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Azimuthal Asymmetry in Unpolarized Drell-Yan

Azimuthal Asymmetry in Unpolarized Drell-Yan. Lingyan Zhu. University of Illinois at Urbana Champaign. SSA Workshop at BNL, Jun 1-3, 2005. Experimental Measurements of the azimuthal cos2  distribution in pion-induced Drell-Yan Theoretical Explanations

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Azimuthal Asymmetry in Unpolarized Drell-Yan

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  1. Azimuthal Asymmetry in Unpolarized Drell-Yan Lingyan Zhu University of Illinois at Urbana Champaign SSA Workshop at BNL, Jun 1-3, 2005 • Experimental Measurements of the azimuthal cos2 distribution in pion-induced Drell-Yan • Theoretical Explanations • The unpolarized proton-induced Drell-Yan from Fermilab E866 data. Referring to: D. Boer’s talk, G. Goldstein’s talk and A. Bacchetta’s talk at SIR2005 J.C. Peng’s talk at E866 collaboration meeting in Oct 2004.

  2. Angular Distribution in the Drell-Yan Process In the simple parton model: ( for massless quarks and  measured relative to the annihilation axis) =1 and ==0 • GJ: Gottfried-Jackson frame • z-axis parallel to the beam momentum • CS: Collins-Soper frame • z-axis parallel to the bisector • of beam and negative target momentum • UC: u-channel frame • z-axis antiparallel to the target momentum

  3. First-order QCD Corrections to Drell-Yan • Increase the overall cross section by a K-factor~2. • The Lam-Tung sum rule still hold (in any reference frame for massless quarks) • Lam & Tung, PRD21,2712(1980) • The NLO correction at O(s2)to the angular distribution is small. • Mirkes & Ohnemus, PRD51,,4891(1995) Conway et al., PRD39,92(1989)

  4. Angular Distribution in the N Drell-Yan Process E615 at Fermilab: 252 GeV π- + W Conway et al., PRD39,92(1989) Also see NA10 results: 140/194 GeV π- + W, 286 GeV π- + W/d Z. Phys. C31, 513 (1986); Z. Phys. C37, 545 (1988)

  5. Transverse Momentum Dependence NA10 results for π- + W Z. Phys. C37, 545 (1988)

  6. Dimuon Mass Dependence NA10 results for π- + W Z. Phys. C37, 545 (1988)

  7. x Dependence NA10 results for π- + W Z. Phys. C37, 545 (1988)

  8. Target Dependence Open: Deuterium Solid: Tungsten NA10 results for π- + W/d Z. Phys. C37, 545 (1988)

  9. Violation of the Lam-Tung Sum Rule E615 at Fermilab: 252 GeV π- + W Conway et al., PRD39,92(1989) • The deviations from 1+cos2 • due to the soft-gluon resummation are less than 5%. • Chiappatta & Bellac,ZPC32,521 (1986) • The correction due to the intrinsic transverse momenta is estimated to be less than 0.05 • Cleymans & Kuroda, PLB105,68(1981) Also see NA10 results: 140/194 GeV π- + W, 286 GeV π- + W/d Z. Phys. C37, 545 (1988)

  10. What did we Learn from Data? • There is a sizable cos2 asymmetry ( up to 0.3) in the unpolarized pion-induced Drell-Yan. The Lam-Tung sum rule is violated beyond the QCD-improved parton model. • The asymmetry is not sensitive to the nuclear correction for nuclei. • The asymmetry increases as PT increases. • The asymmetry remains flat (at 140,194 GeV) or decreases (at 252, 286 GeV) as dimuon mass increases. The dependence of the asymmetry on x also changes with beam energy. • ~1 and ~0 but with some deviation for a few cases.

  11. Higher Twist Effect • Higher twist effect leads to =-1 for low mass as x! 1. • Berger & Brodsky, PRL42, 940 (1979); Berger, ZPC4,289(1980) • Higher twist effect in terms of pion bound state effect: • Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994) The violation of Lam-Tung sum rule may not be fully explained by higher twist effect

  12. QCD Vacuum Effects • Brandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993) • The ansatz for a factorization-breaking spin correlation due to nontrivial QCD vacuum can be used to fit the NA10 data at 194 GeV • More than 104 events are required to see such size of correlation in the factorization of pp scattering at • The helicity flip in the instanton-induced contribution may lead to nonzero . • Boer,Brandenburg,Nachtmann&Utermann, EPC40,55(2005). 0=0.17 mT=1.5

  13. Leading-Twist Quark Distributions Survive K┴ integration K┴ - dependent, Chiral-even K┴ - dependent, Chiral-odd

  14. All Eight Quark Distributions Are Probed in Semi-Inclusive DIS From Jen-Chieh Peng /2 Unpolarized Transversity Polarized target Sivers Polarzied beam and target SL and ST: Target Polarizations;λe: Beam Polarization

  15. Boer-Mulders Function h1? • Boer, PRD60,014012(1999) • An spin-correlation approach in terms of h1? can fit the NA10 data at 194 GeV. • It can also account for the single spin asymmetry in pp"! X. • On the base of quite general arguments, for |qT|<<Q(=m), • Salvo,hep-ph/0407208. 1=0.5 mC=2.3 T=CH=1

  16. Boer-Mulders Function h1? (II) • Initial-state gluon interaction can produce nonzero h1? for the proton in the quark-scalar diquark model. In this model, • h1?=f1T?. • Boer,Brodsky&Hwang, PRD67,054003(2003). • Final-state interaction with one gluon exchange can produce nonzero h1? for the pion in the quark-spectator-antiquark model with constant coupling g. • Lu&Ma, PRD70,094044(2004).

