Abstract
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{{mathrm{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{{mathrm{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.
Highlights
One example of the latter is alignment [4], which occurs in extended scalar sectors with multiple Higgs doublets when one of the CP-even Higgs mass eigenstates is collinear in field space with the total electroweak vacuum expectation value (VEV)
Considering the points for MΦ = 400 GeV – i.e. well within the region where perturbative unitarity conditions are fulfilled – we find that the two-loop corrections can at most become as large as 25%, 52%, and 62% of the one-loop corrections
We have presented new general results, in terms of MSrenormalised parameters, for the derivatives of integrals appearing in the effective potential, which can be applied to further models and served for important cross-checks of our model-specific computations
Summary
One example of the latter is alignment [4], which occurs in extended scalar sectors with multiple Higgs doublets when one of the CP-even Higgs mass eigenstates is collinear in field space with the total electroweak vacuum expectation value (VEV). Various other public tools include, or allow obtaining, results for loop corrections to Higgs couplings and decays in these three BSM models: namely 2HDMC [66], PROPHECY4F [67], and 2HDECAY [68] for the 2HDM; sHDECAY [69] and PROPHECY4F (since version 3.0 [70]) for the singlet extension; and SPheno [71,72] together with SARAH [73,74,75,76,77,78] which implement expressions for generic BSM theories [79] that can be applied automatically to a desired model. [85], studied (part of) the leading corrections from the additional scalars in the Inert Doublet Model and how these affect the strength of the EWPT This calculation found an enhancement of λhhh by a few percent at two loops even if effects of 30–40% appear at one loop; in turn these two-loop contributions slightly weaken the strength of the first-order EWPT. Additional details are presented in appendices, with our conventions and definitions of loop functions in Appendix A, full expressions for 2HDMs in Appendix B, and definitions of the intermediate functions used in Sect. 4 in Appendix C
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