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Exclusive limits of DY processes QNP-2012, Ecole Polytechnique, April 19, 2012

This presentation discusses the inclusive and exclusive aspects of nucleon structure in Drell-Yan processes. Topics covered include the Lam-Tung relations, semi-exclusive pion-nucleon Drell-Yan, exclusive Drell-Yan and generalized parton distributions (GPDs), and the role of factorization mechanisms. The talk also explores the possibility of duality in Drell-Yan processes and the connection between Sivers function and form factors.

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Exclusive limits of DY processes QNP-2012, Ecole Polytechnique, April 19, 2012

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  1. Exclusive limits of DY processesQNP-2012, Ecole Polytechnique,April 19, 2012 Oleg Teryaev JINR, Dubna

  2. Outline • Nucleon structure: inclusive vs exclusive • (Very) simple theory for Lam-Tung relations • Semi-exclusive pion-nucleon DY (COMPASS) and pion DA • Exclusive DY and GPDs • BG-type duality in DY(@COMPASS&PANDA): Sivers function and time-like formfactors

  3. QCD factorization mechanisms 40 years of QCD: Complicated processes without confinement theory – like pre-Darwinian biology – classification of MANY soft ingrediends (TMDs,GPDs – two faces of nucleon structure) Various factorization mechanisms may not be completely independent (duality, matching,…) Exclusivity for DY (TMD)pdf’s->GPDs

  4. Positivity for dilepton angular distribution • Angular distribution • Positivity of the matrix (= hadronic tensor in dilepton rest frame) • + cubic – det M0> 0 • 1st line – Lam&Tung by SF method

  5. Kinematic azimuthal asymmetry from polar one by rotation (~kT ) Only polar z asymmetry with respect to m! - azimuthal angle appears with new

  6. Matching with pQCD results (J. Collins, PRL 42,291,1979) • Direct comparison: tan2 = (kT/Q)2 • Off-shellness effects for colliding (anti)quarks – cancel in GI set • New ingredient – expression for • Linear in kT • Saturates positivity constraint! • Tests by J.-C. Peng,J.Roloff:often close to saturation • Extra probe of transverse momentum

  7. Generalized Lam-Tung relation (OT’05) Relation between coefficients (high school math sufficient!) Reduced to standard LT relation for transverse polarization ( =1) LT - contains two very different inputs: kinematical asymmetry+transverse polarization

  8. Positivity domain with (G)LT relations 2 “Standard” LT Longitudinal GLT 1 -1 -3 -2

  9. LT violation • Azimuthal asymmetries at fundamental level required • Privileged plane • NLO-gluon emission • BM-quark spins • Off-shell quarks (NLO,HT)

  10. Semi-Exclusive DY (large xF) - Pion participates through Distribution Amplitude (Light-cone WF)

  11. GI -> phase • Colour GI -> second diagram -> phase • Unpolarized – Brandenburg, Brodsky, Mueller(94) • Longitudinally polarized –> SSA – Brandenburg, Mueller, OT(95) • Refined DA – Bakulev, Stefanis,OT(07)

  12. Pion DA • Element of ERBL factorization • Describes probability amplitude for the (anti) quark carrying given light-cone momentum fraction • Interest recently increased due to BaBar (and expected BELLE) data for pion-photon transition formfactor-simplest exclusive process

  13. Pion DA • (Conservative) model of Bakulev, Mikhailov, Stefanis vs (3D) fit

  14. Comparison to holographic model

  15. Angular distributions – probes of DA • Unpolarized • Polarized

  16. Asymmetries vs data

  17. Polarization -> scanning of DA

  18. When transition to exclusivity happen? • Pion pdf ~(1-x)a • HT ~ (<1/x> f/Q)2 • Transition: (1-x)a ~ (<1/x> f/Q)2 • Strongly depends on pion pdf ( large x dependence) and DA

  19. From semi-to pure exclusive • Simplest case - pion FF(ERBL) • Change DA to GPD- exclusive electroproduction • Time from right to left- exclusive DY (DAxGPD)- talks of L. Szymanowski, J. Wagner • Second DA->GPD-another mechanism- OT’05 (problems with factorization -analytic continuation to be performed) 1 s1 s s2 2

  20. Properties of exclusive DY • Polarization T->L • Difference in sign between imaginary parts of electroproduction and DY-> exclusive analog of famous Sivers function sign change • Final proton is not mandatory – small missing mass ~at rest for fixed target-possible at COMPASS • PP(NICA): TDA p->pp (to be compared with p->D) • Test of scaling • Estimates for COMPASS ~ 103 events • Exclusive limit with antiproton beam – relation to time-like FF’s

  21. Role of subtractions (related to d term)

  22. SSA in DY TM integrated DY with one transverse polarized beam – unique SSA – gluonic pole (Hammon, Schaefer, OT) – “factor 2” problem (Anikin,OT) Related to the moment of Sivers function

  23. Sivers function and formfactors • Relation between Sivers function and AMM known on the level of matrix elements (Brodsky, Schmidt, Burkardt) • Phase? • Duality for observables?

  24. DY and time-like FF’s • DIS for x -> 1 relation to space-like FF’s (Drell,Yan’70) • Pdf ~(1-x)a (FF)2 ~(1/Q2)(a+1) • DY(OT’08): 2 pdf’s enter • BUT “duality interval” in x-space ~1/Q vs ~(1/Q)2 in DIS • Same Q - dependence but – different normalization

  25. BG/DYW type duality for DY SSA in exclusive limit • Proton-antiproton DY – valence annihilation - cross section is described by Dirac FF squared • The same SSA due to interference of Dirac and Pauli FF’s with a phase shift (Rekalo,Brodsky) • Exclusive (large dilepton mass) limit; x -> 1 : T(x,x)/q(x) -> Im F2/F1 (Q ~ 1 /(1-x)) • Both directions – estimate of Sivers at large x and explanation of phases in FF’s • Compatible with models for Sivers ~(1-x)4-5 • Possibilities; estiamate SCALE of Sivers • Common fits of Sivers and FF’s?

  26. Conclusions • (Semi)exclusive limits of DY – interesting theoretically • Feasibility at various experiments remains to be studied • New relations to time-like FF’s

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