Quartic Scalar Coupling Research Articles

Constraining dark matter from strong phase transitions in a U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} model: implications for neutrino masses and muon g − 2

In this paper, we study a non-minimal gauged U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. The model offers an easy resolution to the muon (g – 2) anomaly, which fixes the scale of spontaneous symmetry breaking. Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. The extended scalar sector can easily induce first-order phase transitions. We identify all possible phase transition patterns in the three-dimensional field space. We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of 10−2 and 10−5 when we consider the DM direct detection bound. Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.

Light mass window of inert doublet dark matter with lepton portal interaction

We study phenomenology of a light scalar dark matter (DM). In the model, there is an inert doublet scalar and a singlet Dirac fermion ψ, both charged under a global Z2 symmetry. The mass of the lightest inert scalar H can be lighter than 10 GeV by imposing appropriate relations between three scalar quartic couplings. The lightest Z2 odd particle is stable and DM. In this paper, focusing on the parameter space where H is lighter than ψ and is DM, we discuss DM physics related to relic density, direct detection, indirect detection, collider searches, and other cosmological observations. We clarify differences from the case where ψ is instead DM, which has been focused on in previous works. Published by the American Physical Society 2024

Asymptotic safety in the Litim-Sannino model at four loops

We consider a four-dimensional SU(Nc) gauge theory coupled to Nf species of color fermions and Nf2 colorless scalars. The quantum field theory possesses a weakly interacting ultraviolet fixed point that we determine from beta functions computed up to four-loop order in the gauge coupling, and up to three-loop order in the Yukawa and quartic scalar couplings. The fixed point has one relevant direction giving rise to asymptotic safety. We compute fixed-point values of dimensionless couplings together with the corresponding scaling exponents up to the first three nontrivial orders in Veneziano parameter ε, both for infinite and finite number of colors Nc. We also consider anomalous dimensions for fields, scalar mass squared, and a class of dimension-three operators. Contrary to previous studies, we take into account possible mixing of the latter and compute eigenvalues of the corresponding matrix. Further, we investigate the size of the conformal window in the Veneziano limit and its dependence on Nc. Published by the American Physical Society 2024

Vacuum stability and radiative symmetry breaking of the scale-invariant singlet extension of type II seesaw model

The questions of the origin of electroweak symmetry breaking and neutrino mass are two major puzzles in particle physics. Neutrino mass generation requires new physics beyond the Standard Model and also suggests reconsideration of physics of symmetry breaking. The aim of this paper is to study radiative symmetry breaking in the singlet scalar extension of type II seesaw neutrino mass model. We derive bounded-from-below conditions for the scalar potential of the model in full generality for the first time. The Gildener–Weinberg approach is utilised in minimising the multiscalar potential. Upon imposing the bounded-from-below and perturbativity conditions, as well as experimental constraints from colliders, we find the parameter space of scalar quartic couplings that can radiatively realise electroweak symmetry breaking at one-loop level. To satisfy all the constraints, the masses of the heavy triplet-like Higgs bosons must be nearly degenerate. The evolution of the Higgs doublet quartic coupling lambda _{H} can be prevented from being negative up to the Planck scale.

PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

We consider the renormalization properties of non-Hermitian Yukawa theories involving a pseudoscalar (axion) field at or near four dimensions. The non-Hermiticity is $\mathcal{P}\mathcal{T}$ symmetric where $\mathcal{P}$ is a linear operator (such as parity) and $\mathcal{T}$ is an antilinear idempotent operator (such as time reversal). The coupling constants of the Yukawa and quartic scalar coupling terms reflect this non-Hermiticity. The path integral representing the field theory is used to discuss the Feynman rules associated with the field theory. The fixed point structure associated with the renormalization group has $\mathcal{P}\mathcal{T}$ symmetric and Hermitian fixed points. At two loops in the massless theory, we demonstrate the flow from Hermitian to non-Hermitian fixed points. From the one-loop renormalization of a massive Yukawa theory, a self-consistent Nambu--Jona-Lasinio gap equation is established and its real solutions are discussed.

