Pi-eta scattering and the resummation of vacuum fluctuation in three-flavour ChPT

Abstract

We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the ss-pairs and the scenario with smaller value of the chiral condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with pi-eta scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p^4) LEC's, namely to the values of the fluctuation parameters L4 and L6. We discuss several issues in detail, namely the choice of `good' observables and properties of their bare expansions, the `safe' reparametrization in terms of physical observables, the implementation of exact perturbative unitarity and exact renormalization scale independence, the role of higher order remainders and their estimates. We make a detailed comparison with standard chiral perturbation theory and use generalized ChPT as well as resonance chiral theory to estimate the higher order remainders.

Version submitted to EPJ C

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Cited by in corpus (9)

• The cusp effect in eta' --> eta pi pi decays
• Topological susceptibility on the lattice and the three-flavour quark condensate
• Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
• The ChPT: top-down and bottom-up
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Constraints on low energy QCD parameters from $\eta \to 3\pi$ and $\pi \pi$ scattering
• Analysis of discrepancies in Dalitz plot parameters in eta to 3 pion decay
• Chiral Nonet Mixing in $\pi \eta$ Scattering
• Constraints on 3-flavor QCD order parameters from eta to pi+pi-pi0 decay width