1 / 44

Gary R. Goldstein Tufts University

Azimuthal Asymmetries in Unpolarized N+anti-N Drell-Yan Processes and Transversity-odd Distributions. Gary R. Goldstein Tufts University With L. Gamberg (Penn.State -Berks) & K. Oganessyan (formerly Frascati). Abstract. Drell-Yan unpolarized processes display large azimuthal asymmetries .

yvonnejackson
Download Presentation

Gary R. Goldstein Tufts University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Azimuthal Asymmetries in Unpolarized N+anti-N Drell-Yan Processes and Transversity-odd Distributions Gary R. Goldstein Tufts University With L. Gamberg (Penn.State -Berks) & K. Oganessyan (formerly Frascati) QCD-N2006 Frascati G.R.Goldstein

  2. Abstract Drell-Yan unpolarized processes display largeazimuthal asymmetries. One such asymmetry, cos(2), is directly related to the leading twist “transversity-odd” distribution h1(x,kT). We use a model developed for semi-inclusive deep inelastic scattering that determines the “Sivers function” f1T (x,kT) to predict the Drell-Yan asymmetry  as a function of Q2, QT and either x or xFor a new variable, . The resulting predictions include a non-leading twist contribution from spin-averaged distributions that measurably affect lower energy results. QCD-N2006 Frascati G.R.Goldstein

  3. Outline • Transversity • Short history • Helicity flip, chirality, phases & k • SIDIS • Asymmetries: SSA & azimuthal • Rescattering & leading twist contributions • Drell-Yan • Transversity-odd distribution functions • N (& ) distributions • cos2 asymmetry • Conclusions QCD-N2006 Frascati G.R.Goldstein

  4. From Frank Close at Dalitz Memorial Meeting Oxford, June 3, 2006 Email from G Rajasekran on origin of quark model: physics/0602131 During one of the lectures, Dalitz questioned him about the triplets. Why is he ignoring them? Gell-Mann managed to evade it, inspite of Dalitz's repeated questioning. If Gell-Mann had answered the question directly, quarks would have been born in Bangalore in 1961 instead of having to wait for another three years...." QCD-N2006 Frascati G.R.Goldstein

  5. Les Houchcs 1965 QCD-N2006 Frascati G.R.Goldstein

  6. O F.Close: What Dalitz had proposed Les Houches 1965 L=1 O O O L=2 O O QCD-N2006 Frascati G.R.Goldstein

  7. PDG 2006 !!! 1720 1710 1690 1700 1690 1550 1520 1520 1405 O L=1 O O QCD-N2006 Frascati G.R.Goldstein

  8. Transversity - some history • 2-body scattering amps - Exclusive hadronic • fa,b;c,d(s,t) with spin projections a,b;c,d • GPD’s bring back 2-body picture • What spin frame leads to simplest description of theory or data? Amps to observables? • helicity has easy relativistic covariance - theory • states of S·p, e.g. |+1/2 ,|-1/2 , etc. • transversity: eigenstates of S·(p1p2) | 1/2 )T = {|+1/2 (i)|-1/2}/√2 for spin 1/2, etc. Especially for relating to single spin asymmetries - only S·n where interference or imaginary parts are relevant QCD-N2006 Frascati G.R.Goldstein

  9. Transversity & simplicity • states of {S·(p1p2)} or {S·(p1 p2)} are transversity normal to or parallel to scattering plane non-diagonal in helicity basis • Spin 1: | 1)T = {|+1> 2 |0> + |-1>}/2 | 0)T = {|+1> - |-1>}/ 2 • photon: | 1)T = {|+1> + |-1>}/2 linear polzn normal to plane | 0)T = {|+1> - |-1>}/2 linear polzn parallel to plane useful in on-shell photoproduction dynamics GRG & M.J.Moravcsik, Ann.Phys.98 (1976) 128. also in other context: Gault, GRG, Jones, NC27 (1975) 174. early: Cohen-Tannoudji, Morel, Navelet, Ann.Phys.46 (1968) 239.GRG & Moravcsik & Arash 1980’s QCD-N2006 Frascati G.R.Goldstein

