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Exploring Higher Twist Effects in Semi-Inclusive DIS

This study delves into higher twist effects in semi-inclusive deep inelastic scattering, investigating azimuthal asymmetries, nuclear effects, and implications in extracting parton distribution functions. It extends collinear expansion to SIDIS and highlights twist-3 and twist-4 corrections, offering insights into partonic behavior within nucleons and nuclei. The research emphasizes the systematic extraction of higher twist effects through a gauge-invariant approach and explores the role of QCD factorization in understanding nucleon structures. Discover the complexities of twist effects and their impact on our understanding of parton dynamics in this comprehensive exploration of semi-inclusive DIS.

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Exploring Higher Twist Effects in Semi-Inclusive DIS

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  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!

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