  17. Boer-Mulders Function h1? (III) • In the quark-diquark model, the cos2 azimuthal asymmetry in unpolarized Drell-Yan was evaluated: • Gamberg, hep-ph/0412367. s=50 GeV2 x=0.2-1.0 q=2.5-5.0GeV s=50 GeV2 qT=2-4 GeV s=500 GeV2 q=4.0-8.6 GeV Red: Leading twist T-odd contribution Blue: Leading and sub-leading twist

  18. Boer-Mulders Function h1? (IV) • Lu & Ma, hep-ph/0504184 • The prediction in quark-spectator-antiquark model with effective pion-quark-antiquark coupling as a dipole form factor can reproduce the Drell-Yan data from NA10.

  19. Sivers Function f1T? • On the basis of time reversal arguments: • f1T?(x,pT2)=0 • Collins, NPB396, 161(1993) • Final-state interaction from gluon exchange between the quark and the spectator lead to nonzero Sivers function. • Brodsky, Hwang & Schmidt, PLB530, 99(2002). • Final-state interaction can be reproduced by a prescription of the light-cone singularities or an extra gauge link at the spatial infinity for the parton distributions. • Ji & Yuan, PLB543,66(2002). • Add final state interaction to the time reversal arguments: • f1T?(x,pT2)SIDIS=-f1T?(x,pT2)DY • Collins, PLB536, 43(2002)

  20. Sivers Function f1T?(II) • Calculation fit with MIT bag model in the presence of final state interaction through one gluon exchange • Yuan, PLB575, 45(2003)[hep-ph/0308157]. • Calculation in a spectator model with axial-vector diquarks in the presence of gluon rescattering • Bacchetta, Schaefer & Yang, PLB578,109(2004)[hep-ph/0309246] • Calculation in a light-cone SU(6) quark-diquark model • Lu & Ma, NPA741,200 (2004). - -

  21. Sivers Function f1T? (III) • A favorable explanation of the transverse asymmetry for Fermilab E704 data pp"! X. • D’Alesio & Murgia, PRD70,074009,2004. • Fit of HERMES transverse SIDIS data ep! e0 X • Efremov, Goeke, Menzel, Metz & Schweitzer PLB612,233(2005) • Fit of HERMES transverse SIDIS data with less assumptions • Anselmino, Boglione, D’Alesio, Kotzinian, Murgia & Prokudin, hep-ph/0501196 Models and fits agree on the sign of Sivers function: negative for u quarkandpositive for d quark.

  22. What did we Learn from Models? • The high twist effect in terms of pion bound state effect is not enough to explain the large cos2 asymmetry and the violation of Lam-Tung sum rule. In this model,  and  also changes with PT. • The spin correlation due to nontrival QCD vacuum may cause cos2 asymmetry. In instanton model, it relates to the helicity flip of one quark/antiquark in the initial state. • The non-zero chiral-odd distribution function h1? may cause cos2 asymmetry, which can be realized in spectator model and MIT bag model with initial/final-state interaction. It is equal to Sivers function f1T? in the quark-diquark spectator model, which can be fitted from transverse SIDIS data with a negative sign. The sign of h1? for d quark is different in spectator model and in MIT bag model, while it is the same for u quark.

  23. From Boer’s talk at SIR2005

  24. Fermilab E866 Experiment Towell et al., Phys.Rev. D64 (2001) 052002

  25. Dimuon Mass Distribution Proton and Deuterium Target Drell-Yan events (for sea asymmetry analysis) High: 4.5<M<9.0, M>10.7; 141k Intermediate: 4.3<M<8.8, M>10.8; 128k Low: 4.0<M<8.8; 89k Towell et al., Phys.Rev. D64 (2001) 052002

  26. The x1 and x2 Coverage High Mass Intermediate Mass Low mass Towell et al., Phys.Rev. D64 (2001) 052002

  27. Angular Distribution of E866 p-Cu Data • J/: = 0.069±0.004±0.08 • Drell-Yan (M=4~7 GeV): • = 0.98±0.04 • T.H. Chang et al., PRL91, 211801 (2003) • (1s),(2s+3s): plotted against PT and xP. • Drell-Yan: • (M=8.1~8.45,11.1~15.0 GeV) • =1.008±0.016±0.020 • C.N. Brown et al., PRL86, 2529 (2001)

  28. What is interesting? • Is there any cos2 asymmetry in proton induced Drell-Yan? • The behavior of cos2 asymmetry () at very high PT. • The flavor dependence of the angular distribution by comparing the data with proton and deuterium target. • Others: the asymmetry at J/ resonance…

  29. E866 Dimuon  Distribution Drell-Yan Events J/ Events Not corrected for acceptance yet

  30. Drell-Yan Data F Distribution 2 < PT < 3 GeV/c 1 < PT < 2 GeV/c Not corrected for acceptance yet

  31. Summary • Large cos2 azimuthal asymmetry has been observed in unpolarized pion-induced Drell-Yan • The are a few possible explanations including the non-zero Boer-Mulders function h1? , which may be related to Sivers function f1T?. • The unpolarized proton-induced Drell-Yan may provide some useful information

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