Low-energy ππ and πK scatterings revisited in three-flavour resummed chiral perturbation theory

• Published in: The European physical journal. C, Particles and fields Vol. 52; no. 1
• Main Author: Descotes-Genon, S.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.09.2007
• Subjects: Broken symmetry; Chiral dynamics; Condensates; Decay rate; Flavor (particle physics); Perturbation theory; Quarks; Variation
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-007-0359-7

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=ms=0). Such a difference may arise due to vacuum fluctuations of ss̄ 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 (ReχPT), 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 ππ and πK scatterings within ReχPT, 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 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.