Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators with Overlap Fermions

TL;DR

This paper computes the one-loop renormalization constants for four-fermion operators in lattice QCD using overlap fermions, aiding precise calculations in weak interaction phenomenology.

Contribution

It provides the first detailed one-loop renormalization constants for general four-fermion operators with overlap fermions, including both unimproved and improved operators.

Findings

Operators with different chirality do not mix.

Parity-conserving and parity-violating operators renormalize identically.

Renormalization constants are the same for unimproved and improved operators.

Abstract

The renormalization of the most general dimension-six four-fermion operators without power subtractions is studied at one loop in lattice perturbation theory using overlap fermions. As expected, operators with different chirality do not mix among themselves and parity-conserving and parity-violating multiplets renormalize in the same way. The renormalization constants of unimproved and improved operators are also the same. These mixing factors are necessary to determine physical matrix elements relevant to many phenomenological applications of weak interactions. The most important are the K0-K0bar and B0-B0bar mixings in the Standard Model and beyond, the Delta I =1/2 rule and epsilon'/epsilon.