Vector current renormalisation in momentum subtraction schemes using the HISQ action

TL;DR

This paper evaluates the effectiveness of momentum subtraction schemes, particularly RI-SMOM, for calculating vector current renormalisation factors in lattice QCD using the HISQ action, demonstrating controlled results with RI-SMOM.

Contribution

The study compares RI-SMOM and RI'-MOM schemes for vector current renormalisation, showing RI-SMOM's superior control over systematic errors in lattice QCD calculations.

Findings

RI-SMOM provides well-controlled $Z_V$ determinations.

RI'-MOM scheme shows larger systematic uncertainties.

Preliminary charm physics applications demonstrate the method's utility.

Abstract

As the only lattice vector current that does not require renormalisation is the point-split conserved current it is convenient to have a robust, precise and computationally cheap methodology for the calculation of vector current renormalisation factors, $Z_V$. Momentum subtraction schemes, such as RI-SMOM, implemented nonperturbatively on the lattice provide such a method if it can be shown that the systematic errors, e.g. from condensates, are well controlled. We present $Z_V$ calculations for the conserved current in both the RI-SMOM and RI$'$-MOM momentum subtraction schemes as well as local current renormalisation in the RI-SMOM scheme. By performing these calculations at various values of the momentum scale $\mu$ and different lattice spacings we can investigate the presence of power suppressed nonperturbative contributions and compare the results to expectations arising from the Ward-Takahashi identity. Our results show that the RI-SMOM scheme provides a well controlled determination of $Z_V$ but the standard RI$'$-MOM scheme does not. We then present some preliminary uses of these $Z_V$ calculations in charm physics.