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Published on November 15, 2007

Author: Garrick

Source: authorstream.com

Slide1:  Single Transverse Spin Asymmetries Jianwei Qiu Iowa State University RBRC Workshop on Single Spin Asymmetries June 1 – 3, 2005 Brookhaven National Lab, Upton, NY Slide2:  Single spin asymmetry – definition Single spin asymmetry before QCD Single spin asymmetry within the collinear factorization – high twist matrix elements KT- factorization – Sivers and Collins effects Connection between high twist matrix elements and Sivers and Collins functions Open questions Outline Single Spin Asymmetry – definition:  Single Spin Asymmetry – definition Slide4:  Symmetry and Single Spin Asymmetry Even though cross section is finite, single spin asymmetries can vanish if the polarized cross sections are independent of spin directions due to the fundamental symmetries of the interactions AL vanishes for Parity conserved interactions: Slide5:  Single transverse spin asymmetry before QCD Almost 40 years ago, AN in inclusive DIS was proposed by Christ and Lee to test the Time-Reversal invariance: In the approximation of one-photon exchange, AN of inclusive DIS vanishes if Time-Reversal is invariant for EM and Strong interactions N. Christ and T.D. Lee, Phys. Rev. 143, 1310 (1966) AN = 0 for inclusive DIS:  AN = 0 for inclusive DIS DIS cross section: Leptionic tensor is symmetric: Lμν = Lνμ Hadronic tensor: Polarized cross section: P and T invariance: Slide7:  Large AN in hadronic collisions process: only one hadron is transversely polarized: Large asymmetries AN observed in hadron collisions: decay of L production of p’s FNAL - E704 Single spin asymmetry corresponds to a T-odd triple product:  Single spin asymmetry corresponds to a T-odd triple product Slide9:  Single transverse spin asymmetry – AN in the parton model the operator for δq has even γ’s quark mass term the phase requires an imaginary part loop diagram transverse spin information at leading twist – transversity: PQCD calculable partonic parts should not depend on light current quark mass – singals a high twist effect in pQCD Slide10:  Single transverse spin asymmetry – AN in collinear factorization approach Leading twist PDF with transverse hadron spin: need an even number g’s: Twist-3 matrix elements An extra transverse index extra gluon (its polarization) extra vector direction Slide11:  Spin flip from interference between a quark state and a quark-gluon composite state Observed hadron momentum provides the 3rd vector Q: pQCD factorization beyond leading twist? High twist contribution to AN Slide12:  Multiple scales in hadronic collisions (3) (2) (1) Hard collision: Q >> ΛQCD Gluon shower: <kT>dynamic ~ F[Q2,log(s/Q2)] Hadron wave function: <kT>intrinsic ~ 1/fm ~ ΛQCD PQCD factorization: (1) Perturbative IR safe single hard partonic “cross section” (2) Leading log DGLAP evolution of PDFs (3) Nonperturbative PDFs Perturbative QCD factorization – (I):  Perturbative QCD factorization – (I) Perturbative pinch poles: Perturbative factorization: Parton state of momentum, k, lives much longer than the time of hard collision: |k2|<<|Q2| Remove soft interactions between different time scales Perturbative QCD factorization (II):  Perturbative QCD factorization (II) Collinear factorization: Provides systematic ways to quantify high order corrections KT –factorization No all-order proof of kT – factorization for an arbitrary kT Factorization fails beyond the next-to-leading powers in hadronic collisions Leading Twist Power corrections perturbative Long lived parton state Slide15:  Factorization: Twist-3 correlation functions: AN from polarized twist-3 correlations Single spin asymmetry within the collinear factorization:  Single spin asymmetry within the collinear factorization Generic twist-3 factorized contributions Even g’s ! Even g’s ! Provides hadron spin dependence transversity Calculated by Qiu and Sterman, Phys. Rev. D, 1999 Calculated by Kanazawa and Koike, Phys. Lett. B, 2000 Leading twist-3 contribution to AN:  Leading twist-3 contribution to AN Minimal approach (within the collinear factorization): Predictive power of the factorization approach:  Predictive power of the factorization approach What is the T(3)(x)?:  What is the T(3)(x)? What the T(3) (x) tries to tells us?:  What the T(3) (x) tries to tells us? Consider a classical (Abelian) situation: Model for