By introducing a Higgs-Dilaton potential, the 2T model has a trigger for a first order electroweak phase transition, namely for the mass of Dilaton between $300 $ GeV and $550$ GeV. We have also compared the transition strengths in the case with and without daisy loops, the difference being always less than $0.2$. The effective Higgs potential has given a sphaleron energy less than $8.4$ TeV. The timescale of phase transition $(β/H^*)$ is larger than $25$ and less than $34$ in all cases that are sufficient to trigger the first order electroweak phase transition. Gravitational wave energy density caused by this transition, may be detected by future detectors, could indirectly confirm Dilaton.
Motivated by the Kaluza-Klein theory with a large number of extra spacetime dimensions, we present a numerical study of static, spherically symmetric sphaleron solutions coupled to the dilaton fields. We show that sphalerons may have different dilaton cloud configurations, resulting in new massive sphalerons, in general. However, there exist different cloud configurations with different values of the dilaton mass.
Sphaleron energies within the standard model with a real Higgs singlet added on are calculated. The coupled non-linear equations of motion are numerically solved and the sphaleron energy evaluated for a set of parameters in the Higgs potential. I find a small difference in the sphaleron energy compared to the standard model. A slightly stronger constraint on the strength of the first order phase transition thus results for this model.
Sphaleron is a non-perturbative solution of electroweak gauge theories, which is crucially important for the scenario of electroweak baryogenesis. The sphaleron energy depends on details of the mechanism for the electroweak symmetry breaking. We find that in many of new physics models the deviation of the sphaleron energy from the prediction in the standard model is proportional to that of the triple Higgs boson coupling with opposite signs. This interesting relation would be useful to determine the sphaleron energy by measuring this couplings at future collider experiments.
We undertake a comprehensive investigation of the properties of the sphaleron in electroweak theories with two Higgs doublets. We do this in as model-independent a way as possible: by exploring the physical parameter space described by the masses and mixing angles of the Higgs particles. If there is a large split in the masses of the neutral Higgs particles, there can be several sphaleron solutions, distinguished by their properties under parity and the behaviour of the Higgs field at the origin. In general, these solutions appear in parity conjugate pairs and are not spherically symmetric, al…
We report on work studying the properties of the sphaleron in models of the electroweak interactions with two Higgs doublets in as model-independent a way as possible: by exploring the physical parameter space described by the masses and mixing angles of the Higgs particles. If one of the Higgs particles is heavy, there can be several sphaleron solutions, distinguished by their properties under parity and the behaviour of the Higgs field at the origin. In general, these solutions are not spherically symmetric, although the departure from spherical symmetry is small.
We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton-anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. A previously predicted bifurcation point, where two branches of periodic solutions meet, appears for Higgs boson masses larger than $3.091 M_W$.
We investigate the effect on the sphaleron in the two Higgs doublet electroweak theory of including CP violation in the Higgs potential. To have better control over the relation between the sphaleron energy and the physical quantities in the theory, we show how to parametrize the Higgs potential in terms of physical masses and mixing angles, one of which causes CP violation. By altering this CP violating angle (and keeping the other physical quantities fixed) the sphaleron energy increases by up to 10%. We also calculate the static minimum energy path between adjacent vacua as a function of Ch…
We improve the sphaleron decoupling condition in the real singlet-extended standard model. The sphaleron energy is obtained using the finite temperature one-loop effective potential with daisy resummation. For moderate values of the model parameters, the sphaleron decoupling condition is found to be $v_C/T_C>(1.1-1.2)$, where $T_C$ denotes a critical temperature and $v_C$ is the corresponding vacuum expectation value of the doublet Higgs field at $T_C$. We also investigate the deviation of the triple Higgs boson coupling from its standard model value in the region where the improved sphaleron …
Theoretical arguments suggest that the Higgs sector of the standard model is an effective theory. We parametrize the new physics by means of an effective Lagrangian technique and study its effect on the energy of the electroweak sphaleron. We found that in the presence of a certain class of higher dimension operators the sphaleron energy becomes arbitrarily large as the Higgs boson mass increases. The physical meaning of this result and its implications to the electroweak baryogenesis in the dynamical models are discussed.
