Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos

We compute the two-loop O(as*at) corrections to the Higgs boson masses in supersymmetric extensions of the Standard Model with Dirac gaugino masses. We rely on the effective-potential technique, allow for both Dirac and Majorana mass terms for the gluinos, and compute the corrections in both the DRbar and on-shell renormalisation schemes. We give detailed results for the MDGSSM and the MRSSM, and simple approximate formulae valid in the decoupling limit for all currently-studied variants of supersymmetric models with Dirac gluinos. These results represent the first explicit two-loop calculation of Higgs boson masses in supersymmetric models beyond the MSSM and the NMSSM.Comment: 36 pages, 5 figures; v2: version published in JHE

Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons

The calculation of the Higgs mass in general renormalisable field theories has been plagued by the so-called "Goldstone Boson Catastrophe", where light (would-be) Goldstone bosons give infra-red divergent loop integrals. In supersymmetric models, previous approaches included a workaround that ameliorated the problem for most, but not all, parameter space regions; while giving divergent results everywhere for non-supersymmetric models! We present an implementation of a general solution to the problem in the public code SARAH, along with new calculations of some necessary loop integrals and generic expressions. We discuss the validation of our code in the Standard Model, where we find remarkable agreement with the known results. We then show new applications in Split SUSY, the NMSSM, the Two-Higgs-Doublet Model, and the Georgi-Machacek model. In particular, we take some first steps to exploring where the habit of using tree-level mass relations in non-supersymmetric models breaks down, and show that the loop corrections usually become very large well before naive perturbativity bounds are reached.Comment: 45 pages, 12 figure

Matching renormalisable couplings: simple schemes and a plot

We discuss different choices that can be made when matching a general high-energy theory -- with the restriction that it should not contain heavy gauge bosons -- onto a general renormalisable effective field theory at one loop, with particular attention to the quartic scalar couplings and Yukawa couplings. This includes a generalisation of the counterterm scheme that was found to be useful in the case of high-scale/split supersymmetry, but we show the important differences when there are new heavy scalar fields in singlet or triplet representations of $SU(2)$. We also analytically compare our methods and choices with the approach of matching pole masses, proving the equivalence with one of our choices. We outline how to make the extraction of quartic couplings using pole masses more efficient, an approach that we hope will generalise beyond one loop. We give examples of the impact of different scheme choices in a toy model; we also discuss the MSSM and give the threshold corrections to the Higgs quartic coupling in Dirac gaugino models.Comment: 59 pages, 7 figures. v2: added some explanations. Matches published versio

External-leg corrections as an origin of large logarithms

Obtaining precise theoretical predictions for both production and decay processes of heavy new particles is of great importance to constrain the allowed parameter spaces of Beyond-the-Standard-Model (BSM) theories, and to properly assess the sensitivity for discoveries and for discriminating between different possible BSM scenarios. In this context, it is well known that large logarithmic corrections can appear in the presence of widely separated mass scales. We point out the existence of a new type of possible large, Sudakov-like, logarithms in external-leg corrections of heavy scalars. To the difference of usual Sudakov logarithms, these can furthermore potentially be enhanced by large trilinear couplings. Such large logarithms are associated with infrared singularities and we review several techniques to address these at one loop. In addition to this discussion, we also present the derivation of the two-loop corrections containing this type of large logarithms, pointing out in this context the importance of adopting an on-shell renormalisation scheme. Finally, we illustrate our calculations and examine the possible magnitude of these corrections for a simple scalar toy model as well as for decay processes involving heavy stop quarks in the Minimal Supersymmetric Standard Model and a heavy Higgs boson in the Next-to-Two-Higgs-Doublet Model.Comment: 8 pages, 2 figures. Contribution to the proceedings of the conference "Loops and Legs in Quantum Field Theory - LL2022," 25-30 April, 2022, Ettal, German

New constraints on extended scalar sectors from the trilinear Higgs coupling

The trilinear Higgs coupling $\lambda_{hhh}$ is a crucial tool to probe the structure of the Higgs potential and to search for possible effects of physics beyond the Standard Model (SM). Focusing on the Two-Higgs-Doublet Model as a concrete example, we identify parameter regions in which $\lambda_{hhh}$ is significantly enhanced with respect to its SM prediction. Taking into account all relevant corrections up to the two-loop level, we show that current experimental bounds on $\lambda_{hhh}$ already rule out significant parts of the otherwise unconstrained parameter space. We illustrate the interpretation of the current results and future measurement prospects on $\lambda_{hhh}$ for a benchmark scenario. Recent results from direct searches for BSM scalars in the $A\to ZH$ channel and their implications will also be discussed in this context.Comment: 6 pages, 2 figures. Contribution to the proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP2023), 21-25 August 2023, Hamburg, German

