# Presentation: 125598

## Cos2φ Asymmetry in p+d/p+p Drell-Yan  

- Lingyan Zhu
- University of Illinois at Urbana-Champaign
- FNAL E866/Nusea Collaboration

- Brookhaven National Lab

- Feb 13,2007

## Sea Asymmetry from Drell-Yan

- Towell et al., Phys.Rev. D64 (2001) 052002

- Drell-Yan enables us to measured dbar/ubar asymmetry precisely.

- Brookhaven National Lab

- Feb 13,2007

## 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

- Brookhaven National Lab

- Feb 13,2007

## First-order QCD Corrections to Drell-Yan

- Conway et al., PRD39,92(1989)

-  Increase the overall cross section by a K-factor~2.
- The Lam-Tung relation still hold (in any reference frame for massless quarks), reflecting the spin-1/2 nature of the quarks. Lam & Tung, PRD21,2712(1980)
-  (Analog to Callan-Gross relation in DIS)
- The NLO correction at *O*(s2) to the angular distribution is small.           Mirkes & Ohnemus, PRD51,,4891(1995)

- The QCD correction to the angular distribution is small.

- Brookhaven National Lab

- Feb 13,2007

## Violation of the Lam-Tung Relation

- Conway et al., PRD39,92(1989)

- E615 at Fermilab: 252 GeV π- + W

- NA10 at CERN:
- 140/194 GeV π- + W, 286 GeV π- + W/d
- Z. Phys. C37, 545 (1988)

- 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)
- Lam-Tung relation not affected by lowest order QCD correction even at small QT.
- Boer & Wogelsang, hep-ph/0604177

- Brookhaven National Lab

- Feb 13,2007

## Angular Distribution in the W Drell-Yan Process

- Conway et al., PRD39,92(1989)

- E615 at Fermilab: 252 GeV π- + W

- Angular Distribution in the W Drell-Yan Process

- Brookhaven National Lab

- Feb 13,2007

## Azimuthal cos2φ Distribution in the W Drell-Yan

- Conway et al., PRD39,92(1989)

- E615 at Fermilab: 252 GeV π- + W

- Azimuthal cos2φ Distribution in the W Drell-Yan

- NA10 at CERN: 140/194/286 GeV π- + W  Z. Phys. C37, 545 (1988)

- Brookhaven National Lab

- Feb 13,2007

## Possible Explanations for the cos2φ Asymmetry

- The _high twist_ effect.
- Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994).
- The _nuclear_ distortion of hadronic projectile wavefunction, typically a spin-orbit effect occurring on the nuclear surface.
- Bianconi & Radici, JPG31,645(2005).
- The spin correlation due to nontrival _QCD vacuum._
- Brandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993); ...
- The hadronic effect due to non-zero _Boer-Mulders function_ h1┴ .
- Boer, PRD60,014012(1999); ...

- Brookhaven National Lab

- Feb 13,2007

## High Twist Effect?

- High  twist effect leads to  =-1 for low mass as x 1.         Berger & Brodsky, PRL42, 940 (1979); Berger, ZPC4,289(1980)
- High twist effect in terms of pion bound state effect: Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994)

- High twist in  terms of pion bound state effect is not big enough.

- Brookhaven National Lab

- Feb 13,2007

## Nuclear Effect?

- NA10 Z. Phys. C37, 545 (1988)

- Open: Deuterium
- Solid: Tungsten

- Nuclear effect should not  be the dominant contribution.

- Brookhaven National Lab

- Feb 13,2007

## 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&Uermann, hep-ph/0605234
- This vacuum effect should be flavor blind.

- 0=0.17
- mT=1.5

- Brookhaven National Lab

- Feb 13,2007

## Leading-Twist Parton Distribution Functions

- Survive kT integration

- kT - dependent, T-odd

- kT - dependent, T-even

- Brookhaven National Lab

- Feb 13,2007

## The Large-x Behavior of the PDFs

- Survive k┴ integration

- k┴-dependent, T-odd

- Brodsky & Yuan, hep-ph/0610236.

