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

  • S. Descotes-GenonEmail author
Regular Article - Theoretical Physics

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=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.

Keywords

Chiral Symmetry Breaking Chiral Perturbation Theory Chiral Limit Quark Condensate Chiral Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2007

Authors and Affiliations

  1. 1.Laboratoire de Physique ThéoriqueCNRS/Univ. Paris-Sud 11 (UMR 8627)Orsay CedexFrance

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