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Singluarity and Gauge Link in Light Cone Gauge

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

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Singluarity and Gauge Link in Light Cone Gauge

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  1. Singluarity and Gauge Linkin 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

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

  3. 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:

  4. 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)

  5. 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) • … …

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

  7. 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)

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

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

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

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

  12. 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:

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

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

  15. 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:

  16. 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

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

  18. 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 !

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