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M. Aa. Solberg

Publications and source records attributed to M. Aa. Solberg.

13 recordsLinked to original sources
arXiv2026

Scalar Lie point symmetries of the Standard Model with one or two real gauge singlets

We present a classification of all scalar Lie point symmetries of the Standard Model with one or two real gauge-singlet scalars (SM+S and SM+2S). By analyzing the associated field equations, we identify all realizable and inequivalent Lie point symmetry algebras of these models, distinguishing strict variational, variational (including divergence symmetries), and Euler--Lagrange cases. In addition, we devise efficient algorithms that, for any given numerical instance of the models, determine the Lie point symmetry algebra in each of the three categories by a parameter-based decision procedure using affine reparametrizations and simple parameter tests, thereby avoiding explicit symmetry analysis and the need to derive and solve the determining equations. Finally, we prove several relevant general results, including a characterization of the three disjoint types of Lie point symmetry generators -- strict variational, divergence, and non-variational -- for a broad class of Lagrangians with potentials, including the SM+S and SM+2S.

hep-ph↗
arXiv2025

Lie symmetry analysis of the two-Higgs-doublet model field equations

We apply Lie symmetry analysis of partial differential equations (PDEs) to the Euler-Lagrange equations of the two-Higgs-doublet model (2HDM), to determine its scalar Lie point symmetries. A Lie point symmetry is a structure-preserving transformation of the spacetime variables and the fields of the model, which is also continuous and connected to the identity. Symmetries of PDEs may, in general, be divided into strict variational, divergence and non-variational symmetries, where the first two are collectively referred to as variational symmetries. Variational symmetries are usually preserved under quantization, and variational Lie symmetries yield conservation laws. We demonstrate that there are no scalar Lie point divergence symmetries or non-variational Lie point symmetries in the 2HDM, and re-derive its well-known strict variational Lie point symmetries, thus confirming the consistency of our implementation of Lie's method. Moreover, we prove three general results that may simplify Lie symmetry calculations for a wide class of particle physics models. Lie symmetry analysis of PDEs is broadly applicable for determining Lie symmetries. As demonstrated in this work, the method can be applied to models with many variables, parameters, and reparametrization freedom, while any missing discrete symmetries can be identified through the automorphism groups of the resulting Lie symmetry algebras.

hep-ph↗
arXiv2024

Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials

By considering the basis-covariant constituents of N-Higgs-doublet potentials, we derive necessary and sufficient conditions for canonical SO(4)_C Custodial Symmetry (CS) of potentials with N>2 doublets, based on representation-theoretical and geometrical relations. In essence, our characterization relates the presence of canonical CS to basis-covariant vectors corresponding to particular bases of the defining representation of the orthogonal Lie algebras. For N=3,4 and 5, the conditions demand little computational effort to be evaluated, and we provide practical algorithms that may be efficiently implemented in a computer program, for deciding whether or not a potential is custodial-symmetric.

hep-ph↗
arXiv2024

Computable conditions for order-2 $CP$ symmetry in NHDM potentials

We derive necessary and sufficient conditions for order-2 $CP$ ($CP2$) symmetry in $N$-Higgs-doublet potentials for $N>2$. The conditions, which are formulated as relations between vectors that transform under the adjoint representation of $\mathsf{SU}(N)$ under a change of doublet basis, are representation theoretical in nature. Making use of Lie algebra and representation theory we devise an efficient, computable algorithm which may be applied to decide whether or not a given numerical potential is $CP2$ invariant.

hep-ph↗
arXiv2023

Weinberg's 3HDM potential with spontaneous CP violation

We study the potential of Weinberg's $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric three-Higgs-doublet model (3HDM). The potential is designed to accommodate CP violation in the scalar sector within a gauge theory, while at the same time allowing for natural flavour conservation. This framework allows for both explicit and spontaneous CP violation. CP can be explicitly violated when the coefficients of the potential are taken to be complex. With coefficients chosen to be real, CP can be spontaneously violated via complex vacuum expectation values (vevs). In the absence of the terms leading to the possibility of CP violation, either explicit or induced by complex vevs, the potential has two global U(1) symmetries. In this case, spontaneous symmetry breaking would in general give rise to massless states. In a realistic implementation, those terms must be included, thus preventing the existence of Goldstone bosons. A scan over parameters, imposing the existence of a neutral state at 125 GeV that is nearly CP-even shows that, in the absence of fine-tuning, the scalar spectrum contains one or two states with masses below 125 GeV that have a significant CP-odd component. These light states would have a low production rate via the Bjorken process and could thus have escaped detection at LEP. At the LHC the situation is less clear. While we do not here aim for a full phenomenological study of the light states, we point out that the $γγ$ decay channel would be challenging to measure because of suppressed couplings to $WW$.

hep-ph↗
arXiv2022

Light scalars in the Weinberg 3HDM potential with spontaneous CP violation

The $\mathbb Z_2\times \mathbb Z_2$-symmetric 3HDM potential, sometimes called Weinberg's 3HDM potential, can accommodate both explicit and spontaneous CP violation as well as natural flavour conservation and is hence relevant for studies of CP violation coming from a realistic extended Higgs sector. The model has an interesting regime, controlled by a single parameter, where it acquires an approximate global $U(1) \times U(1)$ symmetry which causes CP violating effects to be small and two pseudo-Goldstone bosons to be present in the scalar spectrum. From parameter space scans, we find that, in a realistic implementation featuring an SM-like Higgs boson, this model predominantely leads to the existence of light additional Higgs bosons with a mass lower than the SM-like Higgs boson.

