The Higgs boson mass and Ward-Takahashi identity in gauged Nambu-Jona-Lasinio model

A new formula for the composite Higgs boson mass is given, based on the Ward-Takahashi identity and the Schwinger-Dyson(SD) equation. In this formula the dominant asymptotic solution of the SD equation yields a correct answer, in sharp contrast to the Partially Conserved Dilatation Current(PCDC) approach where the sub- and sub-sub-dominant solutions should be taken into account carefully. In the gauged Nambu-Jona-Lasinio model we find MH≃2M for the composite Higgs boson mass MH and the dynamical mass of the fermion M in the case of the constant gauge coupling(with large cut off), which is consistent with the PCDC approach and the renormalization-group approach. As to the case of the running gauge coupling, we find MH≃2(A−1)/(2A−1)M (A>1,Λ→∞), where A≡18C2/(11Nc−2Nf) with C2 being the quadratic Casimir of the fermion representation. We also discuss a straightforward application of our formula to QCD(without 4-Fermi coupling), which yields Mσ∼2Mdyn, with Mσ and Mdyn being the light scalar(“σ-meson”) mass and mass of the constituent quark, respectively.