Experimental Study of Transversity Lattice QCD and Experiment: Revealing the Structure of Hadrons Jefferson Laboratory, November 21 & 22, 2008 M. Grosse Perdekamp, University of Illinois

Experimental Study of Transversity Content A brief history and first transversity extraction from data Connection with lattice: tensor charge Transversity in transverse momentum dependent (TMD) processes Transversity in transverse moment independent processes November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Transverse Spin Phenomena in Hard Scattering QCD QCD: Asymmetries for transverse spin are small at high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) ) Experiment (E704, Fermi National Laboratory): π+ QCD Test ! π0 π- November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Single Transverse Spin Asymmetries AN persist at √=62.4 GeV and 200 GeV √s=200 GeV STAR √s=62.4 PHENIX and BRAHMS AN AN STAR xF Large single spin asymmetries persist at higher √s=62.4 and 200 GeV xF November 22 nd Experimental Study of Transversity

Inspect Factorized Expression for Cross Section fragmentation process Proton Structure Can initial and/or final state effects generate large transverse spin asymmetries? (ALL ~10-1) Jet hard scattering reaction pQCD Proton Structure small spin dependence (aLL~10-4) fragmentation function November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Transverse Spin in QCD: Two Solutions (I) “Transversity” quark-distributions and Collins fragmentation Correlation between proton- und quark-spin and spin dependent fragmentation AN π+ π0 Quark transverse spin distribution Collins FF π- (II) Sivers quark-distribution Correlation between proton-spin and transverse quark momentum xF Sivers distribution November 22 nd Experimental Study of Transversity

Experimental Study of Transversity (I)-a Quark Transversity Distributions proton spin q quark with transverse spin in the final state! gluon probe quark spin Transversity quark distributions For a proton with spin direction transverse to the probe momentum: probability to find a quark with spin parallel to the proton spin minus “ “ “ spin anti-parallel “ “ November 22 nd Experimental Study of Transversity

Experimental Study of Transversity (I)-b Collins Effect in the Quark- fragmentation in the Final State q sq π q NR : pions to the right Collins Effect NL : pions to the left Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence: = 0 AN = NL - NR NL + NR November 22 nd Experimental Study of Transversity

Experimental Study of Transversity The Collins Effect Must be Present In Semi-Inclusive Deep Inelastic Lepton Proton! quark with transverse spin in the final state followed by Collins effect in the quark fragmentation proton spin q photon probe quark spin November 22 nd Experimental Study of Transversity

Experimental Study of Transversity First Observation of the Collins Effect in Polarized Deep Inelastic Electron-Proton Scattering HERMES Collins Asymmetries in semi- inclusive deep inelastic scattering e+p  e + π + X ~ Transversity (x) x Collins(z) AUT sin(f+fs) November 22 nd Experimental Study of Transversity

Experimental Study of Transversity The Collins Effect Must be Present In e+e- Annihilation into Quarks! electron q1 q2 quark-1 spin quark-2 spin Collins effect in e+e- Quark fragmentation will lead to effects in di-hadron correlation measurements! positron November 22 nd Experimental Study of Transversity

Observation of the Collins Effect in e+e- Annihilation with Belle Belle (UIUC/RBRC) group Collins Asymmetries in e+e- annihilation into hadrons e++e-  π+ + π- + X ~ Collins(z1) x Collins (z2) PRELIMINARY j2-p e- Q j1 e+ A12 cos(f1+f2) November 22 nd Experimental Study of Transversity

Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS + e+e- √s=10 GeV e++ e-  π+ + π- +X Program: QCD analysis of Collins asymmetries in SIDIS (HERMES & COMPASS) + Collins asymmetries in e+e- (Belle)  extract quark transversity distributions and Collins fragmentation functions 27.5 GeV e+p  π + X 160 GeV μ+d  π + X November 22 nd Experimental Study of Transversity

Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS + e+e- Fit includes: Soffer Bound HERMES SIDIS New fit + COMPASS SIDIS Old fit + Belle e+e- Old fit New fit  transversity dist. + Collins FF Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk and Melis at Transversity 2008, Ferrara. Previously: Phys. Rev. D75:05032,2007 November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Prokudin et al. at Ferrara November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Prokudin et al. at Ferrara Prokudin et al. at Ferrara November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Prokudin et al. at Ferrara November 22 nd Experimental Study of Transversity

Transversity Extraction + Tensor Charge with Collins FF Done: We solved the (transversity) proton spin problem! ? Theory Lattice QCD: Tensor Charge November 22 nd Experimental Study of Transversity

