Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
Abstract
Chiral symmetry breaking may exhibit significantly different patterns in two chiral limits: Nf=2 massless flavours (mu=md=0, ms physical) and Nf=3 massless flavours (mu=md=0=ms=0). Such a difference may arise due to vacuum fluctuations of s-bars pairs related to the violation of the Zweig rule in the scalar sector, and could yield a numerical competition between contributions counted as leading order and next-to-leading in the chiral expansions of observables. We recall and extend Resummed Chiral Perturbation Theory (ReChPT), 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 ReChPT, which we match in subthreshold regions with dispersive representations obtained from the solutions 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 Nf=3 chiral limit. The results mildly favour significant contributions of vacuum fluctuations suppressing the Nf=3 quark condensate compared to its Nf=2 counterpart.
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