Mesonic low-energy constants

TL;DR

This paper reviews the current understanding of mesonic low-energy constants in chiral Lagrangians, including recent fits at NLO and NNLO, and compares theoretical and lattice QCD results for light meson interactions.

Contribution

It provides new fits of the LECs at NLO and NNLO, incorporating extensive NNLO knowledge and comparing with lattice determinations, advancing the precision in mesonic chiral Lagrangian parameters.

Findings

Updated LEC fits at NLO and NNLO levels.

Comparison of chiral LECs with lattice QCD results.

Discussion on resonance saturation and convergence issues.

Abstract

We review the status of the coupling constants of chiral Lagrangians in the meson sector, the so-called low-energy constants (LECs). Special emphasis is put on the chiral $SU(2)$ and $SU(3)$ Lagrangians for the strong interactions of light mesons. The theoretical and experimental input for determining the corresponding LECs is discussed. In the two-flavour sector, we review the knowledge of the $O(p^4)$ LECs from both continuum fits and lattice QCD analyses. For chiral $SU(3)$, NNLO effects play a much bigger role. Our main new results are fits of the LECs $L_i$ both at NLO and NNLO, making extensive use of the available knowledge of NNLO LECs. We compare our results with available lattice determinations. Resonance saturation of LECs and the convergence of chiral $SU(3)$ to NNLO are discussed. We also review the status of predictions for the LECs of chiral Lagrangians with dynamical photons and leptons.