Higher twist effects in semi-inclusive DIS

1. Higher twist effects in semi-inclusive DIS Yu-kun Song (USTC) 2013.7.29 Weihai YKS, Jian-hua Gao, Zuo-tang Liang, Xin-Nian Wang, Phys.Rev.D83:054010,2011 YKS, Jian-hua Gao, Zuo-tang Liang, Xin-Nian Wang, to be submitted

2. Outline • Introduction to higher twist effects • Collinear expansion extended to SIDIS • Azimuthal asymmetries at twist-3 level • Nuclear effects and higher twist • Conclusions

3. Partonic picture of nucleon Quark model(1960s) Parton model(1970s) • 3 confined quarks • m_q ~ 200-300 MeV • static property • P, J shared by q • a bunch of free partons • m_q ~ several MeV • hard scattering • P, J shared by q,qbar,g • Nucleon is the eigenstate of • → Poincare invariance of induce momentum/ angular momentum sum rules • →Test of QCD in strong coupling regime

4. Semi-inclusive DIS: a nice probe of nucleon Sterman-Libby power counting X X Leading twist Higher twist (1/Q power corrections)

5. Semi-inclusive DIS: a nice probe of nucleon • QCD radiative correction → “A clean test of QCD” [Georgi, Politzer, 1978] • Intrinsic [cahn,1978] → Power suppressed, higher twist(HT)! • Magnitude of higher twist terms ~300 MeV , ~several GeV , ~10% Not negligible for most SIDIS experiments.

6. Higher twist and collinear expansion • Collinear expansion: • Systematic way of calculating higher twist in DIS • [Ellis, Furmanski, Petronzio, 1982, 1983; Qiu, 1990] • Extension to SIDIS [Liang, Wang, 2006] • QCD multiple gluon scattering • → gauge link + Higher twist terms • → nuclear broadening [Liang, Wang, Zhou,2008] • nuclear modification of azimuthal asymmetries • [Liang, Wang, Zhou, 2008] • twist-4 corrections to unpolarized SIDIS • [YKS, Gao, Liang,Wang, 2010] • twist-3 corrections to doubly polarized SIDIS • [YKS, Gao, Liang, Wang, to be submitted]

7. Leading twist: Collinear approximation • Basis of QCD factorization theorem: Sterman-Libby Power counting [Collins, 2011] → Leading contributions ~ Collinear approximation • Example: DIS • Collinear approximation • Ward identity … Gauge invariant parton distribution function

8. Higher twist: Collinear expansion • Leading twist: • Non-leading twist: expansion near collinear limit • Collinear expansion is the natural and systematic way to extract HT effects. • Notice: for a well-defined expansion Expansion parameter Gauge-invariant, So that they can be measured in Exps.

9. 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,

10. Collinear expansion in SIDIS • 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, 2007]

11. Hadronic tensor for SIDIS • Form of hadronic tensor after collinear approximation • : color gauge invariant

12. Structure of correlation matrices • Expand in spinor space • Constraints from parity invariance

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

14. TMD PDF and correlation functions • Twist-2 TMD parton distribution functions • Twist-3 TMD parton correlation functions Unpolarized PDF Sivers Helicity distribution Worm-gear color gauge invariant !

15. Structure of correlation matrices • Similar for • QCD equation of motion, ,induce relations

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

17. Consistency to DIS • Integration over , one has where • because of Time-reversal invariance. • For DIS at twist-3 only contribute.

18. Azimuthal asymmetries at twist-3 level [Liang,Wang,2007] • Cross section for • Twist-3 parton correlation function QCD equation of motion implies

19. Azimuthal asymmetries at twist-4 level • Cross section for • Twist-4 parton correlation functions [YKS, Gao, Liang, Wang,2011] 19

20. Doubly polarized at twist-3 [YKS, Gao, Liang, Wang, to be published] Leading twist Twist-3 asymmetries

21. broadening of PDF in a nucleus [Liang, Wang, Zhou, PRD2008] • QCD multiple scattering cause broadending. • The form of broadening is simplified when • Local color confinement • A>>1 • Weak correlation between nucleons • If nucleon PDF take Gaussian form, Broadening!

22. Nuclear modification of • Nuclear twist-3/4 parton correlation function • Gaussian ansatz for distribution • Take identical Gaussian parameter for parton distribution/correlation functions Suppressed!

23. Nuclear modification of • Nuclear modification for • depend on • dependence

24. Nuclear modification of • dependence Sensitive to the ratio of !

25. Conclusions & outlooks • Collinear expansion is naturally extended to SIDIS. Cross section and azimuthal asymmetries for doubly polarized are obtained up to twist-3, and unpolarized SIDIS up to twist-4. • Much more abundant azimuthal asymmetries at high twist, and their gauge invariant expressions are obtained. • Azimuthal asymetries act as a good probe of nuclear properties. They are sensitive to Gaussian parameters of HT correlation fuctions. • Numeric study of HT correlation functions, HT effects in fragmentation functions, ,…, are underway. Thanks for your attention!