A complete non-perturbative renormalization prescription for quasi-PDFs

Journal Article · Wed Aug 23 00:00:00 EDT 2017 · Nuclear Physics. B

DOI:https://doi.org/10.1016/j.nuclphysb.2017.08.012· OSTI ID:1375962

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha; Hadjiyiannakou, Kyriakos; Jansen, Karl; Panagopoulos, Haralambos; Steffens, Fernanda

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.

• Sponsoring Organization: USDOE Office of Science (SC); National Science Foundation (NSF)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1375962
• Journal Information: Nuclear Physics. B, Journal Name: Nuclear Physics. B Journal Issue: C Vol. 923; ISSN 0550-3213
• Publisher: Elsevier
• Country of Publication: Netherlands
• Language: English