  10. Phases & SSA • Single Spin Asymmetries (SSA) in 2-body • Parity allows only <S·n> non-zero for any single spinning particle. Requires some helicity flip or chirality flip for m=0 quarks & phase. <S·n>f*ab,cd[·n]dd’fab,cd’  Im[f*ab,c+ fab,c-] for particle D’s SSA n requires some p2transverse to p1 (at quark level? m=0 & PQCD conserve helicity no SSA) • Inclusive A+B->X+D: sum&∫ over all C particles & relate to A+B+anti-D forward elastic. GRG & J.F.Owens (76) np1 p2 p2  p1 QCD-N2006 Frascati G.R.Goldstein

  11. Azimuthal asymmetries - kinematics • Why similar to spin asymmetries? • Need plane established (P1P2)  transverse P • Need azimuthal angle relative to 1st plane, i.e. 2nd plane • via fragmentation or decay or pair production • How does orientation information get transferred from 1st plane to 2nd plane? Dynamical question. Polarized intermediate particles &/or plane dependent observables - leading twist (&kinematic mass/Q) or non-leading • SIDIS & Drell-Yan involve off-shell photons - like massive vector particles with  (& longitudinal) polarization via QED QCD-N2006 Frascati G.R.Goldstein

  12. SSA & AzAs dynamics:require loops & k • <S·n> f*AB,CD[·n]DD’fAB,CD’ helicity basis or in transversity basis: {|fAB,C(+)|2 - |fAB,C(-)|2} • Imaginary part or phase requires beyond tree level in field theory • PQCD efforts to explain polarized hyperons via s-quark polzn • What is tree level in soft physics &/or “effective” field theory? • Mixing PQCD & soft physics • Helicity or chirality flip requires a flipping interaction (m≠0,…) & non-zero transverse momentum of participants or k’s QCD-N2006 Frascati G.R.Goldstein

  13. Brodsky, Hwang & Schmidt provided non-trivial model calculation Final state corrections to tree-level DISf1T(x,p2) Sivers & SSA LG&GG: same FSI contribute to other SSA’s & f1T(x,p2) = + h1(x,p2) Boer-Mulders Need SIDIS or D-Y to make functions experimentally accessible in asymmetry or polarization Brodsky, Hwang, Schmidt PLB 2002 Collins PLB 2002; Ji & Yuan PLB 2002 Goldstein & Gamberg ICHEP 2002 Gamberg, Goldstein, Oganessyan PRD 2003-5 &hep-ph QCD-N2006 Frascati G.R.Goldstein

  14. h1 • h1(x,p2) is “Transversity-odd” distribution -(Boer-Mulders) probability of finding quark with non-zero transversity in unpolarized hadron (it is P-even) • Vanishes at tree level in T-conserving models, as in spectator diquark model e.g. N quark+diquark where q is struck quark (like ordinary decay amps - final state interactions are essential - no T violation) • Simple quark-diquark or spectator picture is starting point for getting at properties to expect & observable consequences QCD-N2006 Frascati G.R.Goldstein

  15. SIDIS asymmetries In model yellow inclusive blob becomes diquark - scalar for simplicity (ud flavor) leaving u-quark being struck by q 1+ diquarks include uu (& dd) allowing for d-quark struck - 2 couplings Note: diquark actually has structure also - diq-g-diq form factors alternate method *+Nq+diq SSA CM helicity amps then light-cone limit (Dharmaratna&GG (92)) QCD-N2006 Frascati G.R.Goldstein

