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

TL;DR

This paper explores resummed chiral perturbation theory's ability to incorporate large vacuum fluctuations and smaller chiral condensates, using pi-eta scattering as a sensitive test case to compare with standard approaches.

Contribution

It provides a detailed analysis of resummed chiral perturbation theory, highlighting its advantages in handling vacuum fluctuations and offering a comparison with traditional methods.

Findings

Resummed ChPT effectively includes large vacuum fluctuations.

Pi-eta scattering is sensitive to fluctuation parameters L4 and L6.

The approach maintains unitarity and scale independence.

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.