Nonperturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model

Abstract

We consider a vectorlike gauge theory of fermions that confines at the multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone boson. The weak interactions are embedded in the unbroken subgroup Sp(4) of a spontaneously broken SU(4) flavor group. The meson resonances appear as poles in the two-point correlators of fermion bilinears, and include the Goldstone bosons plus a massive pseudoscalar η′, as well as scalars, vectors and axial vectors. We compute the mass spectrum of these mesons, as well as their decay constants, in the chiral limit, in the approximation where the hypercolor Sp(2N) dynamics is described by four-fermion operators, à la Nambu-Jona Lasinio. By resumming the leading diagrams in the 1/N expansion, we find that the spin-one states lie beyond the LHC reach, while spin-zero electroweak-singlet states may be as light as the Goldstone-boson decay constant, f∼1 TeV. We also confront our results with a set of available spectral sum rules. In order to supply composite top-quark partners, the theory contains additional fermions carrying both hypercolor and ordinary color, with an associated flavor symmetry-breaking pattern SU(6)/SO(6). We identify and analyze several nontrivial features of the complete two-sector gauge theory: the 't Hooft anomaly matching conditions; the higher-dimension operator which incorporates the effects of the hypercolor axial-singlet anomaly; the coupled mass-gap equations; the mixing between the singlet mesons of the two sectors, resulting in an extra Goldstone boson η0, and novel spectral sum rules. Assuming that the strength of the four-fermion interaction is the same in the two sectors, we find that the colored vector and scalar mesons have masses 4f, while the masses of colored pseudo-Goldstone bosons, induced by gluon loops, are 1.5f. We discuss the scaling of the meson masses with the values of N, of the four-fermion couplings, and of a possible fermion mass.