Does unitarity imply finiteness of electroweak oblique corrections at one-loop? - constraining extra neutral Higgs bosons -

TL;DR

This paper demonstrates that unitarity constraints in models with multiple neutral Higgs bosons automatically ensure the finiteness of electroweak oblique corrections at one-loop, providing new bounds on Higgs couplings and masses.

Contribution

It establishes a direct link between unitarity sum rules and the finiteness of electroweak oblique corrections, deriving constraints on Higgs properties without relying on custodial symmetry.

Findings

Unitarity sum rules require the tree level ρ parameter to be 1.

Imposing unitarity sum rules guarantees one-loop finiteness of oblique corrections.

Constraints on the lightest Higgs coupling and second Higgs mass are derived from unitarity and precision tests.

Abstract

Introducing arbitrary number of neutral Higgs bosons in the electroweak symmetry breaking sector, we derive a set of conditions among Higgs couplings which need to be satisfied to maintain the unitarity of the high energy scattering amplitudes of weak gauge bosons at the tree level (unitarity sum rules). It is shown that the unitarity sum rules require the tree level $\rho$ parameter to be 1, without explicitly invoking the custodial symmetry arguments. The one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once these unitarity sum rules are imposed among Higgs couplings. Severe constraints on the lightest Higgs coupling (125GeV Higgs coupling) and the mass of the second lightest Higgs boson are obtained from the unitarity and the results of the electroweak precision tests (oblique parameter measurements). These results are compared with the effective theory of the light Higgs boson, and we find simple relationships between the mass of the second lightest Higgs boson in our framework and the ultraviolet cutoff in the effective theory framework.