# 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:

- 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}

}

DOI: 10.1103/PhysRevD.100.114020