Hadronic Currents and Form Factors in three-body Semileptonic $\tau$ Decays

TL;DR

This paper provides a comprehensive formalism for describing hadronic currents in three-body semileptonic tau decays, improving upon previous models by incorporating detailed angular momentum decomposition and form factor translation, aiding future experimental analyses.

Contribution

It introduces a full decomposition of hadronic currents into orbital angular momentum states and translates this into form factors, correcting prior analysis limitations.

Findings

Formulas for orbital angular momenta up to three are derived.

A formalism for arbitrary mass three-body systems is formulated.

Corrections to previous form factor analyses are provided.

Abstract

Three-body semileptonic $\tau$-decays offer a path to understand the properties of light hadronic systems and CP symmetry violations through searches for electric dipole moments. In studies of electro-weak physics, the hadronic part of the final states has traditionally been described using the language of form factors. Spectroscopic information, resolved in terms of orbital angular momentum quantum-numbers, is best being derived from an explicit decomposition of the hadronic current in the orbital angular momentum basis. Motivated by the upcoming large data samples from B factories, we present the full description of the hadronic currents decomposed into quantum numbers of the hadronic final state using the isobar picture. We present formulas for orbital angular momenta up to three and apply the rules derived from hadron spectroscopy to formulate the decay chain of hadronic three-body systems of arbitrary mass. We also translate this formalism to the language of form factors and thereby correct insufficiencies found in previous analyses of three-body hadronic final states.