The form factors for hadronic tau decay using background field method

TL;DR

This paper develops a theoretical framework using the background field method to compute and renormalize form factors in hadronic tau decays involving vector mesons, incorporating quantum corrections and loop divergences.

Contribution

It introduces a renormalization procedure for the chiral Lagrangian with vector mesons in tau decays using background field method, including one-loop quantum corrections.

Findings

Renormalization of the chiral Lagrangian with vector mesons is achieved.

Quantum corrections to form factors are computed.

Divergences are systematically canceled with counterterms.

Abstract

In the two body hadronic tau decays, such as tau->to K pi (eta)nu, vector mesons play important role. Belle and Babar measured hadronic invariant mass spectrum of tau -> K pi nu decay. To compare the spectrum with theoretical prediction, we develop the chiral Lagrangian with vector mesons in Kimura:2012nx. We compute the form factors of the hadronic tau decay taking account of the quantum corrections of Nambu Goldstone bosons. We also show how to renormalizethe divergence of the Feynman diagrams with arbitrary number of loops and determine the counterterms within one loop using background field method.In this report, we discuss the renormalization of Kimura:2012nx by considering the one loop Feynman diagrams.