1. 9/19/20151 Semi-inclusive DIS: factorization Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

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

3. 3 Inclusive and Semi-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. 4 Different P T Region Integrate out P T -- similar to inclusive DIS, probe int. PDF Large P T (~  QCD ) -- hard gluon radiation, can be calculated from perturbative QCD, Polarized ->q-g-q correlations Low P T (~  QCD ) -- nonperturbative information (TMD): new factorization formula

5. 5 TMD Physics A way to measure Transversity Distribution, the last unkown leading 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. 6 TMD Distribution: the definition Gauge Invariance requires the Gauge Link Brodsky,Hwang,Schmidt 02’ Collins 02’ Belitsky,Ji,Yuan 02’

7. 7 This definition is also consistent with the QCD factorization

8. 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. 9 TMD Dis. At One-loop

10. 10 No soft divergence Collinear divergence : ln(m 2 ) Double Logarithms : ln 2 (  2 b 2 ) --- Collins-Soper equation

11. 11 One-loop Factorization: virtual 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) p p′ k Vertex corrections (single quark target) Vertex corrections (single quark target)

12. 12 One-Loop Factorization: real  Gluon Radiation (single quark target) 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) p p′ k

13. 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. 14 SIR05 JLab Factorization Soft Factor

15. 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. 16 Power Counting at Large P T k t -even distributions have the same dependence on k t k t -odd distributions are suppressed at large k t Power Counting Rule k t -even: 1/k t 2 k t -odd: 1/k t 3

17. 17 SIDIS: at Large P T Large P T 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 P T is not suppressed by 1/Q, but by 1/P T

18. 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 9/19/201519

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

21. 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 P T dependence will provide us information for the perturbative to nonperturbative transition of QCD