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

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.

Figures (2)

• Figure 1: Diagrams resulting from evaluating the Wick contractions in Eq. (\ref{['eq:rm123:path-integral-expansion']}) for the kaon correlation function in Eq. (\ref{['eq:rm123:kaon-corr-func']}) to leading (top left), first order (top middle and top right), and second order (bottom row) in $\Delta m$. Filled black dots denote $\gamma_{5}$ insertions, empty squares denote insertions of $S_{\mathrm{IB}}$, and red and purple lines denote up and strange quark propagator, respectively.
• Figure 2: (Left) Ratio of first to leading order of correlation function of the kaon as a function of time. The blue band denotes the region fitted to the functional form in Eq. (\ref{['eq:fit-m1']}). (Right) Relative difference between the first order of the correlation function of the kaon obtanied with truncated polynomials and RM123, and defined in Eq. (\ref{['eq:rm123-ad-diff']}).