Two-loop analysis of classically scale-invariant models with extended Higgs sectors

We present the first explicit calculation of leading two-loop corrections to the Higgs trilinear coupling $\lambda_{hhh}$ 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 $\lambda_{hhh}$ deviates from its SM prediction by $100\pm10\%$ -- i.e. a quite significant further deviation with respect to the one-loop result of $\sim 82\%$.