Two-loop radiative seesaw, muon g \u2212 2, and \u03c4-lepton-flavor violation with DM constraints

The quartic scalar coupling λ5 term, which violates the lepton-number by two units in the Ma-model, is phenomenologically small when the model is applied to the lepton-flavor violation (LFV) processes. In order to dynamically generate the λ5 parameter through quantum loop effects and retain the dark matter (DM) candidate, we extend the Ma-model by adding a Z2-odd vector-like lepton doublet and a Z2-even Majorana singlet. With the new couplings to the Higgs and gauge bosons, the observed DM relic density can be explained when the upper limits from the DM-nucleon scattering cross sections are satisfied. In addition to the neutrino data and LFV constraints, it is found that the DM relic density can significantly exclude the free parameter space. Nevertheless, the resulting muon g − 2 mediated by the inert charged-Higgs can fit the 4.2σ deviation between the experimental measurement and the SM result, and the branching ratio for τ → μγ can be as large as the current upper limit when the rare μ → (eγ, 3e) decays are suppressed. In addition, it is found that the resulting BR(τ → μρ) can reach the sensitivity of Belle II with an integrated luminosity of 50 ab−1.

Dark matter candidates in the NMSSM with RH neutrino superfields

R-parity conserving supersymmetric models with right-handed (RH) neutrinos are very appealing since they could naturally explain neutrino physics and also provide a good dark matter (DM) candidate such as the lightest supersymmetric particle (LSP). In this work we consider the next-to-minimal supersymmetric standard model (NMSSM) plus RH neutrino superfields, with effective Majorana masses dynamically generated at the electroweak scale (EW). We perform a scan of the relevant parameter space and study both possible DM candidates: RH sneutrino and neutralino. Especially for the case of RH sneutrino DM we analyse the intimate relation between both candidates to obtain the correct amount of relic density.Besides the well-known resonances, annihilations through scalar quartic couplings and coannihilation mechanisms with all kind of neutralinos, are crucial. Finally, we present the impact of current and future direct and indirect detection experiments on both DM candidates.

Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson MH and the top quark Mt. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed MH∼ 125 GeV results in the prediction for the top quark mass Mt∼ 171 GeV, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of an SU(2) triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to Mt ∼ 172.5 GeV for a triplet mass of M∆ ∼ 108GeV. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of Mt due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.

Vacuum stability in inert higgs doublet model with right-handed neutrinos

We analyze the vacuum stability in the inert Higgs doublet extension of the Standard Model (SM), augmented by right-handed neutrinos (RHNs) to explain neutrino masses at tree level by the seesaw mechanism. We make a comparative study of the high- and low-scale seesaw scenarios and the effect of the Dirac neutrino Yukawa couplings on the stability of the Higgs potential. Bounds on the scalar quartic couplings and Dirac Yukawa couplings are obtained from vacuum stability and perturbativity considerations. These bounds are found to be relevant only for low-scale seesaw scenarios with relatively large Yukawa couplings. The regions corresponding to stability, metastability and instability of the electroweak vacuum are identified. These theoretical constraints give a very predictive parameter space for the couplings and masses of the new scalars and RHNs which can be tested at the LHC and future colliders. The lightest non-SM neutral CP-even/odd scalar can be a good dark matter candidate and the corresponding collider signatures are also predicted for the model.

Minimal self-interacting dark matter models with light mediator

The light mediator scenario of self-interacting dark matter is strongly constrained in many ways. After summarizing the various constraints, we discuss minimal options and models which allow to nevertheless satisfy all these constraints. One straightforward possibility emerges if the dark matter and light mediator particles have a temperature sizably smaller than the SM particles. Another simple possibility arises if dark matter doesn't annihilate dominantly into a pair of light mediators but into heavier particles. Both possibilities are discussed with scalar as well as vector boson light mediators. Further possibilities, such as with a hierarchy of quartic scalar couplings, are also identified.

