Mesonic low-energy constants

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.

36 pages, prepared for Annual Review of Nuclear and Particle Science, typos corrected, reference added, results unchanged

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• Scrutinizing the pion condensed phase
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• Spectroscopy of SU(4) gauge theory with two flavors of sextet fermions
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• Finite Volume at Two-loops in Chiral Perturbation Theory
• Feynman-Hellmann theorem for resonances and the quest for QCD exotica
• CHIRON: a package for ChPT numerical results at two loops
• Connected, Disconnected and Strange Quark Contributions to HVP
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Quantum Chromodynamics, Antiferromagnets and XY Models from a Unified Point of View
• Dispersive Treatments of $K_{\ell 4}$ Decays and Hadronic Light-by-Light Scattering
• Kaon semileptonic decays with $N_f=2+1+1$ HISQ fermions and physical light-quark masses
• Status of Chiral Meson Physics