The classical transitions between topologically distinct vacua in a SU(2)-Higgs model, using a Higgs field of mass approximately 120 GeV, is examined to probe the crossover region between the symmetric and broken phase. Assuming the Higgs mass is constant, we find the width of this crossover region is approximately 20% of the average temperature. We suggest that this observable is a better parameter to explore this region of phase space than equal-time correlation functions.
Since the TRIVIALITY argument of the Higgs sector requires the existence of new physics beyond the standard model, there should exist a cutoff $Λ$ beyond which the standard model will breakdown. The cutoff can be determined from the position of the Landau pole. We study the effects of this cutoff on the energy of the electroweak sphaleron, $E^{spha}$, in the large Higgs boson mass limit. We found that $E^{spha}$ becomes arbitrarily large as the Higgs boson mass increases. This is in contrast to the well-known result, which is held in the standard model and a wide class of its extensions, that …
We calculate the dissipation of the baryon number after the electroweak phase transition due to thermal fluctuations above the sphaleron barrier. We consider not only the classical Boltzmann factor but also fermionic and bosonic one-loop contributions. We find that both bosonic and especially fermionic fluctuations can considerably suppress the transition rate. Assuming the Langer--Affleck formalism for this rate, the condition that an initial baryon asymmetry must not be washed out by sphaleron transitions leads, in the Minimal Standard Model ($\sinθ_W=0$), to an upper bound for the Higgs mas…
We revisit the electroweak phase transition and the critical bubble in the scale invariant two Higgs doublet model in the light of recent LHC data. Moreover, the sphaleron decoupling condition is newly evaluated in this model. The analysis is done by using the resumed finite-temperature one-loop effective potential. It is found that the 125 GeV Higgs boson inevitably leads to the strong first-order electroweak phase transition, and the strength of which is always large enough to satisfy the sphaleron decoupling condition, $v_N/T_N > 1.2$, where $T_N$ denotes a nucleation temperature and $v_N$ …
We construct the sphaleron for several temperature dependent effective potentials. We determine the sphaleron energy as a function of temperature and demonstrate that the sphaleron energy at a given temperature $T$ is well approximated by the sphaleron energy at temperature zero scaled by the ratio of the vacuum expectation values of the Higgs field at temperatures $T$ and zero. We address the cosmological upper bound on the Higgs mass.
We discuss the effects of various processes that can be active during the leptogenesis era, and present the Boltzmann equations that take them into account appropriately. A non-vanishing Higgs number asymmetry is always present, enhancing the washout of the lepton asymmetry. This is the main new effect when leptogenesis takes place at $T>10^{12}$ GeV, reducing the final baryon asymmetry and tightening the leptogenesis bound on the neutrino masses. If leptogenesis occurs at lower temperatures, electroweak sphalerons partially transfer the lepton asymmetry to a baryonic one, while Yukawa interac…
It has recently been proposed that the production of long wavelength Higgs and gauge configurations via parametric resonance at the end of inflation may give rise to the required baryon asymmetry at the electroweak scale. We show that the stability of the inflaton oscillations, long after the production of Higgs modes, keeps driving the sphaleron transitions, which then become strongly correlated to the inflaton oscillations. In models where the CP-violation operator is related to time variations of the Higgs field, these correlations immediately lead to an efficient generation of baryons that…
In the electroweak sector of the standard model topologically inequivalent vacua are separated by finite energy barriers, whose height is given by the sphale\-ron. For large values of the Higgs mass there exist several sphaleron solutions and the barriers are no longer symmetric. We construct paths of classical configurations from one vacuum to a neighbouring one and solve the fermion equations in the background field configurations along such paths, choosing the fermions of a doublet degenerate in mass. As in the case of light Higgs masses we observe the level crossing phenomenon also for lar…
We discuss one-loop radiative corrections to the sphaleron-induced baryon number-violating transition rate near the electroweak phase transition in the standard model. We emphasize that in the case of a first-order transition a rearrangement of the loop expansion is required close to the transition temperature. The corresponding expansion parameter, the effective 3-dimensional gauge coupling approaches a finite $λ$ dependent value at the critical temperature. The $λ$ (Higgs mass) dependence of the 1-loop radiative corrections is discussed in the framework of the heat kernel method. Radiative c…
