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The form factors for hadronic tau decay using background field method

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.