The form factors for hadronic tau decay using background field method

Abstract

In the two body hadronic tau decays, such as $\tau \to K\pi \left(\eta \right)\nu$, vector mesons play important role. Belle and Babar measured hadronic invariant mass spectrum of $\tau \to K\pi \nu$ decay. To compare the spectrum with theoretical prediction, we develop the chiral Lagrangian with vector mesons in [D. Kimura, K. Y. Lee and T. Morozumi, arXiv:1201.1794 [hep-ph]]. We compute the form factors of the hadronic τ decay taking account of the quantum corrections of Nambu Goldstone bosons. We also show how to renormalize the 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 [D. Kimura, K. Y. Lee and T. Morozumi, arXiv:1201.1794 [hep-ph]] by considering the one loop Feynman diagrams.