# Quasi parton distributions and the gradient flow

## Abstract

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF.

- Authors:

- Rutgers, the State Univ. of New Jersey, Piscataway, NJ (United States)
- College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

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

- OSTI Identifier:
- 1350963

- Report Number(s):
- JLAB-THY-16-2402; DOE/OR/23177-4026; arXiv:1612.01584

Journal ID: ISSN 1029-8479; PII: 5728; TRN: US1700589

- Grant/Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 3; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Lattice Quantum Field Theory

### Citation Formats

```
Monahan, Christopher, and Orginos, Kostas.
```*Quasi parton distributions and the gradient flow*. United States: N. p., 2017.
Web. doi:10.1007/JHEP03(2017)116.

```
Monahan, Christopher, & Orginos, Kostas.
```*Quasi parton distributions and the gradient flow*. United States. doi:10.1007/JHEP03(2017)116.

```
Monahan, Christopher, and Orginos, Kostas. Wed .
"Quasi parton distributions and the gradient flow". United States.
doi:10.1007/JHEP03(2017)116. https://www.osti.gov/servlets/purl/1350963.
```

```
@article{osti_1350963,
```

title = {Quasi parton distributions and the gradient flow},

author = {Monahan, Christopher and Orginos, Kostas},

abstractNote = {We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernel that relates the smeared quasi PDF and the light-front PDF.},

doi = {10.1007/JHEP03(2017)116},

journal = {Journal of High Energy Physics (Online)},

number = 3,

volume = 2017,

place = {United States},

year = {Wed Mar 22 00:00:00 EDT 2017},

month = {Wed Mar 22 00:00:00 EDT 2017}

}

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Cited by: 11 works

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