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Title: Helicity-dependent generalization of the JIMWLK evolution

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:
ORCiD logo [1]; ORCiD logo [1]
  1. The Ohio State Univ., Columbus, OH (United States). Dept. of Physics
Publication Date:
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.
Cougoulic, Florian, & Kovchegov, Yuri V. Helicity-dependent generalization of the JIMWLK evolution. United States. doi:10.1103/PhysRevD.100.114020.
Cougoulic, Florian, and Kovchegov, Yuri V. Wed . "Helicity-dependent generalization of the JIMWLK evolution". United States. doi:10.1103/PhysRevD.100.114020.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.114020

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