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 WardTakahashi 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 suband sub-subdominant solutions should be taken into account carefully. In the gauged Nambu-JonaLasinio 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 findMH ≃ 2 √ (A− 1)/(2A − 1)M , 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. The Nambu-Jona-Lasinio(NJL) model [1], which is not renormalizable in 4 dimensions, is familiar to us as an example of model for the dynamical symmetry breaking. The Gauged NambuJona-Lasinio(GNJL) model has been studied vigorously [2, 3] and is known to be renormalizable in 4 dimensions [4]. Phenomenologically, it has been applied to the Top Mode Standard Model(TMSM) [5]. Unfortunately, however, it has been complicated to calculate the composite Higgs boson mass in this model by the approach based on the Schwinger-Dyson(SD) equation. Namely, the previous manner to estimate the composite Higgs boson mass [6] was based on the Partially Conserved Dilatation Current (PCDC) relation [7], where we needed inevitably to