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Register a new userOn two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors
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We investigate the possible size of two-loop radiative corrections to the Higgs trilinear coupling $lambda_{hhh}$ in two types of models with extended Higgs sectors, namely in a Two-Higgs-Doublet Model (2HDM) and in the Inert Doublet Model (IDM). We calculate the leading contributions at two loops arising from the additional (heavy) scalars and the top quark of these theories in the effective-potential approximation. We include all necessary conversion shifts in order to obtain expressions both in the $overline{text{MS}}$ and on-shell renormalisation schemes, and in particular, we devise a consistent on-shell prescription for the soft-breaking mass of the 2HDM at the two-loop level. We illustrate our analytical results with numerical studies of simple aligned scenarios and show that the two-loop corrections to $lambda_{hhh}$ remain smaller than their one-loop counterparts, with a typical size being 10-20% of the one-loop corrections, at least while perturbative unitarity conditions are fulfilled. As a consequence, the existence of a large deviation of the Higgs trilinear coupling from the prediction in the Standard Model, which has been discussed in the literature at one loop, is not altered significantly.
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The Higgs trilinear coupling $lambda_{hhh}$ is of great importance to understand the structure of the Higgs sector and allows searching for indirect signs of Beyond-the-Standard-Model (BSM) physics, even if new states are somehow hidden. In particular, in models with extended Higgs sectors, it is known that non-decouplings effects in BSM-scalar contributions at one loop can cause $lambda_{hhh}$ to deviate significantly from its SM prediction, raising the question of what happens at two loops. We review here our calculation of the leading two-loop corrections to $lambda_{hhh}$ in an aligned scenario of a Two-Higgs-Doublet Model. We find their typical size to be 10-20% of the one-loop corrections, meaning that they do not modify significantly the one-loop non-decoupling effects, but are not entirely negligible either.
The Higgs trilinear coupling provides a unique opportunity to study the structure of the Higgs sector and probe indirect signs of BSM Physics -- even if new states are somehow hidden. In models with extended Higgs sectors, large deviations in the Higgs trilinear coupling can appear at one loop because of non-decoupling effects in the radiative corrections involving the additional scalar states. It is then natural to ask how two-loop corrections modify this result, and whether new large corrections can appear again. We present new results on the dominant two-loop corrections to the Higgs trilinear coupling in several models with extended scalar sectors. We illustrate the analytical expressions with numerical examples and show that, while they remain smaller than their one-loop counterparts and do not modify significantly the non-decoupling effects observed at one loop, the two-loop corrections are not entirely negligible -- a typical size being 10-20% of the one-loop corrections.
We compute the dominant two-loop corrections to the Higgs trilinear coupling $lambda_{hhh}$ and to the Higgs quartic coupling $lambda_{hhhh}$ in models with extended Higgs sectors, using the effective-potential approximation. We provide in this paper all necessary details about our calculations, and present general $overline{text{MS}}$ expressions for derivatives of the integrals appearing in the effective potential at two loops. We also consider three particular Beyond-the-Standard-Model (BSM) scenarios -- namely a typical scenario of an Inert Doublet Model (IDM), and scenarios of a Two-Higgs-Doublet Model (2HDM) and of a Higgs Singlet Model (HSM) without scalar mixing -- and we include all the necessary finite counterterms to obtain (in addition to $overline{text{MS}}$ results) on-shell scheme expressions for the corrections to the Higgs self-couplings. With these analytic results, we investigate the possible magnitude of two-loop BSM contributions to the Higgs self-couplings and the fate of the non-decoupling effects that are known to appear at one loop. We find that, at least as long as pertubative unitarity conditions are fulfilled, the size of two-loop corrections remains well below that of one-loop corrections. Typically, two-loop contributions to $lambda_{hhh}$ amount to approximately 20% of those at one loop, implying that the non-decoupling effects observed at one loop are not significantly modified, but also meaning that higher-order corrections need to be taken into account for the future perspective of precise measurements of the Higgs trilinear coupling.
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. Furthermore, a particularly interesting feature is that the Higgs trilinear coupling $lambda_{hhh}$ is universally predicted at one loop in CSI models, and deviates by 67% from its (tree-level) SM prediction. This result is however modified at two loops, and we review in these proceedings our calculation of leading two-loop corrections to $lambda_{hhh}$ in models with classical scale invariance, taking as an example a CSI scenario of a Two-Higgs-Doublet Model. We find that the inclusion of two-loop effects allows distinguishing different scenarios with CSI, although the requirement of reproducing the known 125-GeV Higgs-boson mass severely restricts the allowed values of $lambda_{hhh}$.
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 $100pm10%$ -- i.e. a quite significant further deviation with respect to the one-loop result of $sim 82%$.
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