Exact Matching Condition for Matrix Elements in Lattice and $\overline{MS}$ Schemes

TL;DR

This paper derives an exact matching condition for hadron matrix elements between lattice and $ar{MS}$ schemes, offering a precise method to improve the accuracy of scheme conversions beyond mean field approximations.

Contribution

It provides a rigorous exact matching condition for matrix elements in lattice and $ar{MS}$ schemes, advancing beyond previous mean field approaches.

Findings

Exact matching condition derived for lattice and $ar{MS}$ schemes.

Provides a theoretical framework for scheme conversion accuracy.

Enables improved precision in lattice QCD calculations.

Abstract

The exact matching condition is given for hadron matrix elements calculated in any two different schemes, in particular, in the lattice and dimensional regularization, (modified) minimal subtraction $\overline{\rm MS}$ schemes. The result provides insight into and permits to go beyond Lepage and Mackenzie's mean field theory of removing tadpole contributions in lattice operators.