Electroweak phase transitions

The significance of the electroweak phase transition is undeniable, and although initially it was believed that it was second order, it is now believed that it is a first-order transition. However, it is not a strong first-order phase transition in the context of the standard model, and the remedy to this issue is to use the Higgs portal and directly couple the Higgs to a hidden scalar sector. This can result in a strong electroweak phase transition, while the couplings to a hidden scalar are constrained by several phenomenological constraints, such as the sphaleron rate criterion and the branching ratio of the Higgs to invisible channels. In this work, we consider the standard singlet extensions of the standard model, including dimension-six non-renormalizable operators that couple a real singlet scalar field with the Higgs doublet. As a result, we examine the effects of those Higgs-singlet couplings on the electroweak phase transition. The effective theory, where the nonrenormalizable couplings originate from, is considered to be active beyond 15 TeV. As we show, the Universe experiences a two-step electroweak phase transition, a primary phase transition in the singlet sector at a high temperature, and then a subsequent first-order phase transition from the singlet vacuum to the electroweak vacuum. The singlet’s phase transition can either be second order or first order, depending on the singlet mass and its couplings to the Higgs. In particular, we show that the dimension-six operator assists in generating a strong electroweak phase transition in regions of the parameter space that were excluded in the previous singlet extensions of the standard model. This is further apparent for low singlet masses mS<mH/2, which are rarely taken into account in the literature due to the invisible branching ratio of the Higgs boson. In some limited cases in the parameter space, the electroweak phase transition is weakened by the presence of the higher order operator. Published by the American Physical Society 2024

The electroweak phase transition in GUT inspired $SO(5)\times U(1) \times SU(3)$ gauge-Higgs unification is shown to be weakly first order and occurs at $T = T_c^{\rm EW} \sim 163\,$GeV, which is very similar to the behavior in the standard model in perturbation theory. A new phase appears at higher temperatures. $SU(2)_L \times U(1)_Y$ ($\theta_H=0$) and $SU(2)_R \times U(1)_{Y'}$ ($\theta_H=\pi$) phases become almost degenerate above $T \sim m_{\rm KK}$ where $m_{\rm KK}$ is the Kaluza-Klein mass scale typically around 13$\,$TeV and $\theta_H$ is the Aharonov-Bohm phase along the fifth dimension. The two phases become degenerate at $T = T_c^{\rm LR} \sim m_{\rm KK}$. As the temperature drops in the evolution of the early Universe the $SU(2)_R \times U(1)_{Y'}$ phase becomes unstable. The tunneling rate from the $SU(2)_R \times U(1)_{Y'}$ phase to the $SU(2)_L \times U(1)_Y$ phase becomes sizable and a first-order phase transition takes place at $T=2.5 \sim 2.6\,$TeV. The amount of gravitational waves produced in this left-right phase transition is small, far below the reach of the sensitivity of Laser Interferometer Space Antenna (LISA). A detailed analysis of the $SU(2)_R \times U(1)_{Y'}$ phase is also given. It is shown that the $W$ boson, $Z$ boson and photon, with $\theta_H$ varying from 0 to $\pi$, are transformed to gauge bosons in the $SU(2)_R \times U(1)_{Y'}$ phase. Gauge couplings and wave functions of quarks, leptons and dark fermions in the $SU(2)_R \times U(1)_{Y'}$ phase are determined.

The first computation of Higgs production in association with three jets at NLO in QCD has recently been performed using the effective theory, where the top quark is treated as an infinitely heavy particle and integrated out. This approach is restricted to the regions in phase space where the typical scales are not larger than the top quark mass. Here we investigate this statement at a quantitative level by calculating the leading-order contributions to the production of a Standard Model Higgs boson in association with up to three jets taking full top-quark and bottom-quark mass dependence into account. We find that the transverse momentum of the hardest particle or jet plays a key role in the breakdown of the effective theory predictions, and that discrepancies can easily reach an order of magnitude for transverse momenta of about 1 TeV. The impact of bottom-quark loops is found to be visible in the small transverse momentum region, leading to corrections of up to 5 percent. We further study the impact of mass corrections when VBF selection cuts are applied and when the center-of-mass energy is increased to 100 TeV.

