Yu-kun Song (USTC) 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 Higher twist effects in semi-inclusive DIS

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

Partonic picture of nucleon Nucleon is the eigenstate of → Poincare invariance of induce momentum/ angular momentum sum rules →Test of QCD in strong coupling regime 3 confined quarks m_q ~ 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 Quark model(1960s)Parton model(1970s)

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

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. Semi-inclusive DIS: a nice probe of nucleon

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] Higher twist and collinear expansion

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

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 Gauge-invariant, So that they can be measured in Exps. Expansion parameter

[Ellis, Furmanski, Petronzio, 1982,1983 ;Qiu,1990] Collinear Expansion: 1. Taylor expand at, and decompose 2. Apply Ward Identities 3. Sum up and rearrange all terms, Collinear expansion in DIS

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 Collinear expansion in SIDIS [Liang, Wang, 2007]

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

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

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

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 !

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

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

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

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

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

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

broadening of PDF in a nucleus 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, [Liang, Wang, Zhou, PRD2008] Broadening!

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

Nuclear modification for depend on dependence Nuclear modification of

dependence Nuclear modification of Sensitive to the ratio of !

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!