Phenomenology of the new light Higgs bosons in Gildener-Weinberg models

Gildener-Weinberg (GW) models of electroweak symmetry breaking are especially interesting because the low mass and nearly Standard Model couplings of the 125 GeV Higgs boson $H$ are protected by approximate scale symmetry. Another important but so far underappreciated feature of these models is that a sum rule bounds the masses of the new charged and neutral Higgs bosons appearing in all these models to be below about 500 GeV. Therefore, they are within reach of LHC data currently or soon to be in hand. Also so far unnoticed of these models, certain cubic and quartic Higgs scalar couplings vanish at the classical level. This is due to spontaneous breaking of the scale symmetry. These couplings become nonzero from explicit scale breaking in the Coleman-Weinberg loop expansion of the effective potential. In a two-Higgs doublet GW model, we calculate ${\ensuremath{\lambda}}_{HHH}\ensuremath{\simeq}2({\ensuremath{\lambda}}_{HHH}{)}_{\mathrm{SM}}=64\text{ }\text{ }\mathrm{GeV}$. This corresponds to $\ensuremath{\sigma}(pp\ensuremath{\rightarrow}HH)\ensuremath{\cong}15--20\text{ }\text{ }\mathrm{fb}$, its minimum value for $\sqrt{s}=13--14\text{ }\text{ }\mathrm{TeV}$ at the LHC. It will require at least the 27 TeV HE-LHC to observe this cross section. We also find ${\ensuremath{\lambda}}_{HHHH}\ensuremath{\simeq}4({\ensuremath{\lambda}}_{HHHH}{)}_{\mathrm{SM}}=0.129$, whose observation in $pp\ensuremath{\rightarrow}HHH$ requires a 100 TeV collider. Because of the above-mentioned sum rule, these results apply to all GW models. In view of this unpromising forecast, we stress that LHC searches for the new relatively light Higgs bosons of GW models are by far the surest way to test them in this decade.

Future detectability of a pseudoscalar mediator dark matter model

We investigate the maximum value of the spin-independent cross section in a dark matter (DM) model called the two-Higgs doublet model + a (THDM+a). This model can explain the observed DM energy density while evading the current strict bound from the DM direct detection experiment because the predicted cross section at the tree-level is highly suppressed by the momentum transfer. On the other hand, the loop induced scattering effects are predicted without momentum suppression and might be detectable in the future DM direct detection experiments. The predicted cross section strongly depends on the scalar quartic couplings. We derive the theoretical constraints on these parameters by studying the stability of the electroweak vacuum, and the condition for the potential bounded from below. Considering these constraints, we find that the maximum value of the predicted cross section is larger than the prospects of the LZ and XENONnT experiments and this model has the potential to explain the DM direct detection signal which might be obtained near future.

Vacuum stability and symmetry breaking in left-right symmetric model

We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry breaking and the existence of a correct vacuum. We then compare results obtained from the derived conditions with those from numerical minimization of the scalar potential. Finally, we discuss the renormalization group analysis of the scalar quartic couplings through an example study that satisfies vacuum stability, perturbativity, unitarity and experimental bounds on the physical scalar masses.

Solving the strong CP problem with horizontal gauge symmetry

We present a solution to the strong CP problem, which relies on the horizontal gauge symmetry and CP invariance in a full theory. Similar to other Nelson-Barr type solutions, CP violation in both the strong and weak sectors in the Standard model (SM) is attributed to the condensation of complex scalars $\Phi$ in the model. The model is differentiated by others in that it explains the hierarchy in quark-Higgs Yukawa coupling in the SM based on a series of sequential breaking of the horizontal $SU(3)_{f}$ gauge symmetry. The experimental constraint $\overline{\theta}\lesssim10^{-10}$ requires $<\!\!\Phi\!\!>\,\lesssim\,10^{13}-10^{14}{\rm GeV}$ (vacuum expectation value of complex scalars) and $\lambda\,\lesssim\,10^{-6}$ (scalar quartic coupling). We show that this small coupling is natural in the sense of 'tHooft naturalness. Compared to other models of Nelson-Barr type with CP breaking scale $\Lambda_{CP}\lesssim10^{8}{\rm GeV}$, our model is more advantageous in terms of consistency with the thermal leptogenesis.

