Strong first-order phase transitions (SFOPT) during the evolution of the Higgs potential in the early universe not only allow for the dynamical generation of the observed matter-antimatter asymmetry, they can also source a stochastic gravitational wave (GW) background possibly detectable with future space-based gravitational waves interferometers. As SFOPTs are phenomenologically incompatible with the Standard Model (SM) Higgs sector, the observation of GWs from SFOPTs provides an exciting interplay between cosmology and particle physics in the search for new physics. With the C++ code BSMPTv3, we present for the first time a tool that performs the whole chain from the particle physics model to the gravitational wave spectrum. Extending the previous versions BSMPTv1 and v2, it traces the phases of beyond-SM (BSM) Higgs potentials and is capable of treating multiple vacuum directions and multi-step phase transitions. During the tracing, it checks for discrete symmetries, flat directions, and electroweak symmetry restoration, and finally reports the transition history. The transition probability from the false to the true vacuum is obtained from the solution of the bounce equation which allows for the calculation of the nucleation, percolation and completion temperatures. The amplitude and characteristic frequencies of the GWs originating from bubble collisions and highly relativistic fluid shells, sound waves and turbulence, are evaluated after the calculation of the thermal parameters at the transition temperature, and finally the signal-to-noise ratio at LISa is provided. The code BSMPTv3 is a powerful self-contained tool that comes more than timely and will be of great benefit for investigations of the vacuum structure of the early universe of not only simple but also complicated Higgs potentials involving several vacuum directions, with exciting applications in the search for new physics.

We investigate the potential of the model `CP in the Dark' for providing a strong first-order electroweak phase transition (SFOEWPT) by taking into account all relevant theoretical and experimental constraints. For the derivation of the strength of the phase transition we use the one-loop corrected, daisy-resummed effective potential at finite temperature, implemented in the C++ code BSMPT, to determine the global minimum at the critical temperature. The model `CP in the Dark' provides a dark matter (DM) candidate as well as explicit CP violation in the dark sector. We find a broad range of viable parameter points providing an SFOEWPT. They are within the reach of XENON1T and future invisible Higgs decay searches for DM. `CP in the Dark' also offers SFOEWPT points that feature spontaneous CP violation at finite temperature. Having not only an SFOEWPT that provides the necessary departure from thermal equilibrium, but also a source of additional non-standard CP violation, opens a promising gate towards enabling the generation of the baryon asymmetry of the universe (BAU) through electroweak baryogenesis.

In this paper, we investigate the possibility of a strong first-order electroweak phase transition (SFOEWPT) in the model ‘CP in the Dark’ . The Higgs sector of the model consists of two scalar doublets and one scalar singlet with a specific discrete symmetry. After spontaneous symmetry breaking the model has a Standard-Model-like phenomenology and a hidden scalar sector with a viable Dark Matter candidate supplemented by explicit CP violation that solely occurs in the hidden sector. The model ‘CP in the Dark’ has been implemented in the C++ code BSMPT v2.3 which performs a global minimisation of the finite-temperature one-loop corrected effective potential and searches for SFOEWPTs. An SFOEWPT is found to be allowed in a broad range of the parameter space. Furthermore, there are parameter scenarios where spontaneous CP violation is generated at finite temperature. The in addition spontaneously broken ℤ_2 symmetry then leads to mixing between the dark and the visible sector so that CP violation in the dark is promoted at finite temperature to the visible sector and thereby provides additional sources of CP violation that are not restricted by the electric dipole moment measurements at zero temperature. Thus, ‘CP in the Dark’ provides a promising candidate for the generation of the baryon asymmetry of the universe through electroweak baryogenesis.

