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Semi-inclusive DIS: factorization

Semi-inclusive DIS: factorization. Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory. Outline. Introduction Low P T region: TMD parton distributions and QCD factorization High P T region: quark-gluon-quark correlation (ETQS mechanism) Summary.

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Semi-inclusive DIS: factorization

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  1. Semi-inclusive DIS: factorization Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

  2. Outline • Introduction • Low PT region: TMD parton distributions and QCD factorization • High PT region: quark-gluon-quark correlation (ETQS mechanism) • Summary

  3. Inclusive andSemi-inclusive DIS Inclusive DIS: Partonic Distribution depending on the longitudinal momentum fraction Semi-inclusive DIS: Probe additional information for partons’ transverse distribution in nucleon

  4. Different PT Region • Integrate out PT -- similar to inclusive DIS, probe int. PDF • Large PT (~QCD) -- hard gluon radiation, can be calculated from perturbative QCD, Polarized ->q-g-q correlations • Low PT (~QCD) -- nonperturbative information (TMD): new factorization formula

  5. TMD Physics • A way to measure Transversity Distribution, the last unkownleading twist distribution Collins 1993 • The Novel Single Spin Asymmetries • Connections with GPDs, and Quantum Phase Space Wigner distributions • Quark Orbital Angular Momentum and Many others …

  6. TMD Distribution: the definition Gauge Invariance requires the Gauge Link Brodsky,Hwang,Schmidt 02’ Collins 02’ Belitsky,Ji,Yuan 02’

  7. This definition is also consistent with the QCD factorization

  8. Illustrate the Factorization(one-loop order) • Take an on-shell quark target • Calculate the TMD Dis. and F.F. • Separate the cross section into different pieces • Show the soft divergence is cancelled out

  9. TMD Dis. At One-loop

  10. No soft divergence • Collinear divergence : ln(m2) • Double Logarithms: ln2(2 b2) --- Collins-Soper equation

  11. One-loop Factorization: virtual • Vertex corrections (single quark target) p′ k p Four possible regions for the gluon momentum k: 1) k is collinear to p (parton distribution) 2) k is collinear to p′ (fragmentation) 3) k is soft (Soft factor) 4) k is hard (pQCD correction)

  12. Gluon Radiation (single quark target) One-Loop Factorization: real p′ k p Three reagions for the gluon momentum k: 1) k is collinear to p (parton distribution) 2) k is collinear to p′ (fragmentation) 3) k is soft (Soft factor)

  13. All Orders in Perturbation Theory • Consider an arbitrary Feynman diagram • Find the singular contributions from different regions of the momentum integrations • Power counting to determine the leading regions • Factorize the soft (Grammer-Yennie) and collinear gluons (Ward Identity) • Factorization theorem. (Collins, Soper, Sterman, Perturbative QCD, Mueller ed.)

  14. Factorization Soft Factor SIR05 JLab

  15. The Factorization Applies to • Semi-inclusive DIS (polarized and unpolarized) • Drell-Yan at Low transverse momentum • Di-hadron production in e+e- annihilation (extract the Collins function) • Many others, … • Except for dijet-correlation at hadron colliders because of mixture of ISI and FSI effects • Collins-Qiu, 07; Vogelsang-Yuan, 07; Mulders et al, 04-07 • Heavy quarkonium production in pp collision, Yuan, 08

  16. Power Counting at Large PT • kt-even distributions have the same dependence on kt • kt-odd distributions are suppressed at large kt • Power Counting Rule kt-even: 1/kt2 kt-odd: 1/kt3

  17. SIDIS: at Large PT • Large PT SIDIS can be calculated from perturbative QCD (same for TMDs) • Polarized scattering depends on the quark-gluon correlations in the nucleon • Single Spin Asymmetry (Sivers and Collins) at large PT is not suppressed by 1/Q, but by 1/PT

  18. A unified picture for SSA • In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P • At large P, SSA is dominated by twist-3 correlation effects • At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions • The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006

  19. A difficulty at next-leading-power (1/Q) • Mismatch at low and high transverse momentum SIDIS at 1/Q • Bacchetta-Boer-Diehl-Mulders, 0803.0227 • The factorization needs to be carefully examined at this order • Earlier works indicates possible problems • Afanasev-Carlson, PRD, 2006 • Gamberg-Hwang-Metz-Schlegel, PLB, 2006

  20. Transition from Perturbative region to Nonperturbative region? Nonperturbative TMD Perturbative region

  21. Summary • Semi-inclusive DIS provides important information on nucleon structure and opportunity to study the associated QCD dynamics • QCD factorization and universality of the parton distributions are important aspects in these studies • The PT dependence will provide us information for the perturbative to nonperturbative transition of QCD

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