Extracting the low-energy constant $L_0^r$ at three flavors from pion-kaon scattering

TL;DR

This paper determines the low-energy constant $L_0^r$ at three flavors in SU(4|1) Partially-Quenched Chiral Perturbation Theory by analyzing pion-kaon scattering data from lattice simulations, providing a first such measurement.

Contribution

It provides the first determination of the low-energy constant $L_0^r$ at $ ext{O}(p^4)$ in SU(4|1)$ PQChPT$ using lattice data, including detailed uncertainty analysis.

Findings

$L_0^r( ho)=0.77(20)(25)(7)(7)(2) imes 10^{-3}$

Quantified uncertainties from various sources such as scattering length and lattice parameters

First lattice-based extraction of this low-energy constant at three flavors.

Abstract

Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the only free low-energy constant at $\mathcal{O}(p^4)$, known as $L_0^r$, in SU$(4|1)$ Partially-Quenched Chiral Perturbation Theory using the data from the Extended Twisted Mass Collaboration, $L_0^r(\mu=M_\rho) = 0.77(20)(25)(7)(7)(2)\cdot 10^{-3}$. The theory uncertainties originate from the unphysical scattering length, the physical low-energy constants, the higher-oder chiral corrections, the (lattice) meson masses and the pion decay constant, respectively