarized beam proton, but only ones showing SSA~0.

  20. sampled Overview of transverse spin runs at STAR with forward calorimetry: 2001→2006 FOM (P2L) in Run 6 is ~50 times larger than from all the previous STAR runs, and ~725 times larger than for Run 2

  21. Polarization Measurements 2006 Run

  22. RHIC Luminosity Run-6 vs. Run-5 Plot by Phil Pile An extraordinary Run-6! Average Polarization 60%!

  23. y x z h= 1 RUN6 configuration h=2 FPD++ FPD East-side West-side • Di-jet results: 1<<2 (Barrel EMC, Endcap EMC, 2) • Inclusive 0 in forward region: 4<<3 (FPD), 2.5<<4 (FPD++)

  24. STAR Di-jets at STARp+p, s=200 GeV Large acceptance of STAR ideal for di-jet detection. arXiv:0705.4629v1 [hep-ex]

  25. STAR Results vs. Di-Jet Pseudorapidity Sum Run-6 Result VY 1, VY 2 are calculations by Vogelsang & Yuan, PRD 72 (2005) 054028 AN pbeam  (kT  ST) jet Emphasizes (50%+ ) quark Sivers Boer & Vogelsang, PRD 69 (2004) 094025 pbeam into page jet Idea: directly measure kT by observing momentum imbalance of a pair of jets produced in p+p collision and attempt to measure if kT is correlated with incoming proton spin STAR • AN consistent with zero • ~order of magnitude smaller in pp  di-jets than in semi-inclusive DIS quark Sivers asymmetry! arXiv:0705.4629v1, submitted to PRL

  26. FPD++ Physics for Run6 Run-5 FPD We staged a large version of the FPD to prove our ability to detect jet-like events, direct photons, etc. with the STAR FMS The center annulus of the run-6 FPD++ is similar to arrays used to measure forward p0 SSA. The FPD++ annulus is surrounded by additional calorimetry to increase the acceptance for jet-like events and direct g events.

  27. Acceptance of FPD and FPD++ 6 5 4 3 2 1 0 STAR xF pT GeV/c FPD++ p+p0X s = 200 GeV FPD 0 0.2 0.4 0.6 0.8 • Single <h>  limited acceptance  strongxFand pTcorrelation • Study of pTdependence needs large acceptance.

  28. STAR π0AN at √s=200 GeV – xF-dependence • AN at positive xF grows with • increasing xF • AN at negative xF is consistent • with zero • Run 6 data at <η>=3.7 are • consistent with the existing • measurements • Small errors of the data points • allow quantitative comparison • with theory predictions hep-ex/0612030

  29. AN(pT) at xF > 0.4 Run3+Run5 data (hep-ex/0512013): • Online calibration of CNI • polarimeter • Hint of AN decrease with • increasing pT at pT~1-2 GeV/c residual xF-dependence? => AN mapping in (xF,pT) plane is required • Run6 data (hep-ex/0612030): • more precise measurements • consistent with the previous runs in the overlapping pT region • complicated dependence on pT , but not in agreement with theoretical predictions

  30. STAR AN(pT) in xF-bins • Combined data from three runs at <η>=3.3, 3.7 and 4.0 • In each xF bin, <xF> does not significantly changes with pT • Measured AN is not a smooth decreasing function of pT as predicted by multiple theoretical models • (hep-ex/0612030) D’Alesio & Murgia PRD 70 (2004) 074009 Kouvaris, Qiu, Vogelsang, Yuan PRD 74 (2006) 114013

  31. Brahms • Transvers beam pol • Particle ID • BRAHMS measured ANs=62.4 GeV and 200 GeV • Large xF dependent SSAs seen for pions and kaons • Collinear factorization and (NLO) pQCD describe unpolarized • cross-section at RHIC in wide kinematic region

  32. SOUTH PHENIX Muon Piston Calorimeter 2.22.2 18 cm3 • 192 PbWO4 crystals with APD readout • Better than 80% of the acceptance is okay

  33. PHENIX Goes ForwardFirst results with muon piston calorimeter from run 6p+pp0+X, s = 62 GeV Transverse SSA persists with similar characteristics over a broad range of collision energy (20 < s < 200 GeV)

  34. SummaryFrom RHIC run 6 (“Renaissance Run”) • Firmly established that large transverse single spin asymmetries are observed at s = 200 GeV, where generally cross sections agree with pQCD calculations. • Large transverse single spin asymmetries are observed only at large xF; midrapidity asymmetries are small. • Large xF spin asymmetries show the same pattern for 20 s  200 GeV • First observation of pT dependence, enabled by the run-6 luminosity/performance •  Some aspects of the theory are still not understood • Intense theory activity is underway to understand these spin effects. Most theorists agree the Sivers mechanism is responsible for the dynamics •  evidence for partonic orbital angular momentum?

  35. (hep-ex/0602012) • Ng>3 requirement should allow p0-p0 analysis • (upper left) for each event, examine PYTHIA record for final-state hard scattered partons  event selection chooses jet-like events. • (upper right) event-averaged correlation between photon energy and distance in h,f space from thrust axis  events are expected to exhibit similar jet characteristics as found at h0 • (middle) multi-photon final states enable reconstruction of parent parton kinematics via momentum sum of observed photons. • (bottom) projected statistical accuracy for data sample having 5 pb-1 and 50% beam polarization. • Azimuthal symmetry of FPD++ around thrust axis, selected by Etrig condition, enables • integration over the Collins angle  isolating the Sivers effect, or • dependence on the Collins angle  isolating the Collins/Heppelmann effect Expect that jet-like events are ~15% of p0 events OutlookStill More RHIC Run 6 Results to Come • Is the single spin asymmetry observed for p0also present for the jet the p0 comes from? • Answer discriminates between Sivers and Collins contributions • Trigger on energy in small cells, reconstruct p0 andmeasure the energy in the entire FPD++ • Average over the Collins angle and define a new xF for the event, then measure analyzing power versus xF

  36. OutlookRHIC Run 8, polarized p+p collisions at s=200 GeVProject 95 / pb of Integrated Luminosity http://spin.riken.bnl.gov/rsc/report/RHIC_spin_LRP07.pdf

  37. Au Au FMS Commissioning April 2007 • Summed Energy (ADC cnts) • Cell multiplicity Near full EM coverage -1<<4 Pairs of Forward Pions same side correlations (Fragmentation – Collins) Event by event “x” measurement from two jets. Opposite side correlated pions (dijets) Sivers effect d-Au (Gluon saturation in Nuclei) Other future objectives Forward Lepton pairs Charm Forward Meson Spectrometer Installation completed 2007 FMS for Run 7 NOW!! PHYSICS OBJECTIVES • A d-Au measurement of the parton model gluon density distributions x g(x) in gold nucleifor0.001< x <0.1. For 0.01<x<.1, this measurement tests the universality of the gluon distribution. • Characterization of correlated pion cross sections as a function of Q2 (pT2) to search for the onset of gluon saturation effects associated with macroscopic gluon fields. (again d-Au) • Measurements withtransversely polarized protonsthat are expected toresolve the origin of the large transverse spin asymmetriesin reactions for forward  production. (polarized pp) FMS construction completed installation and commissioning during Run 7 (NOW) FMS Wall FMS ½ Wall Pb. Glass

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