hep-ph↗
arXiv2013

On the terms violating the custodial symmetry in multi-Higgs-doublet models

We prove that a generic multi-Higgs-doublet model (NHDM) generally must contain terms in the potential that violate the custodial symmetry. This is done by showing that the O(4) violating terms of the NHDM potential cannot be excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect higher-order corrections to necessarily introduce such terms. We also note, in the case of custodially symmetric Higgs-quark couplings, that vacuum alignment will lead to up-down mass degeneration; this is not true if the vacua are not aligned.

hep-ph↗
arXiv2011

Symmetry and Mass Degeneration in Multi-Higgs-Doublet Models

We investigate possible symmetry properties of the scalar sector of Multi-Higgs-Doublet Models, and, to some extent, the generalization of such models to gauge groups other than $SU(2)_L\times U(1)_Y$. In models where the ${\cal C}$ (charge conjugation) violating operator $\hat{C}$ is not present, the scalar potential is invariant under a group larger than the gauge group, O(4) when the Higgs fields are doublets. If the Higgs fields develop aligned vacuum expectation values, this symmetry will break to an O(3) subgroup, which in general is further broken by loop corrections involving the gauge bosons. Assuming such corrections are small, the physical properties of the Higgs sector will approximately organize into representations of SO(3). If the vacuum expectation values of the Higgs fields are aligned in the direction of the ${\cal C}$ even fields, the mass spectra of the charged and ${\cal C}$ odd sectors will be degenerate. Moreover, if the Higgs fields develop a pair of non-aligned vacuum expectations values, so that the charge conjugation symmetry is spontaneously broken (but not the U(1) electromagnetic gauge invariance), a pair of light charged Higgs bosons should appear.

hep-ph↗
arXiv2010

Superdense cosmological dark matter clumps

The formation and evolution of superdense clumps (or subhalos) is studied. Such clumps of dark matter (DM) can be produced by many mechanisms, most notably by spiky features in the spectrum of inflationary perturbations and by cosmological phase transitions. Being produced very early during the radiation dominated epoch, superdense clumps evolve as isolated objects. They do not belong to hierarchical structures for a long time after production, and therefore they are not destroyed by tidal interactions during the formation of larger structures. For DM particles with masses close to the electroweak (EW) mass scale, superdense clumps evolve towards a power-law density profile $ρ(r) \propto r^{-1.8}$ with a central core. Superdense clumps cannot be composed of standard neutralinos, since their annihilations would overproduce the diffuse gamma radiation. If the clumps are constituted of superheavy DM particles and develop a sufficiently large central density, the evolution of their central part can lead to a 'gravithermal catastrophe.' In such a case, the initial density profile turns into an isothermal profile with $ρ\propto r^{-2}$ and a new, much smaller core in the center. Superdense clumps can be bserved by gamma radiation from DM annihilations and by gravitational wave detectors, while the production of primordial black holes and cascade nucleosynthesis constrain this scenario.

astro-ph.CO↗
arXiv2010

Annihilations of superheavy dark matter in superdense clumps

Superheavy dark matter (SHDM) exchanges energy with its environment much slower than particles with masses close to the electroweak (EW) scale and has therefore different small-scale clustering properties. Using the neutralino as candidate for the SHDM, we find that free-streaming allows the formation of DM clumps of all masses down to $\sim 260 m_χ$ in the case of bino. If small-scale clumps evolve from a non-standard, spiky spectrum of perturbations, DM clumps may form during the radiation dominated era. These clumps are not destroyed by tidal interactions and can be extremely dense. In the case of a bino, a "gravithermal catastrophe" can develop in the central part of the most dense clumps, increasing further the central density and thus the annihilation signal. In the case of a higgsino, the annihilation signal is enhanced by the Sommerfeld effect. As a result annihilations of superheavy neutralinos in dense clumps may lead to observable fluxes of annihilation products in the form of ultrahigh energy particles, for both cases, higgsinos and binos, as lightest supersymmetric particles.

astro-ph.GA↗
arXiv2009

On the role of electroweak bremsstrahlung for indirect dark matter signatures

Interpretations of indirect searches for dark matter (DM) require theoretical predictions for the annihilation or decay rates of DM into stable particles of the standard model. These predictions include usually only final states accessible as lowest order tree-level processes, with electromagnetic bremsstrahlung and the loop-suppressed two gamma-ray line as exceptions. We show that this restriction may lead to severely biased results for DM tailored to produce only leptons in final states and with mass in the TeV range. For such models, unavoidable electroweak bremsstrahlung of Z and W-bosons has a significant influence both on the branching ratio and the spectral shape of the final state particles. We work out the consequences for two situations: Firstly, the idealized case where DM annihilates at tree level with 100% branching ratio into neutrinos. For a given cross section, this leads eventually to "minimal yields" of photons, electrons, positrons and antiprotons. Secondly, the case where the only allowed two-body final states are electrons. The latter case is typical of models aimed at fitting cosmic ray e^- and e^+ data. We find that the multimessenger signatures of such models can be significantly modified with respect to results presented in the literature.

hep-ph↗
arXiv2008

Supersymmetric superheavy dark matter

We propose the lightest supersymmetric particle (LSP) as a well-suited candidate for superheavy dark matter (SHDM). Various production mechanisms at the end of inflation can produce SHDM with the correct abundance, $Ω_{LSP} h^2 \sim 0.1$, if its mass is sufficiently high. In particular, gravitational production requires that the mass $m_{LSP}$ of the LSP is above $3\times 10^{11} GeV$. Weak interactions remain perturbative despite the large mass hierarchy, $m_{LSP}\gg m_Z$, because of the special decoupling properties of supersymmetry. As a result the model is predictive and we discuss the relevant cosmological processes for the case of a superheavy neutralino within this scheme.

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