We use semiclassical methods to calculate the probability of inducing a change of topology via a high-energy collision in the SU(2)-Higgs theory. This probability is determined by a complex solution to a classical boundary value problem on a contour in the complex time plane. In the case of small particle number it is the probability of instanton-like processes in particle collisions. We obtain numerically configurations with the correct topological features and expected properties in the complex time plane. Our work demonstrates the feasibility of the numerical approach to the calculation of …
The electroweak phase transition and the sphaleron decoupling condition in the MSSM are revisited taking the latest experimental data into account. The light Higgs boson scenario and the ordinary decoupling limit which are classified by the relative size between the CP-odd Higgs boson mass and Z boson mass are considered within the context of electroweak baryogenesis. We investigate v/T at not only the critical temperature at which the effective potential has two degenerate minima but also the nucleation temperature of the critical bubbles, where v is a vacuum expectation value of the Higgs bo…
We measure the sphaleron rate with the physical parameters of the Standard Model. In particular, we plug into the calculations the recently found Higgs mass m_H = 125 GeV. The sphaleron rate tells us about the efficiency of baryon number violation through sphaleron transitions. These occur above the electroweak scale of 100 GeV and get exponentially suppressed at temperatures substantially below the electroweak crossover. The sphaleron rate enters computations of Baryogenesis via Leptogenesis, where it converts non-zero lepton number into non-zero baryon number. We simulate the effective elect…
Recently Bodeker has presented an effective infrared theory for the dynamics of Yang-Mills theory, suitable for studying the rate of baryon number violation in the early universe. We extend his theory to include Higgs fields, and study how much the Higgs affects the baryon number violation rate in the symmetric phase, at the phase coexistence temperature of a first order electroweak phase transition. The rate is about 20% smaller than in pure Yang-Mills theory. We also analyze the sphaleron rate in the analytic crossover regime. Our treatment relies on the ergodicity conjecture for 3-D scalar …
We review nonperturbative calculations of the rate of sphaleron transitions on the lattice in $1+1$-dimensional field theories and introduce a way to perform the gauge-invariant Gibbs averages in the classical non-Abelian Higgs theories.
After the discovery of the Higgs boson and the rather precise measurement of all electroweak boson's masses the local structure of the electroweak symmetry breaking potential is already quite well established. However, despite being a key ingredient to a fundamental understanding of the underlying mechanism of electroweak symmetry breaking, the global structure of the electroweak potential remains entirely unknown. The existence of sphalerons, unstable solutions of the classical action of motion that are interpolating between topologically distinct vacua, is a direct consequence of the Standar…
In this work, we study the electroweak sphalerons in a 5D background, where the fifth dimension lies on an interval. We consider two specific cases: flat space-time and the anti-de Sitter space-time compactified on S^{1}/Z_{2}. In our work, we take the SU(2) gauge-Higgs model, where the gauge fields reside in the 5D bulk; but the Higgs doublet is confined in one brane. We find that the results in this model are close to those of the 4D Standard Model (SM). The existence of the warp effect, as well as the heaviness of the gauge Kaluza-Klein modes make the results extremely close to the SM ones.
We show that the sphaleron energy which identifies with the (instanton) potential barrier for B-violation is reduced in the presence (background) of an electroweak Z-string. We also show that for large enough Higgs coupling, $λ$, the sphaleron energy can go negative. For such $λ$, electroweak Z-strings can reduce their energy by accumulating sphaleron bound states. This further endows them with baryon number. Given our approximation, the value of $λ$ at which this occurs is rather large to be realistic for the standard electroweak model.
The baryon number dissipation rate due to sphaleron transitions at high temperatures in the minimal standard model is evaluated. We find that this rate can be considerably suppressed by one loop contributions of bosonic and fermionic fluctuations which are particularly important for a small mass of the Higgs boson and a large top quark mass. Fixing the latter to its recently stated value of 174 GeV the complete erasure of the baryon asymmetry is prevented within the framework of the minimal standard model if the Higgs mass is less than about 66 GeV.