  16. Brodsky, Hwang, Schmidt rescattering Sivers fn, Collins =1 QCD-N2006 Frascati G.R.Goldstein

  17. Model calculation QCD-N2006 Frascati G.R.Goldstein

  18. Calculating h1(x,kT) QCD-N2006 Frascati G.R.Goldstein

  19. Integration results Spin independent tree level: Transversity T-odd TMD: ( .. k.jfactoron both sides) QCD-N2006 Frascati G.R.Goldstein

  20. Regularization • SSA’s & asymmetries involve moments of distribution & fragmentation functions e.g. h1(1)(x) = ∫ d2k k2 h1(x, k2) which would diverge without k2 damping QCD-N2006 Frascati G.R.Goldstein

  21. Transverse momentum hadronic tensor QCD-N2006 Frascati G.R.Goldstein

  22. h1(x,k) calculation with Gaussian h 1/(m2-k2)=(1-x)/(kT2) result of p->q+diq kinematics h1(x,k)= f1T (x,k) in diquark model Gamberg, Goldstein, Oganessyan PRD 2003 QCD-N2006 Frascati G.R.Goldstein

  23. Drell-Yan coordinates lepton CM frame defines plane tilted at  rel.t. hadron plane of P1 &P2 Coordinates? z is direction of q in initial CM frame or x is direction along qT from initial cm boost (Collins-Soper frame) or … y x l’ P2  P1 z  l QCD-N2006 Frascati G.R.Goldstein

  24. Drell-Yan Cross Sections see early papers ‘70’s Collins&Soper (1977) effects of transverse momenta -> ,, non-zero Boer, Mulders, Teryaev (1998), Boer (1999) & D.Boer, S.J. Brodsky & D.S. Hwang (2002) Unpolarized pair of hadrons  l + l’ + X  involves transversity at leading twist QCD-N2006 Frascati G.R.Goldstein

  25. D-Y angular dependent  How are angular asymmetries calculated? q+anti-q annihilation (& q+anti-q + gluons). Cross sections require convoluting hadron->u with hadron->anti-u distributions.  is related to T-odd distributions at leading twist (D. Boer). QCD-N2006 Frascati G.R.Goldstein

  26. Failure of Lam-Tung relation QCD-N2006 Frascati G.R.Goldstein

  27. AzAs: h1(1) •H1(1) cos2 Both distribution & fragmentation calculated in spectator models with gaussian k π π +h.c. QCD-N2006 Frascati G.R.Goldstein

  28. From SIDIS to Drell-Yan - analogous calculations Beam (π, p, p, …) QCD-N2006 Frascati G.R.Goldstein

  29. Azimuthal asymmetry Integrate over all quark transverse momenta. (p)+pl+l- X is in process; p+anti-p is calculated for various s. x direction is QT direction Notation of Boer, Mulders, Teryaev & Boer, Brodsky, Hwang QCD-N2006 Frascati G.R.Goldstein

  30. QT dependences General form: expectation of a hadronic tensor with distributions from quark model of incoming particles • Asymmetry must vanish as QT0 ; no 1st plane orientation in forward limit of initial state. • What is role of quark spin? • In lepton rest frame or q+q (CM) “fat” photon produced. • Whether q & q polarized or not, photon’s spin tensor (T & L) is fixed by QED. • Unpolarized q+q defines a plane via QT & tensor behaves ~ (QT2 / Q2)2 . • Transversely polarized q+q have ST1 ST2 tensor structure to combine with kT & pT (2 planes) (or 2 planes w/o spins, but higher twist) QCD-N2006 Frascati G.R.Goldstein

  31. Non-leading contributions Spin dependent leading part ~ QT2 for small QT2 / Q2 Non-leading, spin independent part ~ extra QT2 Collins & Soper ‘77 defined tensor A2 = B = (2kTx pTx  kTpT) / M2 QCD-N2006 Frascati G.R.Goldstein

  32. convolutions There will be the tensor B and azimuthal dependence, crucial for transmitting plane orientation information. Integrate numerically to obtain convoluted functions depending on x, mee, QT (and s). Note x ≈ mee2/xs for s >> mee2 >>QT2. Convolutions of h’s have extra factors of S at appropriate scale compared to f’s. But f’s in numerator have QT2relative to h’s. QCD-N2006 Frascati G.R.Goldstein

