Vogelsang

Information about Vogelsang

Published on November 13, 2007

Author: Laurence

Source: authorstream.com

Content

Single-Transverse Spin Asymmetries in Hadronic Scattering :  Single-Transverse Spin Asymmetries in Hadronic Scattering Werner Vogelsang (& Feng Yuan) BNL Nuclear Theory ECT, 06/13/2007 Slide2:  Mostly based on: X. Ji, J.W. Qiu, WV, F. Yuan, Phys. Rev. Lett. 97, 082002 (2006) Phys. Rev. D73, 094017 (2006) Phys. Lett. B638, 178 (2006) C. Kouvaris, J.W. Qiu, WV, F. Yuan, Phys. Rev. D74, 114013 (2006) ( C. Bomhof, P. Mulders, WV, F. Yuan, J.W. Qiu, WV, F. Yuan, arXiv:0704.1153 [hep-ph] (Phys. Lett. B, to appear) Phys. Rev. D75, 074019 (2007) ) arXiv:0706.1196 [hep-ph] Slide3:  Outline: • Single-spin asymmetries in pp  hX • How are mechanisms for Single-spin asymmetries related ? • Conclusions • Introduction Slide4:  I. Introduction Slide5:  • SSA for single-inclusive process  power-suppressed  a single large scale (pT)  example: pp  X  collinear factorization (Efremov,Teryaev / Qiu,Sterman TF) Slide6:  II. Asymmetry in pphX Slide8:  STAR collinear factorization Brahms y=2.95 Slide9:  STAR Slide10:   Resummation of important higher-order corrections beyond NLO de Florian, WV √s=23.3GeV Bourrely and Soffer Apanasevich et al. • typically, hard-scattering calculations based on LO/NLO fail badly in describing the cross section Slide11:  higher-order corrections beyond NLO ? de Florian, WV Slide12:  Leading logarithms expect large enhancement ! de Florian, WV Slide13:  de Florian, WV E706 Slide14:  WA70 Effects start to become visible at S=62 GeV… Rapidity dependence ? Spin dependence ? Slide15:  • lesson from this: AN in pph X is power-suppressed ! Slide16:  • power-suppressed effects in QCD much richer than just mass terms (Efremov,Teryaev; Qiu,Sterman; Kanazawa, Koike) Slide17:  • ingredients: x1 x2 x2-x1 Collinear factorization. Slide18:  • full structure: Kanazawa,Koike Qiu,Sterman Transversity Slide22:  “derivative terms” • plus, non-derivative terms ! Slide24:  Assumptions in Qiu & Sterman : • derivative terms only • valence TF only, • neglect gluonpion fragmentation In view of new data, would like to relax some of these. Kouvaris, Qiu, Yuan, WV Slide25:  Remarkably simple answer: Recently: proof by Koike & Tanaka Slide26:   Ansatz: usual pdf  Fit to E704, STAR, BRAHMS  for RHIC, use data with pT>1 GeV for E704, choose pT=1.2 GeV allow normalization of theory to float (~0.5) Slide27:  Fit I: “two-flavor / valence” Fit II: allow sea as well Slide28:  solid: Fit I, dashed: Fit II Slide30:  Our TF functions: Slide31:  pT dependence Slide32:  Dependence on RHIC c.m.s. energy: Slide33:  III. How are the mechanisms for single-spin asymmetries related ? Slide34:  • have two “mechanisms” Q: In what way are mechanisms connected ? • tied to factorization theorem that applies Slide35:  • consider Drell-Yan process at measured qT and Q Slide36:  Step 1: calculate SSA for DY at qT ~ Q use Qiu/Sterman formalism Because of Q2 ≠ 0, there are also “hard poles”: Propagator (H) has pole at xg0 No derivative terms in hard-pole contributions. Slide37:  soft-pole hard-pole Slide39:  Step 2: expand this for qT << Q Slide40:  Step 3: calculate various factors in TMD factorized formula At QCD << qT can calculate each factor from one-gluon emission Ji, Ma, Yuan Collins, Soper, Sterman Slide41:  Unpolarized pdf: Slide42:  Sivers function: soft-pole hard-pole w/ correct direction of gauge link Slide43:  Precisely what’s needed to make factorization work and match on to the Qiu/Sterman result at small q! So: soft-pole, deriv. hard-pole soft-pole, non-deriv. hard-pole Slide44:  Take a closer look: if one works directly in small q limit   Slide45:  The interesting question now: What happens in more general QCD hard-scattering ? Consider ppjet jet X Underlying this: all QCD 22 scattering processes = jet pair transv. mom. Slide46:  Example: qq’  qq’ • for Qiu/Sterman calculation: subset of diagrams IS FS1 FS2 (these are soft-pole) Slide47:  Simplify: • assume q << P from the beginning • more precisely, assume k’ nearly parallel to hadron A or B and pick up leading behavior in q / P • reproduces above Drell-Yan results Slide48:  (partly even on individual diagram level, as in Drell-Yan) Likewise for hard-pole contributions k’ parallel to pol. hadron: Slide49:  What this means: When k’ nearly parallel to pol. hadron, structure at this order can be organized as Slide50:  Some remarks: • highly non-trivial. Relies on a number of “miracles”: color structure no derivative terms when k’ parallel to hadron B … Calculation seems to “know” how to organize itself Slide51:  Some further remarks: • the obtained Sivers partonic hard parts are identical to the ones obtained by Amsterdam group • the obtained unpolarized partonic hard parts are identical to the standard 22 ones • complete calculation can be redone in context of Brodsky-Hwang-Schmidt model: identical results as from collinear-factorization approach Slide54:  IV. Conclusions Slide55:  • Single-inclusive case: use Qiu/Sterman formalism Non-derivative terms have simple form Not all aspects of data understood Important input for phenomenology (Note: Sudakov logs)

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