Regularization at the next-to-leading order in the top-mode standard model without gauge bosons

Abstract

We study Higgs condensation in the top-mode standard model at the next-to-leading (NTL) order in 1/Nc, by calculating the effective potential as a function of a hard mass term of the top quark. We include the effects of the top and bottom quarks, all the scalars, and the leading QCD effects, but not the effects of the transverse components of the electroweak gauge bosons. The model contains finite UV energy cutoff parameters Lf, Lb for the fermionic and the bosonic momenta. Condensation takes place at energies L \sim Lf \sim Lb. We describe how to regularize the integrals over the fermionic momenta in a way free of momentum branching ambiguities and treat the terms of 1/Nc expansion mutually consistently. We use three different cutoff procedures. We also discuss how to ensure the validity of Goldstone theorem. Demanding that the NTL contributions not ``wash out'' the leading ones, we obtain for the cutoffs: L = O(1 TeV), a result largely independent of the regularization procedure.

LaTeX, 41 pages, 3 eps figures; revised version - extended discussion of conclusions, comparisons to other works, and extended list of references; the version to appear in Ann.Phys.(N.Y.)

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Cited by in corpus (11)

• Top quark condensation
• The Nambu sum rule and the relation between the masses of composite Higgs bosons
• Scalar excitation with Leggett frequency in ${}^3$ He-B and the $125$ GeV Higgs particle in top quark condensation models as Pseudo - Goldstone bosons
• Gauge theory of Lorentz group as a source of the dynamical electroweak symmetry breaking
• Strong dynamics behind the formation of the $125$ GeV Higgs boson
• Spontaneous CP Symmetry Breaking at the Electroweak Scale
• Schwinger - Dyson equation and NJL approximation in massive gauge theory with fermions
• $1/N_c$ Nambu -- Jona-Lasinio model: Electrically charged and strange pseudoscalars
• $1/N_c$ Nambu -- Jona-Lasinio model: ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons
• Modified model of top quark condensation
• Modified top quark condensation model with the extra heavy fermion, the $125$ GeV Pseudo - Goldstone boson, and the additional heavy scalar bosons