- k┴ - dependent, T-even

- Brookhaven National Lab

- Feb 13,2007

## Boer-Mulders Function h1┴ 

- An spin-correlation approach in terms of h1┴ can fit the NA10 data at 194 GeV.   Boer, PRD60,014012(1999)
- On the base of quite general arguments, for |qT|<<Q(=m ),
- Salvo,hep-ph/0407208.

- 1=0.5
- mC=2.3
- T=CH=1

- Brookhaven National Lab

- Feb 13,2007

## Models for Boer-Mulders Function h1┴ 

- 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).
- Twist 2 (as well as the kinematic twist 4) contribution in a parton-spectator framework  Gamberg&Goldstein, hep-ph/0506127.

- Brookhaven National Lab

- Feb 13,2007

## Pion Boer-Mulders Function 

- 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).
- The quark-spectator-antiquark model with effective pion-quark-antiquark coupling as a dipole form factor Lu & Ma, hep-ph/0504184

- Brookhaven National Lab

- Feb 13,2007

## Sivers Function 

- 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)

- Sivers Function

- Brookhaven National Lab

- Feb 13,2007

## Models for Sivers Function f1T┴

- 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).

- -

- -

- These calculations are before HERMES’  transverse data .

-  scalar

-  axial-vector

- Brookhaven National Lab

- Feb 13,2007

## Sivers Function Extraction from HERMES Data

- Fits to the Hermes data

- “Prediction” of the Compass data

- Vogelsang and Yuan, Phys.Rev.D72(2005)054028 [hep-ph/0507266]

- Striking flavor dependence of the Sivers function

- Brookhaven National Lab

- Feb 13,2007

## Comparing Sivers Functions from HERMES

- Ref.[20] M.Anselmino *et al*, Phys.Rev.D72(2005)094007[hep-ph/0507181]  Ref.[21] W.Vogelsang & F.Yuan, Phys.Rev.D72(2005)054028[hep-ph/0507266]
- Ref.[23] J.C.Collins *et al*, hep-ph/0510342

- Satisfactory agreement between different models to fit HERMS data.

- M.Anselmino *et al*, hep-ph/0511017

- Brookhaven National Lab

- Feb 13,2007

## An Intuitive Explanation of Sivers Asymmetry 

- An Intuitive Explanation of Sivers Asymmetry

- M. Burkardt, Phys. Rev. D66(2002)114005[hep-ph/0209179].

- Кu=1.67
- Кd=-2.03

- Attractive FSIf1T┴,q Кq  <0 [+Кu Кd<0]  f1T┴,u f1T┴,d <0

- Attractive FSI

- The quark distribution in transverse polarized nucleon is deformed because the superposition of translational and orbital motion misleads the photons in the *x*.

- Brookhaven National Lab

- Feb 13,2007

## Vacuum Contribution to Sivers Function f1T┴

- Vacuum Contribution to Sivers Function f1T┴

- Sizable instanton-induced QCD vacuum contribution to the Sivers function, adopting MIT bag model for the quark wave functions.
- Cherednikov, D_['](http://arxiv.org/find/hep-ph/1/au:+DAlesio_U/0/1/0/all/0/1)_Alesio, Kochelev & Murgia Phys.Lett.B642:39-47,2006    [hep-ph/0606238].

- thin:
- instanton
**thick:**
**one-gluon**

- thin:
- HERMES
**thick:**
**total**

- Brookhaven National Lab

- Feb 13,2007

## Comparing Boer-Mulders Functions from Models

- (a)MIT bag model: F. Yuan, Phys. Lett. B575,45(2003).
- (b)Spectator model with axial-vector diquark: Bacchetta, Schaefer & Yang, Phys. Lett. B578,109(2004).
- (c)Large-NC limit, P.V. Pobylitsa, hep-ph/0301236

- Knowledge of the Boer-Mulders functions is very poor.

