Eur. Phys. J. C (2008) 56: 231-266
https://doi.org/10.1140/epjc/s10052-008-0645-z

Regular Article - Theoretical Physics

πη scattering and the resummation of vacuum fluctuation in three-flavor χPT

Institute of Particle and Nuclear Physics, Charles University, V. Holešovičkách 2, 18000, Prague 8, Czech Republic

^* e-mail: kolesar@ipnp.troja.mff.cuni.cz

Received: 8 April 2008
Revised: 8 May 2008
Published online: 1 July 2008

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 s̄s pairs and the scenario with smaller value of the q̄q condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with πη scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p⁴) LECs, 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 estimates of their influence. We make a detailed comparison with standard chiral perturbation theory and use generalized χPT as well as resonance chiral theory to estimate the higher order remainders.