New Constraints on Extended Higgs Sectors from the Trilinear Higgs Coupling

The trilinear Higgs coupling $λ_{hhh}$ is crucial for determining the structure of the Higgs potential and for probing possible effects of physics beyond the standard model. Focusing on the two-Higgs-doublet model as a concrete example, we identify parameter regions in which $λ_{hhh}$ is significantly enhanced with respect to the standard model. Taking into account all relevant corrections up to the two-loop level, we show that already current experimental bounds on $λ_{hhh}$ rule out significant parts of the parameter space that would otherwise be unconstrained. We illustrate the interpretation of the results on $λ_{hhh}$ for a benchmark scenario. Similar results are expected for wide classes of models with extended Higgs sectors

N-loop running should be combined with N-loop matching

We investigate the high-scale behaviour of Higgs sectors beyond the Standard Model, pointing out that the proper matching of the quartic couplings before applying the renormalisation group equations (RGEs) is of crucial importance for reliable predictions at larger energy scales. In particular, the common practice of leading-order parameters in the RGE evolution is insufficient to make precise statements on a given model's UV behaviour, typically resulting in uncertainties of many orders of magnitude. We argue that, before applying N-loop RGEs, a matching should even be performed at N-loop order in contrast to common lore. We show both analytical and numerical results where the impact is sizeable for three minimal extensions of the Standard Model: a singlet extension, a second Higgs doublet and finally vector-like quarks. We highlight that the known two-loop RGEs tend to moderate the running of their one-loop counterparts, typically delaying the appearance of Landau poles. For the addition of vector-like quarks we show that the complete two-loop matching and RGE evolution hints at a stabilisation of the electroweak vacuum at high energies, in contrast to results in the literature.Comment: 16 pages, 11 figures; v2: title changed, accepted for publication in PR

Experimental probes and theoretical concepts for BSM trilinear couplings: a case study for scalar top quarks

After the possible discovery of new particles, it will be crucial to determine the properties, and in particular the couplings, of the new states. Here, we focus on scalar trilinear couplings, employing as an example the case of the trilinear coupling of scalar top quarks (stops) to the Higgs boson in the Minimal Supersymmetric Standard Model (MSSM). We discuss possible strategies for experimentally determining the stop trilinear coupling parameter, which controls the stop--stop--Higgs interaction, and we demonstrate the impact of different prescriptions for the renormalisation of this parameter. We find that the best prospects for determining the stop trilinear coupling arise from its quantum effects entering the model prediction for the mass of the SM-like Higgs boson in comparison to the measured value, pointing out that the prediction for the Higgs-boson mass has a high sensitivity to the stop trilinear coupling even for heavy masses of the non-standard particles. Regarding the renormalisation of the stop trilinear coupling, we identify a renormalisation scheme that is preferred given the present level of accuracy, and we clarify the origin of potentially large logarithms that cannot be resummed with standard renormalisation group methods.Comment: 6 pages, 2 figures. Contribution to the proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP2023), 21-25 August 2023, Hamburg, German

Precise predictions for the trilinear Higgs self-coupling in the Standard Model and beyond

Deviations in the trilinear self-coupling of the Higgs boson at 125 GeV from the Standard Model (SM) prediction are a sensitive test of physics Beyond the SM (BSM). The LHC experiments searching for the simultaneous production of two Higgs bosons start to become sensitive to such deviations. Therefore, precise predictions for the trilinear Higgs self-coupling in different BSM models are required in order to be able to test them against current and future bounds. We present the new framework $\texttt{anyH3}$, which is a $\texttt{Python}$ library that can be utilized to obtain predictions for trilinear scalar couplings up to the one-loop level in any renormalisable theory. The program makes use of the $\texttt{UFO}$ format as input and is able to automatically apply a wide variety of renormalisation schemes involving minimal and non-minimal subtraction conditions. External-leg corrections are also computed automatically, and finite external momenta can be optionally taken into account. The $\texttt{Python}$ library comes with convenient command-line as well as $\texttt{Mathematica}$ user interfaces. We perform cross-checks using consistency conditions such as UV-finiteness and decoupling, and also by comparing against results know in the literature. As example applications, we obtain results for the trilinear self-coupling of the SM-like Higgs boson in various concrete BSM models, study the effect of external momenta as well as of different renormalisation schemes.Comment: 6 pages, The European Physical Society Conference on High Energy Physics (EPS-HEP2023