- Z. Lu, B.Q. Ma and I. schmidt, Phys. Lett. B639(2006)494.

- Brookhaven National Lab

- Feb 13,2007

## Unpolarized Semi-Inclusive DIS

- _TWIST-2_

- _Cahn Effect_
- QED Modulation of f1D1 term due to intrinsic transverse momentum.

- Anselmino et al., PRD71(2005) 074006 [hep-ph/0501196].

- Add to 2(1-y+y2/2):

- H. Avakian, Z.-E.Meziani,K.Joo and B.Seitz, JLab proposal PR12-06-112

- Brookhaven National Lab

- Feb 13,2007

## FNAL E866/NuSea Experiment

- Completed Data analysis:
- dbar/ubar sea asymmetry
- Drell-Yan cross section
- lambda for J/Ψ production
- lambda for upsilon production

- Brookhaven National Lab

- Feb 13,2007

## Drell-Yan Cross Section from E866

- J.C.Webb et al., hep-ex/0302019.

- Brookhaven National Lab

- Feb 13,2007

## 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)

- Brookhaven National Lab

- Feb 13,2007

## Dimuon Mass Distribution

- Data used for cos2φ analysis:
- High Mass: dset7-39k (+ polarity)
- 	      dset8-85k (+ polarity)
- 	      dset11-25k (- polarity)
- Low Mass:  dset5-68k (+ polarity)

- Towell et al., Phys.Rev. D64 (2001) 052002

- Target: Proton, Deuterium

- Brookhaven National Lab

- Feb 13,2007

## Comparison of data and simulation

- Blue: simulation
- Red: data
- (dset8)

- Brookhaven National Lab

- Feb 13,2007

## Azimuthal cos2Φ Distribution in p+d Drell-Yan

- ν(π-Wμ+μ-X)~ valence h1┴(π)  * valence h1┴(p)
- ν(pdμ+μ-X)~ valence h1┴(p) * sea h1┴(p)

- Azimuthal cos2Φ Distribution in p+d Drell-Yan

- L.Y. Zhu,J.C. Peng, P. Reimer et al., hep-ex/0609005.

- Brookhaven National Lab

- Feb 13,2007

## Full Angular Distribution in p+d Drell-Yan

- L.Y. Zhu,J.C. Peng, P. Reimer et al., hep-ex/0609005.

- No significant azimuthal asymmetry in p+d Drell-Yan.

- Brookhaven National Lab

- Feb 13,2007

## Angular Distribution in E866 p+p/p+d Drell-Yan

-  p+p and p+d Drell-Yan show similar angular distribution.

- Preliminary

- Preliminary

- Preliminary

- Preliminary

**P****T**** (GeV/c)**

- Brookhaven National Lab

- Feb 13,2007

## Modeling Sea Boer-Mulders Functions 

- Modeling Sea Boer-Mulders Functions

- Z. Lu, B.-Q. Ma and I. Schmidt, hep-ph/0701255
- Meson-baryon fluctuation model:
- Predictions depend on the choice of
- valence Boer-Mulders functions:
- I--scalar diquark;
- II—scalar & vector diquark
- Group led by L. Gamburg and G. Goldstein
- Two possible contributions to sea
- from the gauge link.

- p(I)
****d(I)
****d(II)
- p(II)

- Probing the sea Boer-Mulders functions may constrain the valence ones.

- Brookhaven National Lab

- Feb 13,2007

## Summary

- Large cos2 azimuthal asymmetry has been observed in unpolarized -induced Drell-Yan.
- The are a few possible explanations including the non-trivial vacuum effect and the non-zero Boer-Mulders function . The latter is related to the Sivers 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 availble from the future experiments at FNAL, RHIC with proton beam, COMPASS with pion beam and especially GSI with anti-proton beam, complementary to the SIDIS data at JLab and HERMES.

- Brookhaven National Lab

- Feb 13,2007