Reconstructing the shape of the Higgs potential realised in Nature is a central part of the physics programme at the LHC and future colliders. In this context, accurate theoretical predictions for trilinear and quartic Higgs couplings are becoming increasingly important. In this paper, we present results that enable significant progress in the automation of these calculations at the two-loop level in a wide range of models. Specifically, we calculate the generic two-loop corrections for scalar $\textit{n}$-point functions with $\textit{n}$ ≤ 4 assuming that all external scalars are identical. Working in the zero-momentum approximation, we express the results in terms of generic couplings and masses. Additionally, by exploiting permutation invariances, we reduce the number of Feynman diagrams appearing to a substantially smaller set of basis diagrams. To ease the application of our setup, we also provide routines that allow to map our generic results to scalar two-loop amplitudes generated with the package FeynArts. We perform a series of calculations to cross-check our results with existing results in the literature. Moreover, we present new two-loop results for the trilinear Higgs coupling in the general singlet extension of the Standard Model. We also present the public Python package Tintegrals, which allows for fast and stable evaluations of all relevant two-loop integrals with vanishing external momenta.

Germany

Henning Bahl

Johannes Braathen

Martin Gabelmann

Sebastian Paßehr

Generic two-loop results for trilinear and quartic scalar self-interactions

The di-top final state is an important search channel for additional Higgs bosons at the LHC. In this channel, large signal-background interference contributions can strongly distort a resonance peak as it would be expected from a pure signal contribution. Moreover, signal-signal interference effects can have a significant impact if more than one additional scalar particle is present. In this work, we perform a comprehensive model-independent analysis of the various interference contributions considering two additional heavy scalars that can mix with each other. We point out the importance of taking into account loop-level mixing between the scalars. A proper treatment of these mixing effects, which has not been previously carried out for the di-top final state, introduces additional relative phases between different parts of the amplitudes entering the interference contributions which we find to have a strong impact on the di-top invariant mass distribution. We study the interference effects both in an idealistic setting as well as taking into account experimental limitations using Monte-Carlo simulations. We demonstrate that the emerging experimental signatures can be unexpected and difficult to interpret. In particular, we point out that an experimental signature manifesting itself as an excess near the $$ t\overline{t} $$ threshold may actually be caused by new scalar particles with much higher masses. We comment in this context on the recent excess that has been observed by the CMS collaboration near the $$ t\overline{t} $$ threshold in their searches in the di-top final state.

Romal Kumar

Georg Weiglein

Impact of interference effects on Higgs-boson searches in the di-top final state at the LHC

The   <math> <mi>CP</mi> </math>  $$ \mathcal{CP} $$  structure of the Higgs boson is a fundamental property which has not yet been constrained with high precision.   <math> <mi>CP</mi> </math>  $$ \mathcal{CP} $$  violation in the Yukawa coupling between the Higgs boson and top quark pair can be probed directly at the Large Hadron Collider by measuring top-quark-associated Higgs production. Multivariate analysis techniques commonly developed so far by the experiments are designed for a specific signal model and, therefore, complicate reinterpretations and statistical combinations. With this motivation in mind, we propose a   <math> <mi>CP</mi> </math>  $$ \mathcal{CP} $$ -sensitive extension of the simplified template cross-section (STXS) framework. Considering multiple Higgs decay channels, we perform an in-depth comparison of   <math> <mi>CP</mi> </math>  $$ \mathcal{CP} $$ -sensitive observables and combinations thereof. Our resulting proposal is to extend the existing binning in the transverse momentum of the Higgs boson p  T,H  by either the pseudorapidity difference of the two top-quarks   <math> <mtext>∆</mtext> <msub> <mi>η</mi> <mrow> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </mrow> </msub> </math>  $$ \Delta {\eta}_{t\overline{t}} $$ , or a variable that is based on the top quark momenta, namely b 2 or the Collins-Soper angle |cosθ ∗|. We demonstrate that this variable selection provides close to optimal sensitivity to the   <math> <mi>CP</mi> </math>  $$ \mathcal{CP} $$  mixture in the top Yukawa coupling for an integrated luminosity of 300 fb−1, by comparing it to the results of a multivariate analysis. Our results also suggest a benefit of the two-dimensional STXS extension at 3000 fb−1.

France

Alberto Carnelli

Frédéric Déliot

Elina Fuchs

Anastasia Kotsokechagia

Tanguy Marsault

Marco Menen

Laurent Schoeffel

Matthias Saimpert

<math> <mi>CP</mi> </math>  $$ \mathcal{CP} $$ -sensitive simplified template cross-sections for   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>H</mi> </math>  $$ t\overline{t}H $$

The discovery of the top quark, the most massive elementary particle yet known, has given us a distinct window into investigating the physics of the Standard Model and beyond. With a plethora of top quarks to be produced in the high luminosity era of the LHC, the exploration of its rare decays holds great promise in revealing potential new physics phenomena. We consider higher-dimensional operators contributing to flavour-changing-neutral-current top decays in the SMEFT and its extension by a light singlet species of spin 0, 1/2, or 1, and exhibit that the HL-LHC (and other future colliders) may observe many exotic top decays in a variety of channels. Light singlets which primarily talk to the SM through such a top interaction may also lead to distinctive long-lived particle signals. Searching for such long-lived particles in top-quark decays has the additional advantage that the SM decay of the other top quark in the same event provides a natural trigger.

