Non-Perturbative Renormalization for Staggered Fermions (Self-energy Analysis)

TL;DR

This paper reports preliminary non-perturbative renormalization results for quark self-energy using HYP improved staggered fermions on MILC lattices, estimating key renormalization factors.

Contribution

It introduces a data analysis approach for NPR of quark self-energy with HYP staggered fermions on MILC lattices, providing initial estimates of renormalization factors.

Findings

Preliminary estimates of $Z_q'$ and $Z_q imes Z_m$ obtained.

Use of momentum source and projection operators for renormalization.

Results are consistent with theoretical expectations.

Abstract

We present preliminary results of data analysis for the non-perturbative renormalization (NPR) on the self-energy of the quark propagators calculated using HYP improved staggered fermions on the MILC asqtad lattices. We use the momentum source to generate the quark propagators. In principle, using the vector projection operator of $(\bar{\bar{\gamma_\mu \otimes 1}})$ and the scalar projection operator $(\bar{\bar{1 \otimes 1}})$, we should be able to obtain the wave function renormalization factor $Z_q'$ and the mass renormalization factor $Z_q \cdot Z_m$. Using the MILC coarse lattice, we obtain a preliminary but reasonable estimate of $Z_q'$ and $Z_q \cdot Z_m$ from the data analysis on the self-energy.