Helicity-dependent generalization of the JIMWLK evolution

doi:10.1103/PhysRevD.100.114020

Title: Helicity-dependent generalization of the JIMWLK evolution

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Abstract

We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller in [Phys. Lett. B 523, 243 (2001)] for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived in J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 95, 014033 (2017); J. High Energy Phys. 10 (2017) 198; Phys. Rev. D 99, 054032 (2019)]. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").

Authors:

^[1];

^[1]

The Ohio State Univ., Columbus, OH (United States). Dept. of Physics

Publication Date:: 2019-12-11

Research Org.:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

OSTI Identifier:: 1579283

Alternate Identifier(s):: OSTI ID: 1579342

Grant/Contract Number:: SC0004286

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 100; Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; perturbative QCD; proton spin; helicity; Electron-Ion Collider

Citation Formats


                    Cougoulic, Florian, and Kovchegov, Yuri V. Helicity-dependent generalization of the JIMWLK evolution.  United States: N. p., 2019. 
        Web.  doi:10.1103/PhysRevD.100.114020.

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                    Cougoulic, Florian, & Kovchegov, Yuri V. Helicity-dependent generalization of the JIMWLK evolution.  United States.  doi:10.1103/PhysRevD.100.114020.

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                    Cougoulic, Florian, and Kovchegov, Yuri V. Wed .  
        "Helicity-dependent generalization of the JIMWLK evolution".  United States.  doi:10.1103/PhysRevD.100.114020.

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@article{osti_1579283,

  title        = {Helicity-dependent generalization of the JIMWLK evolution},

  author       = {Cougoulic, Florian and Kovchegov, Yuri V.},

  abstractNote = {We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller in [Phys. Lett. B 523, 243 (2001)] for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived in J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 95, 014033 (2017); J. High Energy Phys. 10 (2017) 198; Phys. Rev. D 99, 054032 (2019)]. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").},

  doi          = {10.1103/PhysRevD.100.114020},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {12}

}

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