1. Angular Distribution in Unpolarized Proton-induced Drell-Yan Process
Lingyan Zhu
Jen-Chieh Peng
University of Illinois at Urbana-Champaign
Paul Reimer
Argonne National Laboratory
FNAL E866/Nusea Collaboration
Apr 12, 2008
APS Meeting at St. Louis, MO

2. Proton-induced Drell-Yan Process
Towell et al., Phys.Rev. D64 (2001)
Apr 12, 2008
APS meeting at St. Louis, MO

3. 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
Apr 12, 2008
APS meeting at St. Louis, MO

4. APS meeting at St. Louis, MO
QCD Corrections
The cross section is increased by a factor of ~2.
The Lam-Tung relation holds in any reference frame. Lam & Tung, PRD21,2712(1980)
The NLO correction at O(s2) to the angular distribution is small Mirkes & Ohnemus, PRD51,,4891(1995)
The Lam-Tung relation not affected by QCD resummation effects at small QT. Small corrections to lambda and nu in the Collins-Soper frame.
Boer&Wogelsang, PRD74,014006(2006)
Lam-Tung relation: a unique opportunity to test QCD-improved quark model.
Apr 12, 2008
APS meeting at St. Louis, MO

5. Violation of the Lam-Tung Relation
E615 at Fermilab: 252 GeV π- + W
Conway et al., PRD39,92(1989)
Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994)
Apr 12, 2008
APS meeting at St. Louis, MO

6. cos2φ Distribution in the W Drell-Yan
Conway et al., PRD39,92(1989)
E615 at Fermilab: 252 GeV π- + W
NA10 at CERN: 140/194/286 GeV π- + W Z. Phys. C37, 545 (1988)
Apr 12, 2008
APS meeting at St. Louis, MO

7. Nuclear Effect? NA10 Z. Phys. C37, 545 (1988) Open: Deuterium
Solid: Tungsten
Nuclear effect seems not to be the dominant contribution.
Apr 12, 2008
APS meeting at St. Louis, MO

8. APS meeting at St. Louis, MO
QCD Vacuum Effect
The factorization-breaking spin correlation due to nontrivial QCD vacuum may fit the NA10 data at 194 GeV
Brandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993)
The helicity flip in the instanton-induced contribution may lead to nontrivial vacuum and violation of the Lam-Tung relation.
Boer,Brandenburg,Nachtmann&Utermann, EPC40,55(2005).
Brandenburg,Ringwald&Utermann, NPB754,107(2006).
This vacuum effect should be flavor blind.
0=0.17
mT=1.5
Apr 12, 2008
APS meeting at St. Louis, MO

9. Leading-Twist Parton Distribution Functions
Survive kT integration
kT - dependent, T-even
kT - dependent, T-odd
Apr 12, 2008
APS meeting at St. Louis, MO

10. Boer-Mulders Function h1┴
An spin-correlation approach in terms of h1┴ can fit the NA10 data at 194 GeV. Boer, PRD60,014012(1999)
There are different models to calculate the Boer-Mulders function in
proton and pion.
Boer,Brodsky&Hwang, PRD67,054003(2003);
Gamberg&Goldstein, PLB650,362(2007);
Lu&Ma, PRD70,094044(2004); PLB615,200(2005)
1=0.5
mC=2.3
T=CH=1
Apr 12, 2008
APS meeting at St. Louis, MO

11. Full Angular Distribution in p+d Drell-Yan
L.Y. Zhu,J.C. Peng, P. Reimer et al., PRL99,082301(2007).
No significant azimuthal asymmetry in p+d Drell-Yan.
Apr 12, 2008
APS meeting at St. Louis, MO

12. Azimuthal cos2Φ Distribution in p+d Drell-Yan
L.Y. Zhu,J.C. Peng, P. Reimer et al., PRL99,082301(2007).
With Boer-Mulders function h1┴:
ν(π-Wµ+µ-X)~ valence h1┴(π) * valence h1┴(p)
ν(pdµ+µ-X)~ valence h1┴(p) * sea h1┴(p)
Apr 12, 2008
APS meeting at St. Louis, MO

13. Angular Distribution in E866 p+p/p+d Drell-Yan
Preliminary
Preliminary
Preliminary
Preliminary
PT (GeV/c)
p+p and p+d Drell-Yan show similar angular distribution.
Apr 12, 2008
APS meeting at St. Louis, MO

14. APS meeting at St. Louis, MO
Summary
Large cos2 azimuthal asymmetry has been observed in unpolarized -induced Drell-Yan. The Lam-Tung relation is violated.
The are a few possible explanations including the non-trivial vacuum effect and the non-zero TMD Boer-Mulders function . The unpolarized p-induced Drell-Yan data show only percent-level cos2φ azimuthal asymmetry. This may disfavor the flavor blind explanation such as vacuum effect.
More data on unpolarized Drell-Yan will be available from the future experiment E906 at FNAL with proton beam, and GSI with anti-proton beam, as well as some SIDIS data from JLab and HERMES.
Apr 12, 2008
APS meeting at St. Louis, MO

15. APS meeting at St. Louis, MO
Apr 12, 2008
APS meeting at St. Louis, MO