Abstract
We present the first explicit calculation of leading two-loop corrections to the Higgs trilinear coupling λhhh in models with classical scale invariance (CSI), using the effective-potential approximation. Furthermore, we also study — for the first time at two loops — the relation that appears between the masses of all states in CSI theories, due to the requirement of reproducing correctly the 125-GeV Higgs-boson mass. In addition to obtaining analytic results for general CSI models, we consider two particular examples of Beyond-the-Standard-Model theories with extended Higgs sectors, namely an N-scalar model (endowed with a global O(N) symmetry) and a CSI version of the Two-Higgs-Doublet Model, and we perform detailed numerical studies of these scenarios. While at one loop the value of the Higgs trilinear coupling is identical in all CSI models, and deviates by approximately 82% from the (one-loop) SM prediction, we find that the inclusion of two- loop corrections lifts this universality and allows distinguishing different BSM scenarios with CSI. Taking into account constraints from perturbative unitarity and the relation among masses, we find for both types of scenarios we consider that at two loops λhhh deviates from its SM prediction by 100 ± 10% — i.e. a quite significant further deviation with respect to the one-loop result of ∼ 82%.
Highlights
The discovery of a Higgs boson of mass 125 GeV at the CERN Large Hadron Collider [1, 2] has completed the particle spectrum of the Standard Model (SM) of particle physics, and has established the Higgs sector as the origin of electroweak symmetry breaking (EWSB)
While at one loop the value of the Higgs trilinear coupling is identical in all classical scale invariance (CSI) models, and deviates by approximately 82% from the SM prediction, we find that the inclusion of twoloop corrections lifts this universality and allows distinguishing different BSM scenarios with CSI
For the wide range of CSI models in which the scalon/Higgs direction does not mix with other states — so that we can compute Veff as in eq (2.16) — we have derived general two-loop results relating the coefficients of the effective potential to the corrections to the Higgs trilinear coupling
Summary
The discovery of a Higgs boson of mass 125 GeV at the CERN Large Hadron Collider [1, 2] has completed the particle spectrum of the Standard Model (SM) of particle physics, and has established the Higgs sector as the origin of electroweak symmetry breaking (EWSB). Couplings of the Higgs boson — and especially its trilinear coupling — can potentially differ significantly from their SM values in BSM theories with extended scalar sectors, because of non-decoupling effects from loop corrections involving the BSM states — this was found at one loop, first in the 2HDM in refs. The universality of this prediction is a strong and unique property of CSI models, and follows (as we will see in section 2) from the especially simple form that the effective potential takes at one-loop order along the “scalon” direction This value of (λChhShI )(1) means that the EWPT is always of strong first order in CSI theories — this, together with the synergy between the measurements of gravitational waves and of the Higgs trilinear coupling was investigated in ref. We provide in appendix D generic results for the coefficients in the effective potential that can be applied for any CSI model without mixing
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