TF(x,x):  Model for TF(x,x) TF (x,x) tells us something about quark’s transverse motion in a transversely polarized hadron One parameter and one sign! It is non-perturbative, has unknown x-dependence Numerical results – (I) (compare apples with oranges):  Numerical results – (I) (compare apples with oranges) Qiu and Sterman Phy. Rev. D, 1999 Numerical results – (II) (compare apples with oranges):  Numerical results – (II) (compare apples with oranges) Qiu and Sterman Phy. Rev. D, 1999 Numerical results – (III) (comparison with RHIC data):  Numerical results – (III) (comparison with RHIC data) Comparison with STAR data Too small PT value to be comfortable for initial state twist-3 See Koike’s talk on final state twist-3 New data from STAR, BRAHMS, PHENIX Slide25:  Twist-3 vs KT approach Twist-3 contribution in collinear factorization – leading corrections from parton correlation (a minimal approach) Effect of non-vanish parton kT (when kT ~ pT): M = Non-perturbative scale, e.g., di-quark mass, … Slide26:  Sivers’ functions Sivers’ functions: Sivers’ functions are connected to a polarized hadron beam Sivers’ functions are T- odd, but do not need another T- odd function to produce nonvanish asymmetries – the extracted proportional factor is T- odd, proportional to AN Polarized SIDIS cross section: Slide27:  Collins’ functions Collins’ functions: Collins’ functions are connected to the unpolarized Fragmentation contributions to a hadron Collins’ functions are T- odd, need another T- odd function to produce nonvanish asymmetries Polarized SIDIS cross section: Slide28:  KT - Factorization Factorization requires a separation of perturbative hard scale from nonperturbative hadronic scale a physical hard scale, Q, much larger than the kT Q ~ pT >> kT kT-factorization measures parton kT directly, while twist-expansion gives integrated kT information No formal proof of kT-factorization for hadronic collisions at kT ~ pT kT-factorization works for semi-inclusive DIS and Drell-Yan, or others with a large scale Q Semi-inclusive deeply inelastic scattering:  Semi-inclusive deeply inelastic scattering Breit frame: Two scale problem: Q2=-q2, pT Fixed order pQCD: Sudakov resummation: Single spin asym: low pT data sensitive to parton kT If P is anti-parallel to p Intrinsic vs dynamical kT:  In q-P frame, if we can neglect in partonic part But, we cannot neglect One can define kT-dependent and gauge invariant parton distributions Soft interaction between the hadrons can spoil factorization S Sudakov resummation (done in b- or kT-space) resums dynamical kT from gluon shower Parton orbital motion is more relevant to the intrinsic kT Intrinsic vs dynamical kT Slide31:  Open questions – (I) How much overlap between kT-approach at low pT and twist expansion at high pT? What these nonperturbative functions try to tell us? “direct kT” vs “kT – moments” Slide32:  Although there is kT-factorization in SIDIS, Drell-Yan and the others, how to separate dynamical kT from intrinsic kT ? How Sivers and Collins functions are affected by the process dependent gluon shower (resummation)? … Open questions – (II) If there is no KT – factorization, how universal are Sivers and Collins functions? Backup transparencies:  Backup transparencies Slide34:  Collinear approximation is important With collinear approximation:  = In general, matrix elements with different cuts are not equal: IR safe When does the factorization lose its predictive power?:  When does the factorization lose its predictive power? At the time when the nonperturbative functions lose their universality For final-state fragmentation: Factorization breaks if the fragmentation took place inside the hadronic medium If the lifetime of the parton state of momentun k is shorter than the medium size Lifetime: Slide36:  Asymmetries Double longitudinal spin asymmetries: Reduce under parity to: Double transverse spin asymmetries: Single longitudinal spin asymmetries: Single transverse spin asymmetries: Slide37:  Measure Sivers’ and Collins’ functions SIDIS: Collins functions: Slide38:  Seperate Sivers’ and Collins’ functions Slide39:  Initial success of RHIC pp runs p0 cross section measured over 8 order of magnitude [PRL 91, 241803 (2003)] Good agreement with NLO pQCD calculation at low pT Can be used in interpretation of spin-dependent results 9.6% normalization error not shown

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