A first study of strong isospin breaking effects in lattice QCD using truncated polynomials

TL;DR

This paper introduces a novel automatic differentiation method to compute high-order derivatives in lattice QCD, enabling detailed studies of isospin-breaking effects and electromagnetic corrections.

Contribution

The work presents a new approach using automatic differentiation to evaluate derivatives in lattice QCD, focusing on strong isospin-breaking effects and derivative propagation through algorithms.

Findings

High-order derivatives can be computed efficiently using the proposed method.

The approach enhances the study of isospin-breaking effects in lattice QCD.

Propagation of derivatives through algorithms is successfully demonstrated.

Abstract

Computing derivatives of observables with respect to parameters of the theory is a powerful tool in lattice QCD, as it allows the study of physical effects not directly accessible in the original Monte Carlo simulation. Prominent examples of this include the impact of the up-down quark mass difference and electromagnetic corrections. In this work, we present a new approach based on automatic differentiation to evaluate such derivatives to arbitrarily high orders, where particular emphasis will be placed on strong isospin-breaking effects and on the propagation of derivatives through the conjugate gradient algorithm in the computation of correlation functions.