United States

Seth Koren

Lian-Tao Wang

Topportunities at the LHC: rare top decays with light singlets

Results for the full electroweak two-loop contributions of  $$\mathcal {O}\left( N_c^2\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </mfenced> </mrow> </math>  , where  $$N_c$$  <math> <msub> <mi>N</mi> <mi>c</mi> </msub> </math>   is the colour factor, to the Higgs-boson masses in the MSSM are obtained using a Feynman-diagrammatic approach including the full dependence on the external momentum. These corrections are expected to constitute the dominant part of the two-loop corrections that were still missing up to now. As a consequence of working at  $$\mathcal {O}\left( N_c^2\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </mfenced> </mrow> </math>  , the relevant two-loop self-energies decompose into products of one-loop integrals, giving rise to a transparent analytical structure of the self-energies. We compare different renormalisation schemes for  $$\tan (\beta )$$  <math> <mrow> <mo>tan</mo> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> </math>  , the ratio of the vacuum expectation values of the two Higgs doublets, and demonstrate under which conditions different renormalisation schemes can be related to each other via a simple reparametrisation. We explicitly show that this is in general not possible for mixed renormalisation schemes due to the presence of evanescent terms. In our numerical analysis, the new corrections are compared with already known two-loop contributions and the experimental uncertainty of the mass of the observed Higgs boson. While smaller than the already known two-loop corrections, the new terms are typically larger in size than the experimental uncertainty. This underlines the relevance of the so-far unknown electroweak two-loop contributions.

Daniel Meuser

Complete electroweak  $$\mathcal {O}\left( N_c^2\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </mfenced> </mrow> </math>   two-loop contributions to the Higgs boson masses in the MSSM and aspects of two-loop renormalisation

The resummation of large thermal corrections to the effective potential is mandatory for the accurate prediction of phase transitions. We discuss the accuracy of different prescriptions to perform this resummation at the one- and two-loop level and point out conceptual issues that appear when using a high-temperature expansion at the two-loop level. Moreover, we show how a particular prescription called partial dressing, which does not rely on a high-temperature expansion, consistently avoids these issues. We introduce a novel technique to apply this resummation method to the case of multiple mixing fields. Our approach significantly extends the range of applicability of the partial dressing prescription, making it suitable for phenomenological studies of beyond the Standard Model extensions of the Higgs sector.

Marcela Carena

Aurora Ireland

Carlos Wagner

Improved thermal resummation for multi-field potentials

Erratum to: anyH3: precise predictions for the trilinear Higgs coupling in the Standard Model and beyond

The trilinear Higgs coupling  $$\lambda _{hhh}$$  <math> <msub> <mi>λ</mi> <mrow> <mi>hhh</mi> </mrow> </msub> </math>   of the detected Higgs boson is an important probe for physics beyond the Standard Model. Correspondingly, improving the precision of the theoretical predictions for this coupling as well as the experimental constraints on it are among the main goals of particle physics in the near future. In this article, we present the public Python code anyH3, which provides precise theoretical predictions for  $$\lambda _{hhh}.$$  <math> <mrow> <msub> <mi>λ</mi> <mrow> <mi>hhh</mi> </mrow> </msub> <mo>.</mo> </mrow> </math>   The program can easily be used for any renormalisable model, where for the input the UFO format is adopted. It allows including corrections up to the full one-loop level with arbitrary values of the external squared momenta and features a semi-automatic and highly flexible renormalisation procedure. The code is validated against known results in the literature. Moreover, we present new results for  $$\lambda _{hhh}$$  <math> <msub> <mi>λ</mi> <mrow> <mi>hhh</mi> </mrow> </msub> </math>   in models which so far have not been investigated in the literature.

anyH3: precise predictions for the trilinear Higgs coupling in the Standard Model and beyond

Searches for dark matter produced via scalar resonances in final states consisting of Standard Model (SM) particles and missing transverse momentum are of high relevance at the LHC. Motivated by dark-matter portal models, most existing searches are optimized for unbalanced decay topologies for which the missing momentum recoils against the visible SM particles. In this work, we show that existing searches are also sensitive to a wider class of models, which we characterize by a recently presented simplified model framework. We point out that searches for models with a balanced decay topology can be further improved with more dedicated analysis strategies. For this study, we investigate the feasibility of a new search for bottom-quark associated neutral Higgs production with a   <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>Z</mi> <mo>+</mo> <msubsup> <mi>p</mi> <mi>T</mi> <mtext>miss</mtext> </msubsup> </math>  $$ b\overline{b}Z+{p}_{\textrm{T}}^{\textrm{miss}} $$  final state and perform a detailed collider analysis. Our projected results in the different simplified model topologies investigated here can be easily reinterpreted in a wide range of models of physics beyond the SM, which we explicitly demonstrate for the example of the Two-Higgs-Doublet model with an additional pseudoscalar Higgs boson.

Danyer Adan

Alexander Grohsjean

Spain

Victor Lozano

Christian Schwanenberger

A new LHC search for dark matter produced via heavy Higgs bosons using simplified models

After the possible discovery of new heavy particles at the LHC, it will be crucial to determine the properties and the underlying physics of the new states. In this work, we focus on scalar trilinear couplings, employing as an example the case of the trilinear coupling of scalar partners of the top quark to the Higgs boson. We discuss possible strategies for experimentally determining the scalar top (stop) trilinear coupling parameter, which controls the stop–stop–Higgs interaction, and we demonstrate the impact of different renormalisation prescriptions for 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. We point 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 in view of the present level of accuracy and we clarify the source of potentially large logarithms that cannot be resummed with standard renormalisation group methods.

Theoretical concepts and measurement prospects for BSM trilinear couplings: a case study for scalar top quarks