The consequences of phase transitions in the early universe are becoming testable in a variety of manners, from colliders physics to gravitational wave astronomy. In particular one phase transition we know of, the electroweak phase transition (EWPT), could potentially be first order in BSM scenarios and testable in the near future. If confirmed this could provide a mechanism for baryogenesis, which is one of the most important outstanding questions in physics. To reliably make predictions it is necessary to have full control of the finite temperature scalar potentials. However, as we show the standard methods used in BSM physics to improve phase transition calculations, resumming hard thermal loops, introduces significant errors into the scalar potential. In addition, the standard methods make it impossible to match theories to an EFT description reliably. In this paper we define a thermal resummation procedure based on partial dressing (PD) for general BSM calculations of phase transitions beyond the high-temperature approximation. Additionally, we introduce the modified optimized partial dressing (OPD) procedure, which is numerically nearly as efficient as old incorrect methods, while yielding identical results to the full PD calculation. This can be easily applied to future BSM studies of phase transitions in the early universe. As an example, we show that in unmixed singlet scalar extensions of the SM, the (O)PD calculations make new phenomenological predictions compared to previous analyses. An important future application is the study of EFTs at finite temperature.

Probing the Higgs potential and new physics behind the electroweak symmetry breaking is one of the most important issues of particle physics. In particular, nature of electroweak phase transition is essential for understanding physics at the early Universe, such that the strongly first order phase transition is required for a successful scenario of electroweak baryogenesis. The strongly first order phase transition is expected to be tested by precisely measuring the triple Higgs boson coupling at future colliders like the International Linear Collider. It can also be explored via the spectrum of stochastic gravitational waves to be measured at future space-based interferometers such as eLISA and DECIGO. We discuss complementarity of both the methods in testing the strongly first order phase transition of the electroweak symmetry in models with additional isospin singlet scalar fields with and without classical scale invariance. We find that they are synergetic in identifying specific models of electroweak symmetry breaking in more details.

We propose a new alternative to the weakly interacting massive particle paradigm for dark matter. Rather than being determined by thermal freeze-out, the dark matter abundance in this scenario is set by dark matter decay, which is allowed for a limited amount of time just before the electroweak phase transition. More specifically, we consider fermionic singlet dark matter particles coupled weakly to a scalar mediator S_{3} and to auxiliary dark sector fields, charged under the standard model gauge groups. Dark matter freezes out while still relativistic, so its abundance is initially very large. As the Universe cools down, the scalar mediator develops a vacuum expectation value (VEV), which breaks the symmetry that stabilizes dark matter. This allows dark matter to mix with charged fermions and decay. During this epoch, the dark matter abundance is reduced to give the value observed today. Later, the SM Higgs field also develops a VEV, which feeds back into the S_{3} potential and restores the dark sector symmetry. In a concrete model we show that this "VEV flip-flop" scenario is phenomenologically successful in the most interesting regions of its parameter space. We also comment on detection prospects at the LHC and elsewhere.

The existence of a second Higgs doublet in Nature could lead to a cosmological first order electroweak phase transition and explain the origin of the matter-antimatter asymmetry in the Universe. We explore the parameter space of such a two-Higgs-doublet-model and show that a first order electroweak phase transition strongly correlates with a significant uplifting of the Higgs vacuum w.r.t. its Standard Model value. We then obtain the spectrum and properties of the new scalars H0, A0 and H± that signal such a phase transition, showing that the decay A0 → H0Z at the LHC and a sizable deviation in the Higgs self-coupling λhhh from its SM value are sensitive indicators of a strongly first order electroweak phase transition in the 2HDM.

We study the strength of a first-order electroweak phase transition in the Inert Doublet Model (IDM), where particle dark matter (DM) is comprised of the lightest neutral inert Higgs boson. We improve over previous studies in the description and treatment of the finite-temperature effective potential and of the electroweak phase transition. We focus on a set of benchmark models inspired by the key mechanisms in the IDM leading to a viable dark matter particle candidate, and illustrate how to enhance the strength of the electroweak phase transition by adjusting the masses of the yet undiscovered IDM Higgs states. We argue that across a variety of DM masses, obtaining a strong enough first-order phase transition is a generic possibility in the IDM. We find that due to direct dark matter searches and collider constraints, a sufficiently strong transition and a thermal relic density matching the universal DM abundance is possible only in the Higgs funnel regime.

We study the effect of BSM particles receiving most of their mass from their coupling to the Higgs boson (“Loryons”) on the electroweak phase transition. The existence of BSM Loryons would imply that electroweak symmetry must be non-linearly realized in the effective theory of the Standard Model. Since, by definition, Loryons have a significant coupling to the Higgs, they are expected to have a significant effect on the Higgs effective potential and thereby the electroweak phase transition. We show that the BSM Loryon parameter space viable under current experimental and theoretical constraints overlaps heavily with the parameter space in which a strongly first-order phase transition is predicted. The portion of the experimentally allowed parameter space which gives a strongly first-order phase transition is significantly larger for Loryons as compared to non-Loryons.

