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Advances in Semi-Inclusive Deep Inelastic Scattering: Insights into QCD Dynamics

This document explores Semi-Inclusive Deep Inelastic Scattering (SIDIS) to deepen our understanding of nucleon structure and Quantum Chromodynamics (QCD). It discusses the factorization in both low and high transverse momentum (PT) regions, addressing TMD parton distributions and the quark-gluon-quark correlation. The study emphasizes new factorization formulas, the role of soft divergences, and the significance of polarizations in measuring Transversity Distribution and Single Spin Asymmetries. A unified framework linking various SIDIS phenomena is presented, highlighting the transition from perturbative to nonperturbative QCD.

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Advances in Semi-Inclusive Deep Inelastic Scattering: Insights into QCD Dynamics

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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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