By adding the dimension-six operator for the Higgs potential (denoted $\mathcal{O}_6$) in Standard Model, we have a first-order electroweak phase transition (EWPT) whose strength is larger than unity. The cutoff parameter of the dimension-six Higgs operator ($Λ$) is found to be in the range 593-860 GeV with the Wilson parameter equals to unity; it is also shown that the greater the $Λ$, the lower the phase transition strength and the larger the Wilson parameter, the wider the domain of $Λ$. At zero temperature, the sphaleron energy is calculated with a smooth ansatz and an ansatz with scale-fr…
In this paper, two dilatonic fields that capture two conformal symmetries in the Georgi-Glashow SU(5) model are introduced. Then, one of the fields is associated with the Higgs, and the other one with inflation. By using the Higgs portal, the mass of the dilatonic Higgs can be tuned by the coupling constant between the two dilatonic fields.
We construct the sphaleron solution, at zero and finite temperature, in the Minimal Supersymmetric Standard Model as a function of the supersymmetric parameters, including the leading one-loop corrections to the effective potential in the presence of the sphaleron. At zero temperature we have included the one-loop radiative corrections, dominated by the top/stop sector. The sphaleron energy $E_{\rm MSSM}$ mainly depends on an effective Higgs mass ${\displaystyle m_h^{\rm eff}=\lim_{m_A\gg m_W} m_h}$, where $m_h$ is the lightest CP-even Higgs mass and $m_A$ the pseudoscalar mass. We have compar…
The discovery of the Higgs boson marks a key ingredient to establish the electroweak structure of the Standard Model. Its non-abelian gauge structure gives rise to, yet unobserved, non-perturbative baryon and lepton number violating processes. We propose to use cosmic ray air showers, as measured at the Pierre Auger Observatory, to set a limit on the hadronic production cross section of sphalerons. We identify several observables to discriminate between sphaleron and QCD induced air showers.
We consider the Abelian Higgs model in a (p+2)-dimensional space time with topology M^{p+1} x S^1 as a field theoretical toy model for tachyon condensation on Dp-branes. The theory has periodic sphaleron solutions with the normal mode equations resembling Lame-type equations. These equations are quasi-exactly solvable (QES) for specific choices of the Higgs- to gauge boson mass ratio and hence a finite number of algebraic normal modes can be computed explicitely. We calculate the tachyon potential for two different values of the Higgs- to gauge boson mass ratio and show that in comparison to p…
We complete the construction of the sphaleron $\widehat{S}$ in $SU(3)$ Yang-Mills-Higgs theory with a single Higgs triplet by solving the reduced field equations numerically. The energy of the $SU(3)$ sphaleron $\widehat{S}$ is found to be of the same order as the energy of a previously known solution, the embedded $SU(2)\times U(1)$ sphaleron $S$. In addition, we discuss $\widehat{S}$ in an extended $SU(3)$ Yang-Mills-Higgs theory with three Higgs triplets, where all eight gauge bosons get an equal mass in the vacuum. This extended $SU(3)$ Yang-Mills-Higgs theory may be considered as a toy mo…
New results for the rate are presented using the canonical ensemble in the classical approximation on a spatial lattice. We find that the rate at high temperatures is proportional to $T^2$, and strongly dependent on the lattice spacing $a$. We conclude that a better effective action is needed for the classical approximation.
We report the results of a numerical search for non-topological solitons in the two-Higgs standard model, characterized by the non-trivial winding, $π_3(S^3)$, of the relative phase of the two doublets. In a region of (weak-coupling) parameter space we identify a branch of winding solutions, which are lower in energy than the embedded standard sphaleron and deformed (bi)sphalerons. Contrary, however, to what happens in 2d toy models, these solutions remain unstable even for very large Higgs masses.
