# A complete non-perturbative renormalization prescription for quasi-PDFs

## Abstract

In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI' scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the $$\overline{MS}$$-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with $$N_f = 2+1+1$$ dynamical quarks, and a pion mass of around 375 MeV.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)

- OSTI Identifier:
- 1375962

- Alternate Identifier(s):
- OSTI ID: 1565661

- Grant/Contract Number:
- AC05-00OR22725; PHY-1714407

- Resource Type:
- Published Article

- Journal Name:
- Nuclear Physics. B

- Additional Journal Information:
- Journal Name: Nuclear Physics. B Journal Volume: 923 Journal Issue: C; Journal ID: ISSN 0550-3213

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Physics

### Citation Formats

```
Alexandrou, Constantia, Cichy, Krzysztof, Constantinou, Martha, Hadjiyiannakou, Kyriakos, Jansen, Karl, Panagopoulos, Haralambos, and Steffens, Fernanda. A complete non-perturbative renormalization prescription for quasi-PDFs. Netherlands: N. p., 2017.
Web. doi:10.1016/j.nuclphysb.2017.08.012.
```

```
Alexandrou, Constantia, Cichy, Krzysztof, Constantinou, Martha, Hadjiyiannakou, Kyriakos, Jansen, Karl, Panagopoulos, Haralambos, & Steffens, Fernanda. A complete non-perturbative renormalization prescription for quasi-PDFs. Netherlands. doi:10.1016/j.nuclphysb.2017.08.012.
```

```
Alexandrou, Constantia, Cichy, Krzysztof, Constantinou, Martha, Hadjiyiannakou, Kyriakos, Jansen, Karl, Panagopoulos, Haralambos, and Steffens, Fernanda. Wed .
"A complete non-perturbative renormalization prescription for quasi-PDFs". Netherlands. doi:10.1016/j.nuclphysb.2017.08.012.
```

```
@article{osti_1375962,
```

title = {A complete non-perturbative renormalization prescription for quasi-PDFs},

author = {Alexandrou, Constantia and Cichy, Krzysztof and Constantinou, Martha and Hadjiyiannakou, Kyriakos and Jansen, Karl and Panagopoulos, Haralambos and Steffens, Fernanda},

abstractNote = {In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI' scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the $\overline{MS}$-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with $N_f = 2+1+1$ dynamical quarks, and a pion mass of around 375 MeV.},

doi = {10.1016/j.nuclphysb.2017.08.012},

journal = {Nuclear Physics. B},

number = C,

volume = 923,

place = {Netherlands},

year = {2017},

month = {8}

}

DOI: 10.1016/j.nuclphysb.2017.08.012

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Works referencing / citing this record:

##
Computation of parton distributions from the quasi-PDF approach at the physical point

journal, January 2018

- Alexandrou, Constantia; Bacchio, Simone; Cichy, Krzysztof
- EPJ Web of Conferences, Vol. 175

##
A complete non-perturbative renormalization prescription for quasi-PDFs

text, January 2017

- Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
- Deutsches Elektronen-Synchrotron, DESY, Hamburg

##
Computation of parton distributions from the quasi-PDF approach at the physical point

journal, January 2018

- Alexandrou, Constantia; Bacchio, Simone; Cichy, Krzysztof
- EPJ Web of Conferences, Vol. 175

##
Light-Cone Parton Distribution Functions from Lattice QCD

text, January 2018

- Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
- Deutsches Elektronen-Synchrotron, DESY, Hamburg