1 Possible Additional Measurements in E906 Azimuthal angular distributions of Drell-Yan and J/ Ψ p+d/p+p ratios for J/ Ψ production Nuclear effects of open-charm production Recent E866 results  E906 prospect Jen-Chieh Peng E906 Collaboration Meeting Fermilab, June 20-21, 2008 University of Illinois at Urbana-Champaign Outline

2 Three parton distributions describing quark’s transverse momentum and/or transverse spin 1) Transversity distribution function 2) Sivers function 3) Boer-Mulders function

3 Unpolarized Polarized target Polarzied beam and target S L and S T : Target Polarizations; λe: Beam Polarization Sivers Transversity Boer-Mulders TMD and transversity PDFs are probed in Semi-Inclusive DIS

4 TMD and transversity PDFs are also probed in Drell-Yan

5 Drell-Yan decay angular distributions Collins-Soper frame Θ and Φ are the decay polar and azimuthal angles of the μ + in the dilepton rest-frame A general expression for Drell-Yan decay angular distributions: In general :

6 Decay Angular Distribution of “Naïve” Drell-Yan Data from Fermilab E772 McGaughey, Moss, JCP ; Annu. Rev. Nucl. Part. Sci. 49 (1999) 217 (hep/ph )

7 Drell-Yan decay angular distributions Collins-Soper frame Θ and Φ are the decay polar and azimuthal angles of the μ + in the dilepton rest-frame A general expression for Drell-Yan decay angular distributions:

8 Decay angular distributions in pion-induced Drell-Yan Z. Phys. 37 (1988) 545 Dashed curves are from pQCD calculations NA10 π - +W

9 Decay angular distributions in pion-induced Drell-Yan Data from NA10 (Z. Phys. 37 (1988) 545) Is the Lam-Tung relation violated? 140 GeV/c194 GeV/c286 GeV/c

10 Decay angular distributions in pion-induced Drell-Yan Phys. Rev. D 39 (1989) 92 E615 Data 252 GeV π - + W

11 Boer-Mulders function h 1 ┴  1 =0.47, M C =2.3 GeV Boer, PRD 60 (1999) ν>0 implies valence BM functions for pion and nucleon have same signs

12 With Boer-Mulders function h 1 ┴ : ν(π - W  µ + µ - X)~ [valence h 1 ┴ (π)] * [valence h 1 ┴ (p)] ν(pd  µ+µ-X)~ [valence h 1 ┴ (p)] * [sea h 1 ┴ (p)] Azimuthal cos2Φ Distribution in p+d Drell-Yan Lingyan Zhu et al., PRL 99 (2007) ν>0 suggests same sign for the valence and sea BM functions

13 Extraction of Boer-Mulders functions from p+d Drell-Yan (B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv: ) c

14 Extraction of Boer-Mulders functions from p+d Drell-Yan (B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv: ) Fit to the p+d Drell-Yan data Satisfy the positivity bound

15 Extraction of Boer-Mulders functions from p+d Drell-Yan It seems unlikely that p+d data alone can determine the flavor structure of BM functions! Additional Drell-Yan data are needed (B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv: ) c Prediction on the p+p Drell-Yan

16 Angular Distribution in E866 p+p/p+d Drell-Yan p+p and p+d Drell-Yan show similar angular distributions. Should be analysed togther for better constraints on BM. Preliminary P T (GeV/c)

17 What more could be done in Fermilab E906? 1) Boer-Mulders functions can be measured at larger x 2) Study Nuclear effects of Boer-Mulders functions 3) Measure azimuthal angular dependence of J/ Ψ decay

18 Nuclear modification of spin-dependent PDF? Bentz, Cloet et al., arXiv: EMC effect for g 1 (x) Very difficult to measure !

19 Nuclear Dependence of the Boer-Mulders function? NA10 Z. Phys. C37, 545 (1988) Open: Deuterium Solid: Tungsten We might have a better measurement of the nuclear effects of the Boer-Mulders function in E906

20 Nuclear effects of J/Ψ and Ψ’ and open-charm p + A → J/Ψ or Ψ’ at s 1/2 = 38.8 GeV α(x F ) is largely the same for J/Ψ and Ψ’ ‘Universal’ behavior for α(p T ) (similar for J/Ψ, Ψ’)

21 Nuclear effects of open-charm production p + A → D + x at s 1/2 = 38.8 GeV E789 open-aperture, silicon vertex + dihadron detection h + h - mass spectrum (after vertex cut) D 0 → K - π + No nuclear effect for D production (at xF ~ 0) Need to extend the measurements to large x F region

22 Targets (Z = -24.0”) 0 = Empty 1 = “ Copper 2 = “ Beryllium 3 = “ Copper High-p T Single Muon Trigger Single muon measurement in E866 p+A Thesis of Stephen Klinksiek High-p T single muon events are dominated by D-meson decays

23 Preliminary E866 results on the single-muon (open-charm) nuclear-dependence Cu / Be Ratios P T (GeV/C)Rapidity (y) P T and X F (y) dependences have similar trend as J/Ψ

24 A universal x F -dependence in p-A hadron production? Kopeliovich et al., hep-ph/ Data cover energy range from 70 to 400 GeV X F -scaling for a broad energy range  nuclear shadowing alone can not explain the data Do open-charm and quarkonium also follow the same trend?

25 Gluon distributions in proton versus neutron? Lingyan Zhu et al., PRL, 100 (2008) (arXiv: ) Gluon distributions in proton and neutron are very similar

26 How large is the EMC effect for deuteron? This can not be extracted from DIS or Drell-Yan using σ(p+d)/2σ(p+p)

27 Constraints on the gluon distributions in nuclei from quarkonium A-dependence p + A → J/Ψ or Ψ’ at s 1/2 = 38.8 GeV α(x F ) is practically flat over the region -0,1 < xF < 0.3 The flat nuclear dependence for gluon distributions over < x < 0.12 can put constraints on some parametrizations Arleo, arXiv: Additional constraints could be provided from E906 A-dependence measurement

28 Future tasks Monte-Carlo simulations for the acceptance and count rates for these measurements (need to have the updated E906 M-C code). Triggers required for these measurements. Other additional physics in E906.

29 Quark-diquark Models for Boer-Mulders Function h 1 ┴ Initial-state gluon interaction can produce nonzero h 1 ┴ for the proton in the quark-scalar diquark model. In this model, h 1 ┴ =f 1T ┴. Boer,Brodsky&Hwang, PRD67,054003(2003). Recent diquark-spectator model Gamberg, Goldstein & Schlegel, arXiv:

30 Pion Boer-Mulders Function Final-state interaction with one gluon exchange can produce nonzero h 1 ┴ 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/ Pion-cloud model gives proton sea-quark BM

31 Comparison of data and simulation Blue: simulation Red: data (dset8)