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QCD Factorization for Semi-inclusive DIS

QCD Factorization for Semi-inclusive DIS. Feng Yuan RBRC , Brookhaven National Laboratory. Outline. Introduction: physics of TMD QCD factorization for semi-inclusive DIS Some phenomenological results Summary. Inclusive and Semi-inclusive DIS. Inclusive DIS:

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QCD Factorization for Semi-inclusive DIS

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  1. QCD Factorization for Semi-inclusive DIS Feng Yuan RBRC , Brookhaven National Laboratory APS/JPS Hawaii

  2. Outline • Introduction: physics of TMD • QCD factorization for semi-inclusive DIS • Some phenomenological results • Summary APS/JPS Hawaii

  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 APS/JPS Hawaii

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

  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 … APS/JPS Hawaii

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

  7. This definition is also consistent with the QCD factorization APS/JPS Hawaii

  8. 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) APS/JPS Hawaii

  9. 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) APS/JPS Hawaii

  10. 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.) APS/JPS Hawaii

  11. Factorization Soft Factor APS/JPS Hawaii Ma, Ji, Yuan, 2004

  12. SIDIS Cross Section: QCD Factorization At leading power of 1/Q Sivers Asym. Collins Asym. APS/JPS Hawaii

  13. 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) • Di-jet and/or di-hadron correlation at hadron collider (work in progress) • Many others, … APS/JPS Hawaii

  14. Phenomenology • Semi-inclusive DIS (Vogelsang, Yuan, 05) • See also Efremov, et al., 04, 05; Anselmino, et al., 05 APS/JPS Hawaii

  15. COMPASS APS/JPS Hawaii

  16. At RHIC APS/JPS Hawaii

  17. Summary • The QCD factorization theorem has been proved for semi-inclusive DIS • Some phenomenological studies showed very promising results as compared with the old data and on the predictions for the future experiments as well APS/JPS Hawaii

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