Leading logarithms in N-flavour mesonic Chiral Perturbation Theory

TL;DR

This paper extends the calculation of leading logarithms in mesonic chiral perturbation theory for N flavors, providing high-loop order results for various physical quantities and analyzing flavor trace factors.

Contribution

It introduces higher-loop order calculations of leading logarithms in SU(N) chiral perturbation theory and analyzes flavor trace structures, extending previous work on nonlinear sigma models.

Findings

Leading logarithms computed up to six or seven loops for key quantities.

Explicit results for vector and scalar form factors and meson-meson scattering at five loops.

Elementary proof of flavor trace factor properties at each loop order.

Abstract

We extend earlier work on leading logarithms in the massive nonlinear O(n) sigma model to the case of SU(N)xSU(N)/SU(N) which coincides with mesonic chiral perturbation theory for N flavours of light quarks. We discuss the leading logarithms for the mass and decay constant to six loops and for the vacuum expectation value <\bar{q}q> to seven loops. For dynamical quantities the expressions grow extremely large much faster such that we only quote the leading logarithms to five loops for the vector and scalar form factor and for meson-meson scattering. The last quantity we consider is the vector-vector to meson-meson amplitude where we quote results up to four loops for a subset of quantities, in particular for the pion polarizabilities. As a side result we provide an elementary proof that the factors of N appearing at each loop order are odd or even depending on the order and the remaining traces over external flavours.