A new global fit of the $L^r_i$ at next-to-next-to-leading order in Chiral Perturbation Theory

TL;DR

This paper presents a new comprehensive fit for the low-energy constants in Chiral Perturbation Theory at NNLO, incorporating recent data and observables to improve the understanding of low-energy QCD phenomena.

Contribution

It provides a novel global fit of the $L_i^r$ constants at NNLO in Chiral Perturbation Theory, including updated data, observables, and analysis of $p^6$ constants, with insights into large $N_c$ behavior.

Findings

Updated low-energy constants $L_i^r$ with new data

Identified deviations from expected large $N_c$ behavior

Proposed scenarios for $p^6$ constants with good convergence

Abstract

A new fit is done to obtain numerical values for the order $p^4$ low-energy-constants $L_i^r$ in Chiral Perturbation Theory. This includes both new data and new calculated observables. We take into account masses, decay constants, $K_{\ell4}$, $\pi\pi$ and $\pi K$ scattering lengths and slopes and the slope of the pion scalar formfactor. We compare in detail where the changes w.r.t. to the 10 year old "fit 10" come from. We discuss several scenarios for estimating the order $p^6$ constants $C_i^r$ and search for possible values of them that provide a good convergence for the ChPT series. We present two such sets. One big change is that the fits do not have the expected behaviour in the limit of large $N_c$ as well as before.