Recently we presented the upgrade of our code BSMPT for the calculation of the electroweak phase transition (EWPT) to BSMPT v2 which now includes the computation of the baryon asymmetry of the universe (BAU) in the CP-violating 2-Higgs-Doublet Model (C2HDM). In this paper we use BSMPT v2 to investigate the size of the BAU that is obtained in the C2HDM with the two implemented approaches FH and VIA to derive the transport equations, by taking into account all relevant theoretical and experimental constraints. We identify similarities and differences in the results computed with the two methods. In particular, we analyse the dependence of the obtained BAU on the parameters relevant for successful baryogenesis. Our investigations allow us to pinpoint future directions for improvements both in the computation of the BAU and in possible avenues taken for model building. Recently, it was argued that the source term in the VIA method vanishes at leading order which would have consequences for the derived BAU in this method.

Direct detection experiments are the only way to obtain indisputable evidence of the existence of dark matter (DM) in the form of a particle. These experiments have been used to probe many extensions of the Standard Model (SM) that provide DM candidates. Experimental results like the latest ones from XENON1T lead to severe constraints in the parameter space of many of the proposed models. In a simple extension of the SM, the addition of a complex singlet to the SM content, one-loop corrections need to be taken into account because the tree-level cross section is proportional to the DM velocity, and therefore negligible. In this work we study the case of a DM particle with origin in a singlet but in a larger framework of an extension by an extra doublet together with the extra singlet providing the DM candidate. We show that in the region of interest of the present and future direct detection experiments, electroweak corrections are quite stable with a K-factor very close to one.

We study the impact of additional beyond-the-Standard Model (BSM) fermions, charged under the Standard Model (SM) SU(2)L ⊗ U(1)Y gauge group, on the electroweak phase transition (EWPT) in a 2-Higgs-Doublet-Model (2HDM) of type II. We find that the strength of the EWPT can be enhanced by about 40% compared to the default 2HDM. Therefore, additional light fermions are a useful tool to weaken the tension between increasing mass constraints on BSM scalars and the requirement of additional light scalar degrees of freedom to accommodate a strong first order EWPT. The findings are of particular interest for a variety of (non-minimal) split supersymmetry scenarios which necessarily introduce additional light fermion degrees of freedom.

We present the C++ code BSMPT v2 which is an extension of the previous code BSMPT for the calculation of the strength of the electroweak phase transition in extended Higgs sectors. The new version BSMPT v2 includes the features of BSMPT and extends the already implemented models (the 2-HiggsDoublet model (2HDM) in its CP-conserving and CP-violating versions and the Next-to-2HDM) by the Complex Singlet Extension of the Standard Model (CxSM). The major upgrade is the implementation of the computation of the baryon asymmetry of the Universe for the CP-violating 2HDM (C2HDM), which is performed in two different approximations. These changes and further smaller modifications are described in this manual. Additionally, a detailed explanation of the procedure for the implementation of new models is given, which has also changed with respect to the previous version. Program summary Program Title: BSMPT CPC Library link to program files: https://doi .org /10 .17632 /sjtp7bb33t .1 Licensing provisions: GPL-3.0 License Programming Language: C++14 Nature of problem: Non-minimal extended Higgs sector models provide non-trivial vacuum structures which allow for a strong first order electroweak phase transition. Such a phase transition is one of the three Sakharov conditions that are required for a dynamical generation of the observed baryon asymmetry of the universe (BAU) through an electroweak phase transition. The actual calculation of the electroweak baryogenesis requires the solution of the quantum transport equation system describing the non-thermal equilibrium state of the early universe during the phase transition. BSMPT v2 provides a numerical tool to investigate the vacuum structure of the one-loop effective potential at finite temperature including thermal masses, for an arbitrary extended Higgs sector. It allows for the computation of the strength of the electroweak phase transition for the implemented models. For the CP-violating 2HDM (C2HDM) also the generated BAU is calculated. For the latter task BSMPT v2 has two different approaches implemented for the formulation of the quantum transport equations, given by the FH approach based on the semi-classical force and the vacuum expectation value insertion method VIA. Solution Method: Numerical minimization of the one-loop effective potential including thermal masses, at finite temperature with three different numerical minimizers, GSL, cmaes and NLopt, in order to determine the relevant parameters required for the phase transition dynamics at the critical temperature and the criticial field configuration. Furthermore, with the updated version BSMPT v2 it is possible to numerically solve for the C2HDM the system of coupled differential transport equations and calculate the BAU for this model. Additional comments including restrictions and unusual features: The BSM extensions are restricted to the Higgs sectors. New gauge bosons and fermions would require an adaption in the thermal corrections of the one-loop potential, which is not implemented in BSMPT v2. At present, the BAU is only calculated for the C2HDM. In the computation of the BAU the wall velocity is an input parameter and assumed to be

