Nonperturbative renormalisation of composite operators with overlap quarks

TL;DR

This paper non-perturbatively computes renormalisation constants for composite operators using overlap quarks on a lattice, testing continuum relations and performing RG analysis to convert to the ar{MS} scheme.

Contribution

It provides the first non-perturbative determination of renormalisation constants for overlap fermions on a specific lattice, including RG running and scheme conversion.

Findings

Perturbative relations Z_A=Z_V and Z_S=Z_P hold above 1.6 GeV.

Renormalisation constants are successfully converted to the ar{MS} scheme.

Non-perturbative results agree with perturbative expectations at high scales.

Abstract

We compute non-perturbatively the renormalisation constants of composite operators on a $16^3 \times 32 $ lattice with lattice spacing $a$ = 0.093 fm for the overlap fermion action by using the regularisation independent (RI) scheme. The quenched gauge configurations are generated by tadpole improved plaquette plus rectangle action. We test the perturbative continuum relation $Z_A = Z_V$ and $ Z_S=Z_P$ and find that they agree well above $\mu$ = 1.6 GeV. We also perform a Renormalisation Group analysis at the next-to-next-to-leading order and convert the renormalisation constants to the $\bar{MS}$ scheme.