Dispersive evaluation of the second-class amplitude $\tau \to \eta \pi {\nu }_{\tau }$ in the standard model

Abstract

We reevaluate the two form factors relevant for the $\eta \pi$ second-class $\tau$ decay mode, making systematic use of analyticity, unitarity, combined with updated inputs to the NLO chiral constraints. We focus, in particular, on the shape of the $\rho$ resonance peak which is a background-free signature of a second-class current. Its dispersive construction requires the $\eta \pi \to \pi \pi$ scattering amplitude which we derive from a family of Khuri-Treiman equations solutions constrained with accurate recent results on the $\eta \to 3\pi$ Dalitz plot.

Presented at the 12th International workshop on Tau lepton physics (TAU2012) in Nagoya, Japan

References in corpus (5)

• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Analytical dispersive construction of $\eta \to 3\pi$ amplitude: First order in isospin breaking
• Tests of non-standard electroweak couplings of right-handed quarks
• Estimate of the branching fraction ${\tau }^{-}\to \eta {\pi }^{-}{\nu }_{\tau }$, the $a_0^{-}(980)$, and non-standard weak interactions
• On meson dominance in the `second class' tau \to eta pi nu_tau decay