  33. Drell-Yan kinematics Asymmetry  is function of 3 variables: x, √Q2 =m ,qT (after separating sin2 cos2 dependence) Want to obtain  integrated over 2 variables to c.f. experiments. How to do this while keeping “symmetry” x1, x2 Using xFtreats x1, x2 symmetrically, but different range vs. q. Use = xF/2(1-) from -1/2 to +1/2 QCD-N2006 Frascati G.R.Goldstein

  34. AzAs function Insert convolutions into asymmetry expression: Obtained for range of x, mee, QT (and s). Choose kinematic ranges of Conway, et al. (FNAL fixed target π p) applied to p p . Sum over their (limited) ranges to obtain (x), (mee2), (QT) . QCD-N2006 Frascati G.R.Goldstein

  35. (QT2) leading h1 contribution Calculated s50 Gev2 - lower kinematic range than Conway, et al. E615. Antiproton beam vs. π Very similar to Boer, Brodsky, Hwang But gaussian supressed Data for π-p at s=500 GeV2 E615 f f part is at most 10% At higher s 500 Gev2 with comparable range curve decreases a bit f f part can be 10 - 15% of this for some values of 3 variables. QCD-N2006 Frascati G.R.Goldstein

  36. Including qT2 kinematic corrections Values lower ~10% QCD-N2006 Frascati G.R.Goldstein

  37. (m) leading h1 contribution (s=50 GeV2) Data for π-p at s=500 GeV2 E615 QCD-N2006 Frascati G.R.Goldstein

  38. (Q2+QT2) vs.  vs. x x = 0.9 x = 0.8 x = 0.7 x = 0.6 x = 0.5 x = 0.4 x = 0.3 x = 0.2 x = 0.1 QCD-N2006 Frascati G.R.Goldstein

  39. () s=50 GeV2 () Blue -leading Red - with non-leading  QCD-N2006 Frascati G.R.Goldstein

  40.  versus x1s=50 GeV2 Leading twist only Including non-leading QCD-N2006 Frascati G.R.Goldstein

  41.  vs. xF s=50 GeV2 QCD-N2006 Frascati G.R.Goldstein

  42. p+p Drell-Yan model Need anti-quark from sea to annihilate valence quark pganti-q + q Fermilab E866 ppl+l- X asymmetry QCD-N2006 Frascati G.R.Goldstein

  43. Summary& Conclusions • Transversity is important for full understanding of hadron spin composition. Accessed experimentally via SIDIS & Drell-Yan with SSA’s & azimuthal asymmetries. • Require helicity flips & loops; combinations of factorized soft-hadronic & PQCD. • BHS rescattering is mechanism for generating TMD’s at leading twist that can be measured via SSA’s & AzAs’s. • quark-diquark (S=0) model with gaussian regulators allows simple calculations to demonstrate existence & size of interesting TMD’s and thus SSA’s & AzAs’s. QCD-N2006 Frascati G.R.Goldstein

  44. Summary (cont’d) • Example considered: “Transversity-odd” contributions to cos2 in D-Y compared to non-leading spin independent piece (Collins&Soper). • Does data support “Transversity-odd” TMD? Large effect in π+p at hi s makes this very plausible. Cleanest determination would be AzAs data on anti-p+p (GSI - PAX?). p+p data also. • Improvements: • S=1 diquark is I=1 uu flavor  p->d+diq • better starting model (2-body constraints are limiting) • Questions: • How do Transversity-odd TMD’s evolve? • Are Sudakov effects important for low qT in AzAs’s? • Gluon bremsstrahlung, Qui-Sterman mechanism at other kinematics • π and p to anti-quark - analog of h1T? QCD-N2006 Frascati G.R.Goldstein

More Related