We present the CP-violating Next-to-2-Higgs-Doublet Model (CN2HDM) which is based on the extension of the CP-violating 2-Higgs-Doublet-Model (C2HDM) by a complex singlet field that obeys a discrete $\mathbb{Z}_2$ symmetry. The model thus features not only CP violation required for successful electroweak baryogenesis but also a Dark Matter (DM) candidate. The model has an extended Higgs sector with four CP-mixing visible neutral Higgs bosons, a DM candidate and a pair of oppositely charged Higgs bosons. The possibility of singlet and CP-odd admixtures to the observed Higgs boson in addition to the large number of visible scalar particles leads to an interesting Higgs phenomenology. We find that the model can easily provide 100\% of the DM relic density and investigate interesting LHC and DM observables within the model. We provide all the tools necessary to study the CN2HDM in detail and point out future research directions for this interesting benchmark model that can address some of the most pressing open questions of the Standard Model.

Higgs sector extensions beyond the Standard Model (BSM) provide additional sources of CP violation and further scalar states that help to trigger a strong first order electroweak phase transition (SFOEWPT) required to generate the observed baryon asymmetry of the Universe through electroweak baryogenesis. We investigate the CP-violating 2-Higgs-Doublet Model (C2HDM) and the Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) with respect to their potential to generate an SFOEWPT while being compatible with all relevant and recent theoretical and experimental constraints. The implications of an SFOEWPT on the collider phenomenology of the two models are analysed in detail in particular with respect to Higgs pair production. We provide benchmark points for parameter points that are compatible with an SFOEWPT and provide distinct di-Higgs signatures.

Having so far only indirect evidence for the existence of Dark Matter a plethora of experiments aims at direct detection of Dark Matter through the scattering of Dark Matter particles off atomic nuclei. For the correct interpretation and identification of the underlying nature of the Dark Matter constituents higher-order corrections to the cross section of Dark Matter-nucleon scattering are important, in particular in models where the tree-level cross section is negligibly small. In this work we revisit the electroweak corrections to the dark matter-nucleon scattering cross section in a model with a pseudo Nambu-Goldstone boson as the Dark Matter candidate. Two calculations that already exist in the literature, apply different approaches resulting in different final results for the cross section in some regions of the parameter space leading us to redo the calculation and analyse the two approaches to clarify the situation. We furthermore update the experimental constraints and examine the regions of the parameter space where the cross section is above the neutrino floor but which can only be probed in the far future.

In this work we present an update to a previous calculation of the Next-to-Leading Order (NLO) corrections to the Vector Dark Matter (VDM) direct detection cross section. The model under investigation is a minimal extension of the Standard Model (SM) with one extra vector boson and one extra complex scalar field, where the vector is the DM candidate. We have computed the spin-independent cross section for the scattering of the VDM particle with a nucleon. We now provide an update to the NLO cross section for the direct detection of the DM particle. We further discuss the phenomenological implications of the NLO corrections for the sensitivity of the direct detection DM experiments.

Although many astrophysical and cosmological observations point towards the existence of Dark Matter (DM), the nature of the DM particle has not been clarified to date. In this paper, we investigate a minimal model with a vector DM (VDM) candidate. Within this model, we compute the cross section for the scattering of the VDM particle with a nucleon. We provide the next-to-leading order (NLO) cross section for the direct detection of the DM particle. Subsequently, we study the phenomenological implications of the NLO corrections, in particular with respect to the sensitivity of the direct detection DM experi- ments. We further investigate more theoretical questions such as the gauge dependence of the results and the remaining theoretical uncertainties due to the applied approximations.