The dynamics of five dimensional Wilson line phases at finite temperature is studied in the one-loop approximation. We show that at temperatures of order T \sim 1/L, where L is the length of the compact space, the gauge symmetry is always restored and the electroweak phase transition appears to be of first order. Particular attention is devoted to the study of a recently proposed five dimensional orbifold model (on S1/Z2) where the Wilson line phase is identified with the Higgs field (gauge-Higgs unification). Interestingly enough, an estimate of the leading higher-loop ``daisy'' (or ``ring'') diagram contributions to the effective potential in a simple five dimensional model, seems to suggest that the electroweak phase transition can be studied in perturbation theory even for Higgs masses above the current experimental limit of 114 GeV. The transition is still of first order for such values of the Higgs mass. If large localized gauge kinetic terms are present, the transition might be strong enough to give baryogenesis at the electroweak transition.

The ATLAS and CMS experiments observed a particle at the LHC with a mass ≈126 GeV, which is compatible with the Higgs boson of the Standard Model. A crucial question is, if for such a Higgs mass value, one could extrapolate the model up to high scales while keeping the minimum of the scalar potential that breaks the electroweak symmetry stable. Vacuum stability requires indeed the Higgs boson mass to be MH≳129±1 GeV, but the precise value depends critically on the input top quark pole mass which is usually taken to be the one measured at the Tevatron, mtexp=173.2±0.9 GeV. However, for an unambiguous and theoretically well-defined determination of the top quark mass one should rather use the total cross section for top quark pair production at hadron colliders. Confronting the latest predictions of the inclusive pp¯→tt¯+X cross section up to next-to-next-to-leading order in QCD to the experimental measurement at the Tevatron, we determine the running mass in the MS¯-scheme to be mtMS¯(mt)=163.3±2.7 GeV which gives a top quark pole mass of mtpole=173.3±2.8 GeV. This leads to the vacuum stability constraint MH⩾129.4±5.6 GeV to which a ≈126 GeV Higgs boson complies as the uncertainty is large. A very precise assessment of the stability of the electroweak vacuum can only be made at a future high-energy electron–positron collider, where the top quark pole mass could be determined with a few hundred MeV accuracy.

In this work, we perform the electroweak phase transition study with the Georgi-Machacek model. We investigate both the one-step and two-step strong first order electroweak phase transition (SFOEWPT). The SFOEWPT viable parameter spaces could be tested by the future 14TeV LHC, HL-LHC, and ILC. The LHC Higgs signal strength measurements severely bound the SFOEWPT valid parameter spaces, a tinny region of the mixing angle between the neutral fields of the isospin-doublet and isospin-triplet scalars around α ∼ 0 can allow the two-step SFOEWPT to occur. The triplet vacuum expectation value (VEV) is crucial for both SFOEWPT and related Higgs phenomenology. The two-step SFOEWPT can be distinguished from the one-step SFOEWPT through the triple Higgs coupling searches and the low mass doubly charged Higgs searches at colliders.

The Standard Model and its extensions predict multiple phase transitions in the early universe. In addition to the electroweak phase transition, one or several of these could occur at energies close to the weak scale. Such phase transitions can leave their imprint on the relic abundance of TeV-scale dark matter. In this paper, we enumerate several physical features of a generic phase transition and parameterize the effect of each on the relic abundance. In particular, we include among these effects the presence of the scalar field vacuum energy and the cosmological constant, which is sensitive to UV physics. Within the context of the Standard Model Higgs sector, we find that the relic abundance of generic TeV-scale dark matter is affected by the vacuum energy at the order of a fraction of a percent. For scalar field sectors with strong first order phase transitions, an order one percent apparent tuning of coupling constants may allow corrections induced by the vacuum energy to be of order unity.

The MSSM electroweak phase transition on the lattice

The role of the top quark in completing the Standard Model quark sector is reviewed, along with a discussion of production, decay, and theoretical restrictions on the top quark properties. Particular attention is paid to the top quark as a laboratory for perturbative QCD. As examples of the relevance of QCD corrections in the top quark sector, the calculation of e{sup +}e{sup -} + t{bar t} at next-to-leading-order QCD using the phase space slicing algorithm and the implications of a precision measurement of the top quark mass are discussed in detail. The associated production of a t{bar t} pair and a Higgs boson in either e{sup +}e{sup -} or hadronic collisions is presented at next-to-leading-order QCD and its importance for a measurement of the top quark Yulrawa coupling emphasized. Implications of the heavy top quark mass for model builders are briefly examined, with the minimal supersymmetric Standard Model and topcolor discussed as specific examples.