Singluarity and Gauge Link in Light Cone Gauge

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Presentation transcript:

Singluarity and Gauge Link in Light Cone Gauge Jianhua Gao Shandong Unversity at Weihai J.H. Gao, “Singularities, boundary conditions and gauge link in the light cone gauge ” arXiv:1309.4970 J.H. Gao, “A Derivation of the Gauge Link in Light Cone Gauge ” PRD 83, 094017(2011) The 9th Circum-Pan-Pacific Symposium on High-Energy Spin Physics October 28-31, 2013, Shandong University, Jinan, China

Outline Introduction Singularity and regularization in light cone gauge Derivation of the gauge link in light cone guage Summary

Collinear quark distribution function Collinear quark distribution function in covariant gauge: Gauge link along the light cone direction: All fields are fixed at Collinear quark distribution function in light cone gauge:

TMD quark distribution function Transverse momentum dependent quark distribution function (TMD): All fields are fixed at Gauge link in TMD in SIDIS: Sivers function X. Ji and F. Yuan Phys.Lett.B543,66 (2002); A. Belitsky, X. Ji and F. Yuan Nucl. Phys. B 656,165 (2003)

Some works on transverse gauge link X. Ji and F. Yuan Phys.Lett.B543,66 (2002) A. Belitsky, X. Ji and F. Yuan Nucl. Phys. B 656,165 (2003) D. Boer, P. Mulders, F. Pijlman Nucl.Phys.B667,201(2003) A.Idilbi, A.Majumder, Phys. Rev. D80,054022(2009) I. Cherednikov and N. Stefanis Int.J.Mod.Phys.Conf.Ser.4,135(2011) … …

Some Definition and Notations Light cone coordinate system: Vector in light cone coordinate: Some useful decomposition: where where Gauge field: In light cone gauge:

Boundary conditions and singularity Maxwell equations in coordinate space: Boundary constraint: Maxwell equations in momentum space: In light cone gauge: Gluon propagator: A. Bassetto, I. Lazizzera and R. Soldati Phys.Lett. B107,278 (1981)

Regularization of the Singularity Three different boundary conditions: Advanced: Retarded: Antisymmetric: Typical calculation procedure we often deal with:

Gauge link in light cone gauge in SIDIS Tree diagram in SIDIS: One gluon exchange contribution: Quark propagator decomposition:

Gauge link in light cone gauge in SIDIS Pole contribution: Integrating by parts:

Gauge link in light cone gauge in SIDIS Retarded boundary condition: Advanced boundary condition: Antisymmetry boundary condition:

Gauge link in light cone gauge in SIDIS It follows that (for the retarded boundary condition) : Gauge field at the infinity: Only keep the first term and integrate by parts:

Gauge link in light cone gauge in SIDIS General n-gluon exchange contribution: Integrating from to one by one:

Gauge link in light cone gauge in Drell-Yan Tree diagram in Drell-Yan: One gluon exchange contribution:

Gauge link in SIDIS vs Drell-Yan Retarded boundary condition: SIDIS: Drell-Yan: Advanced boundary condition: SIDIS: Drell-Yan: Antisymmetry boundary condition: SIDIS: Drell-Yan:

Gauge link in light cone gauge General n-gluon exchange contribution: Retarded in SIDIS: Advanced in Drell-Yan: Sum over all the orders ( for Drell-Yan): For the pure gauge , and the equation has the solution: The gauge link from pure gauge is independent on the link path! J.H. Gao, arXiv:1309.4970

Gauge link in light cone gauge More general gauge link in light cone gauge: Transverse gauge link in light cone gauge:

Thanks ! Summary A proper regularization method is provided to deal with the light cone singularity in high-twist calculations. A more general gauge link at light cone infinity can be obtained naturally from the pinched poles. The difference of the gauge link between SIDIS and DY process can be obtained directly in our derivation. The gauge link at light cone infinity is independent on the path not only for Abelian but also non-Abelian gauge. Thanks !