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%.
The Higgs trilinear coupling is a crucial tool to investigate the structure of the Higgs sector and the nature of the electroweak phase transition, and to search for indirect signs of New Physics. Classical scale invariance (CSI) is an attractive concept for BSM model building, explaining the apparent alignment of the Higgs sector and potentially relating to the hierarchy problem. A particularly interesting feature of CSI theories is that, at one loop, they universally predict the Higgs trilinear coupling to deviate by 67% from the SM prediction at tree level. This result is however modified at two loops, and we present here results from the first explicit computation of two-loop corrections to the Higgs trilinear coupling in classically scale-invariant BSM models. Taking as example a CSI variant of the Two-Higgs-Doublet Model, we show that the inclusion of two-loop effects allows distinguishing different scenarios with CSI, even though the requirement of correctly reproducing the mass of the Higgs boson, as well as unitarity, severely restrict the possible values of the Higgs trilinear coupling.
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