Low-energy pi pi and pi K scatterings revisited in three-flavour resummed chiral perturbation theory

摘要

Chiral symmetry breaking may exhibit significantly different patterns in two chiral limits: N-f = 2 massless flavours (m(u) = m(d) = 0, m(s) physical) and N-f = 3 massless flavours (m(u) = m(d) = m(s) = 0). Such a difference may arise due to vacuum fluctuations of s (s) over bar pairs related to the violation of the Zweig rule in the scalar sector, and it could yield numerical competition between contributions counted as leading and next-to-leading order in the chiral expansions of the observables. We recall and extend resummed chiral perturbation theory (Re chi PT), a framework that we introduced previously to deal with such instabilities: it requires a more careful definition of the relevant observables and their one-loop chiral expansions. We analyse the amplitudes for low-energy pi pi and pi K scatterings within Re chi PT, which we match in subthreshold regions with dispersive representations obtained from the solutions of the Roy and Roy-Steiner equations. Using a frequentist approach, we constrain the quark mass ratio as well as the quark condensate and the pseudoscalar decay constant in the N-f = 3 chiral limit. The results mildly favour significant contributions of vacuum fluctuations suppressing the N-f = 3 quark condensate compared to its N-f = 2 counterpart.