The decay tau -> 3 pi + nu(tau) as a probe of the mechanism of dynamical chiral symmetry breaking

TL;DR

This paper investigates tau decays into three pions and a neutrino using Generalized Chiral Perturbation Theory to probe the size of spontaneous chiral symmetry breaking, suggesting measurable asymmetries at high-energy colliders.

Contribution

It introduces a novel method to test the magnitude of chiral symmetry breaking parameters through tau decay asymmetries, offering an independent check of quark condensate measurements.

Findings

Azimuthal asymmetry varies from 17% to 40% depending on condensate size.

The S-wave contribution is detectable at high-energy colliders.

Feasibility of measurement at colliders like CLEO is discussed.

Abstract

The decays tau -> 3 pi + nu(tau) are analyzed at one loop order in the framework of Generalized Chiral Perturbation Theory, in order to test the sensitivity to the size of spontaneous chiral symmetry breaking parameters, contained in the S-wave. The latter, due to a kinematical suppression, at threshold, of the P-wave, is relatively large enough to be detectable at high energy machines, through azimuthal left-right asymmetries. This quantity (for the pi- pi- pi+ mode), integrated from threshold to Q^2 = 0.35 GeV^2, varies from (17 +- 3) % in the standard case of large condensate up to (40 +- 5) % in the extreme case of tiny condensate. The feasibility of such measurement at high luminosity colliders (e.g. CLEO) is discussed. This method provides a completely independent cross-check of forthcoming experimental determination of the quark condensate, based on low energy pi-pi scattering.