Double copy for massive quantum particles with spin

The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of black-hole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point examples. For concreteness, we focus on the double copy of QCD with massive quarks, for which we work out the gravitational Lagrangian up to quartic scalar and vector-scalar couplings. We find new gauge-invariant double-copy formulae for tree-level amplitudes with two distinct-flavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the well-known Kawai-Lewellen-Tye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

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.

Safe trinification

We provide a UV safe trinification theory in which the Standard Model is embedded. Using recently developed large number-of-flavor techniques, safety is achieved by adding to the theory gauged vectorlike fermions. We find that all gauge, scalar quartic, and Yukawa couplings achieve an interacting ultraviolet fixed point below the Planck scale. We find renormalization group flow solutions matching the Standard Model in the IR, indicating a truly UV completion of the Standard Model. Imposing constraints that realistic top, Higgs, bottom, and tau masses are recovered, we find the set of allowed solutions to be quite restrictive. Furthermore, we find there exists a lower bound of about 10 TeV for the symmetry breaking scale, making this model vulnerable to experiment.

Revisiting RGEs for general gauge theories

We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the β-functions of the dimensionful Lagrangian parameters (the fermion mass, the bilinear and trilinear scalar couplings) as well as the dimensionless quartic scalar couplings. There are two sources for these discrepancies. Firstly, the known expressions for the scalar couplings assume a diagonal wave-function renormalisation which is not appropriate for models with mixing in the scalar sector. Secondly, the dimensionful parameters have been derived in the literature using a dummy field method which we critically re-examine, obtaining revised expressions for the β-function of the fermion mass. We perform an independent cross-check using well-tested supersymmetric RGEs which confirms our results. The numerical impact of the changes in the β-function for the fermion mass terms is illustrated using a toy model with a heavy vector-like fermion pair coupled to a scalar gauge singlet. Unsurprisingly, the correction to the running of the fermion mass becomes sizeable for large Yukawa couplings of the order of O(1). Furthermore, we demonstrate the importance of the correction to the β-functions of the scalar quartic couplings using a general type-III Two-Higgs-Doublet-Model. All the corrected expressions have been implemented in updated versions of the Mathematica package SARAH and the Python package PyR@TE.

Asymptotically safe Pati-Salam theory

We provide an asymptotically safe Pati-Salam embedding of the Standard Model. Safety is achieved by adding to the theory gauged vector-like fermions and by employing recently developed large number-of-flavor techniques and results. We show that the gauge, scalar quartic and Yukawa couplings achieve an interacting ultraviolet fixed point below the Planck scale. The minimal model is a relevant example of a Standard Model extension in which unification of all type of couplings occurs because of a dynamical principle, i.e. the presence of an ultraviolet fixed point. This extension differs from the usual Grand Unified Theories scenario in which only gauge couplings unify and become free with the remaining couplings left unsafe. We find renormalization group flow solutions that match the Standard Model couplings values at low energies allowing for realistic safe extensions of the Standard Model.

Can measurements of 2HDM parameters provide hints for high scale supersymmetry?

Two-Higgs-doublet models (2HDMs) are minimal extensions of the Standard Model (SM) that may still be discovered at the LHC. The quartic couplings of their potentials can be determined from the measurement of the masses and branching ratios of their extended scalar sectors. We show that the evolution of these couplings through renormalization group equations can determine whether the observed 2HDM is a low energy manifestation of a more fundamental theory, as for instance, supersymmetry, which fixes the quartic couplings in terms of the gauge couplings. At leading order, the minimal supersymmetric extension of the SM (MSSM) dictates all the quartic couplings, which can be translated into a predictive structure for the scalar masses and mixings at the weak scale. Running these couplings to higher scales, one can check if they converge to their MSSM values, and more interestingly, whether one can infer the supersymmetry breaking scale. Although we study this question in the context of supersymmetry, this strategy could be applied to any theory whose ultraviolet completion unambiguously predicts all scalar quartic couplings.