Eur. Phys. J. C (2005) 39: 1-8
https://doi.org/10.1140/epjcd/s2004-01-001-3

Original Articles

Dynamically spontaneous symmetry breaking and masses of lightest nonet scalar mesons as composite Higgs bosons

Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China

Received: 23 June 2003
Accepted: 2 November 2003
Published online: 10 February 2004

Abstract

Based on the (approximate) chiral symmetry of QCD Lagrangian and the bound state assumption of effective meson fields, a nonlinearly realized effective chiral Lagrangian for meson fields is obtained from integrating out the quark fields by using the new finite regularization method. As the new method preserves the symmetry principles of the original theory and meanwhile keeps the finite quadratic term given by a physically meaningful characteristic energy scale M _c , it then leads to a dynamically spontaneous symmetry breaking in the effective chiral field theory. The gap equations are obtained as the conditions of minimal effective potential in the effective theory. The instanton effects are included via the induced interactions discovered by ’t Hooft and found to play an important role in obtaining the physical solutions for the gap equations. The lightest nonet scalar mesons (σ, f ₀, a ₀ and κ) appearing as the chiral partners of the nonet pseudoscalar mesons are found to be composite Higgs bosons with masses below the chiral symmetry breaking scale Λ _χ ~ 1.2 GeV. In particular, the mass of the singlet scalar (or the σ) is found to be m _σ ≃ 677 MeV.

PACS :12.38.Aw – 11.30.Qc – 14.40.-n – 14.65.Bt