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: N_f=2 massless flavours (m_u=m_d=0, m_s physical) and N_f=3 massless flavours (m_u=m_d=0=m_s=0). Such a difference may arise due to vacuum fluctuations of s-bar{s} 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 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.

arXiv comment35 pages, 3 figures, accepted for publication in Eur. Phys. J. C

References in corpus (45)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Roy equation analysis of pi pi scattering
• A New Approach to a Global Fit of the CKM Matrix
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Generalized Dimensional Analysis
• $\pi \pi$ Scattering in Three Flavour ChPT
• The Low Energy $\pi \pi$ Amplitude to One and Two Loops
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• What $\pi -\pi$ Scattering Tells Us About Chiral Perturbation Theory
• Chiral Perturbation Theory Beyond One Loop
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• The quark condensate from K_{e_4} decays
• Cusps in K --> 3 pi decays
• High statistics measurement of Ke4 decay properties
• Scalar K pi form factor and light quark masses
• Determination of the a0-a2 pion scattering length from K->pi+ pi0 pi0 decay
• Study of tau decays involving kaons, spectral functions and determination of the strange quark mass
• Pion-pion scattering and the K->3pi decay amplitudes
• Analysis and interpretation of new low-energy Pi-Pi scattering data
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• Spectral distribution for the decay tau -> nu_tau K pi
• Paramagnetic effect of light quark loops on Chiral Symmetry Breaking
• $\pi K$ Scattering in Three Flavour ChPT
• Two Meson Systems with Ginsparg-Wilson Valence Quarks
• Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
• Staggered Chiral Perturbation Theory at Next-to-Leading Order
• Measurement of the Strange Spectral Function in Hadronic tau Decays
• Ginsparg-Wilson Pions Scattering in a Sea of Staggered Quarks
• Low Energy Constants from Kl4 Form-Factors
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• Tests of the naturalness of the coupling constants in ChPT at order p^6
• Flavour Stability of the Chiral Vacuum and Scalar Meson Dynamics
• Vacuum fluctuations of \bar{q}q and values of low-energy constants
• Zweig rule violation in the scalar sector and values of low-energy constants
• Exploring twisted mass Lattice QCD with the Clover term
• Chiral order and fluctuations in multi-flavour QCD
• Model Independent Measurement of Form Factors in the Decay D^+ --> K^- pi^+ e^+ nu_e
• Analysis of the semileptonic decay $D^0\to {\bar{K}}^0{\pi }^{-}{\mu }^{+}\nu$
• N_f Dependence of the Quark Condensate from a Chiral Sum Rule
• Finite-volume analysis of N_f-induced chiral phase transitions
• Comment on evidence for new interference phenomena in the decay D+ -> K- pi+ mu+ nu
• The role of strange sea quarks in chiral extrapolations on the lattice

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