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Collinear expansion and SIDIS at twist-3

Collinear expansion and SIDIS at twist-3. Yu-kun Song (USTC) 2013.10.28 Jinan YKS , Jian-hua Gao , Zuo -tang Liang, Xin-Nian Wang, arXiv:1308.1159. Outline. Introduction Collinear expansion extended to SIDIS Azimuthal asymmetries & nuclear effects Discussions and outlook.

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Collinear expansion and SIDIS at twist-3

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  1. Collinear expansion and SIDIS at twist-3 Yu-kun Song (USTC) 2013.10.28 Jinan YKS, Jian-huaGao, Zuo-tang Liang, Xin-Nian Wang, arXiv:1308.1159

  2. Outline • Introduction • Collinear expansion extended to SIDIS • Azimuthal asymmetries & nuclear effects • Discussions and outlook

  3. Semi-inclusive DIS • A large scale (Q) and a small scale (k) • Large scale →factorization • Small scale →structure information (intrinsic k ) An ideal probe of nucleon/nuclear structure ! • TMD factorization works at leading twist • Higher twist • Gauge invariant parton correlation functions • Factorization proof/arguments • NLO calculations • Experiments : Compass, Jlab, EIC,…

  4. Leading twist: collinear approximation • Gauge invariant parton distribution functions • Finite, perturbatively calculable partonic cross section Sterman-Libby power counting X Leading twist

  5. Higher twist: collinear expansion • Gauge invariant parton correlation functions • Finite, perturbatively calculable partonic cross section X Higher twist (1/Q power corrections)

  6. Systematic applications to SIDIS • Collinear expansion in DIS Ellis, Furmanski, Petronzio, 1982, 1983 Qiu, 1990 • Collinear expansion applied to SIDIS e+N →e+q+X Liang, Wang, 2006 • Nuclear medium effects of azimuthal asymmetries • Gauge link →nuclear modification of PDFs Liang, Wang, Zhou, 2008 • SIDIS e+N →e+q+Xat twist-4 YKS, Gao, Liang, Wang, 2011 • Doublelypolarized SIDIS e+N →e+q+Xat twist-3 YKS, Gao, Liang, Wang, Arxiv: 1308.1159

  7. Collinear expansion in DIS • [Ellis, Furmanski, Petronzio, 1982,1983 ;Qiu,1990] • Collinear Expansion: • Taylor expand at , and decompose • Apply Ward Identities • Sum up and rearrange all terms,

  8. Collinear expansion in SIDIS e+N→e+q+X • In the low region, we consider the case when final state is a quark(jet) Compared to DIS, the only difference is the kinematical factor Collinear expansion is naturally extended to SIDIS Parton distribution/correlation functions are -dependent [Liang, Wang, 2006]

  9. Hadronic tensor for SIDIS • : color gauge invariant

  10. Structure of correlation matrices • Time reversal invariance relate and • Lorentz covariance + Parity invariance, SIDIS DY

  11. Structure of correlation matrices • QCD equation of motion, , induce relations

  12. Relations from QCD EOM • Sum up and , one has (up to twist-3) • Explicit color gauge invariance for and . • Explicit EM gauge invariance

  13. Unpolarized SIDIS at twist-4 level • Cross section for • Twist-4 parton correlation functions [YKS, Gao, Liang, Wang,2011] 13

  14. Doubly polarized e+N →e+q+Xat twist-3 [YKS, Gao, Liang, Wang, 2013] Leading twist Twist-3

  15. kT- broadening of PDF in a nucleus • Two facts about the gauge link • Generated by QCD multiple gluon scattering between struck quark and medium • It induce physical effects, cannot be removed by a wise choice of gauge →Different interaction induce different PDFs: fNq & fAq More FSI !

  16. kT- broadening of PDF in a nucleus • Relations between nucleon and nuclear PDFs simplify under “maximal two-gluon exchange ” approximation. • It is just Gaussian broadening. More FSI diffuse the scattered parton!

  17. Nuclear modification of ˂cosφ>˂cos2φ> • Nuclear twist-3/4 parton correlation function • Gaussian ansatz for distribution • Take identical Gaussian parameter for parton distribution/correlation functions ˂cosφ>˂cos2φ> are Suppressed!

  18. Nuclear modification of ˂sinφ>LU • Nuclear modification for • depend on • dependence

  19. Nuclear modification of ˂sinφ>LU • kT- dependence Sensitive to the ratio of γ/α!

  20. Discussions and outlook • Collinear expansion is the systematic and essential method to calculate higher twist effects to SIDIS. • Gauge invariance ofcorrelation functions are automatically fulfilled as a result of collinear expansion. • Azimuthal asymmetries for doubly polarized e+N →e+q+Xare obtained up to twist-3, and for unpolarized case up to twist-4. Much more abundant azimuthal asymmetries at high twist, and their gauge invariant expressions are obtained. • Extension to hadronic production process are interesting and are underway. Thanks for your attention!

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