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

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, $K_{\ell 4}$, $\pi \pi$ 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.

Comments: 41 pages, p^4 values of the l_i added, numerical values for f_+(0) in Kl3 added, a comparison with the LECS from Ecker et al., Phys. Lett. B692 (2010) 184 [arXiv:1004.3422 [hep-ph]] added