Cross Checks with Different Targets: (I) proton-target at COMPASS Preliminary COMPASS Collins Asymmetries for Proton Target vs predictions from Anselmino et al. Stefan Levorato at Transversity 2008, Ferrara 20% of collected data have been used. Futher analysis in progress! Good agreement of COMPASS proton data with preditions from fit to HERMES, Belle and COMPASS-d! November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Cross Checks with Different Targets: (II) 3He-target at JLab, E06-010/06-011 Projected Collins Asymmetries for 3He Target vs predictions from Vogelsang & Yuan Spokespersons: X. Jiang (Los Alamos) J.P. Chen (JLab) E. Cisbani (INFN) H. Gao (Duke) J.-C. Peng (UIUC) First 6 GeV JLab neutron (3He) measurement presently taking data! November 22 nd Experimental Study of Transversity

Can we gain a consistent description of the original AN asysmmetries? Work in progress: complete analysis of SIDIS (Collins & Sivers) + e+e- (Collins) + pp AN (Collins & Sivers) Anselmino et al. Note: impact of unpolarized FFs thick line DSS thin line Kretzer November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Collins Extraction of Transversity: model dependence from Transverse Momentum Dependences! transversity Collins FF hadron FF quark pdf k┴ transverse quark momentum in nucleon p┴ transverse hadron momentum in fragmentation Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 The transversse momentum dependencies are unknown and difficult to obtain experimentally! November 22 nd Experimental Study of Transversity

Future measurement of kT- (PDFs) and pT- (FFs) dependencies (I) pT dependence of Collins and the unpolarized fragmentation functions can be measured with present data sample at Belle (1.5 Billion hadronic events). Super KEK-B will have 50 x more luminosity! (II) pT dependence of Collins effect can be also measured with high precision at JLab 12 GeV, later at EIC. Need ideas to get at the kT dependence of pdfs using The pT dependence from e+e-! 12 GeV - solenoid November 22 nd Experimental Study of Transversity

Sudakov Suppression of TMDs Convolution integral sensitive to soft factor that leads to (Sudakov)_ suppression of Collins asymmetries ~ 1/√Q in SIDIS ~ 1/Q in e+e- D. Boer Nucl. Phys. B603 192 (2001) Convolution in SIDIS can be avoided by weighted integration in SIDIS. However, not possible in in e+e- ! November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Measurements of transversity with transverse momentum independent functions !! Drell Yan  req. polarized anti-protons need to improve systematics on rel. luminosity need Lambda-FF  e+e- need Lambda-FF  e+e- need IFF  e+e- need IFF  e+e- November 22 nd Experimental Study of Transversity

First IFF Asymmetries in Hermes and COMPASS 2002-2004 data all +/- pairs preliminary proton target A. Bacchetta, M. Radici hep-ph/0608037 model calculations proton HERMES kin deuteron COMPASS kin November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Transversity Quark Distributions at RHIC: Di-Hadron “Interference Fragmentation Functions IFF Asymmetries in proton-proton collisions p+p  π+ + π- + X ~ Transversity (x) x IFF(z)  k┴, p┴ integrate out Ongoing work: AT in PHENIX IFF in Belle November 22 nd Experimental Study of Transversity

First PHENIX Results on IFF Asymmetries for Pion Pairs Ruizhe Yang, Transverse Spin Workhop in Beijing, July 2008 Expect small asymmetries at mid-rapidity (Bachetta et al.) More statistics is on tape. Need to move measure- ment forward! Systematic errors Polarization 5% Relative lumi. 5x10-4 No systematic effects detected from bunch shuffling Consistent with 0, despite the second bin of p0h- pairs and the last bin of h+h- pairs are 2s from 0 November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Projections for IFF measurement at BELLE j2-p p-j1 e+ e- thrust axis IFF sensitivity projection from data Artru and Collins, Z. Phys. C69, 277 (1996) Boer, Jakob, and Radici, PRD67, 094003 (2003) November 22 nd Experimental Study of Transversity

Measurements of quark transversity Courtesy Ruizhe Yang 1991 2002-2008 Underway Future p+p RHIC Collins in jets E704, 1991 Large forward SSA STAR, PHENIX, BRAHMS Inclusive AN RHIC IFF asym. JParc, FAIR Drell-Yan HERMES COMPASS AUT SIDIS COMPASS p target JLab 3He JLab 12 GeV Collins, IFF EIC Collins in jets e++e- BELLE Collins FF BELLE IFF BELLE pT dependence November 22 nd Experimental Study of Transversity

Experimental Study of Transversity Summary First measurements of transversity quark distributrions are available. TMD dependence of Collins function makes theoretical interpretation difficult. Knowledge of pT and (?) kT dependence may come from future measurements in e+e- and SIDIS. Non-TMD processes are available. Within the next few years measurements using di-hadron interference fragmentation functions will be available. We can aim to extract the tensor charge in a theoretically clean way and compare to lattice QCD! November 22 nd Experimental Study of Transversity