We investigate the effect of dynamical fermions on the sphaleron transition rate at finite temperature for the Abelian Higgs model in one spatial dimension. The fermion degrees of freedom are included through bosonization. Using a numerical simulation, we find that massless fermions do not change the rate within the measurement accuracy. Surprisingly, the exponential dependence of the sphaleron energy on the Yukawa coupling is not borne out by the transition rate, which shows a very weak dependence on the fermion mass.
We re-examine the feasibility of the higgs-like particle discovered at the LHC being a dilaton: the Goldstone boson of spontaneous breaking of scale invariance. We review the expected phenomenological deviations from the SM higgs and compare with other Goldstone higgs scenarios, with particular emphasis on double higgs production.
We consider the model containing a dilaton vs Higgs boson in the nearly conformal sector (NCS). The potential of a dilaton in NCS is linearly rising with distances. The light scalar dilaton would be one of the best candidates to explain the LHC data in recent discovery of a Higgs-like resonance at 125 GeV.
A Higgs-like dilaton owns couplings that differ from those of the Standard Model Higgs and of a generic Composite Higgs. The complete bosonic basis for a Higgs-like dilaton is presented at the first subleading order. A comparison with the Standard Model, the Standard Model Effective Field Theory and the generic Lagrangian for the minimal $SO(5)/SO(4)$ Composite Higgs model is performed. Observables that can disentangle the different hypotheses are identified.
We study under which conditions a scalar particle is a viable WIMP Dark Matter candidate with Higgs and dilaton interactions. The theory is a composite Higgs model with top partial compositeness where both the Higgs and the Dark Matter candidate arise as pseudo Goldstone boson of the coset SO(6)/SO(5) from a new physics sector. We highlight the role of the dilaton in direct and indirect searches. We find that a Dark Matter particle with a mass around 200-400 GeV and a relatively light dilaton are a fair prediction of the model.
We investigate analytically the fermionic fluctuation determinant at finite temperatures in the minimal standard model, including all operators up to dimension 6 and all contributions to the effective potential to all orders in the high $T$ expansion, to 1 loop. We apply the results to find corrections to the Sphaleron erasure rate in the broken phase. We conclude that the analytic treatment of fermions is very reliable and that there is a great deal of baryon erasure after the phase transition for any physical Higgs mass.
We construct multisphaleron solutions in the weak interactions. The multisphaleron solutions carry Chern-Simons charge $n/2$, where $n$ is an integer. The well-known sphaleron has $n=1$ and is spherically symmetric for vanishing mixing angle. In contrast the multisphalerons with $n>1$ are only axially symmetric, even for vanishing mixing angle. The greater $n$, the stronger the energy density deforms. While for small Higgs masses the energy of the multisphalerons is smaller than $n$ times the energy of the sphaleron, the energy of the multisphalerons is larger than $n$ times the energy of the …
The Minimal Dilaton Model (MDM) extends the Standard Model (SM) by a singlet scalar, which can be viewed as a linear realization of general dilaton field. This new scalar field mixes with the SM Higgs field to form two mass eigenstates with one of them corresponding to the 125 GeV SM-like Higgs boson reported by the LHC experiments. In this work, under various theoretical and experimental constrains, we perform fits to the latest Higgs data and then investigate the phenomenology of Higgs boson in both the heavy dilaton scenario and the light dilaton scenario of the MDM. We find that: (i) If on…
We study possible phenomenological consequences of the recently proposed new approach to the Weinberg-Salam model. The electroweak theory is considered as a gravity and the Higgs particle is interpreted in it as a dilaton, without the usual potential of interaction in the Higgs sector. We have taken as a test the process of photons pair production, $e^+ + e^- \to Z + γ+ γ$. In the framework of new formulation this reaction is mediated in the lowest order by the dilaton. The cross section is found to be rather small.
We study a model with a Higgs-like dilaton and a Standard Model gauge-singlet scalar dark matter candidate. We begin by updating the status of identifying the observed 125 GeV Higgs-like boson with the pseudo Nambu-Goldstone boson that arises from the spontaneous breaking of scale invariance using recent Higgs boson signal strength measurements by the ATLAS and CMS collaborations. We then constrain the extended model with recent constraints on the Higgs invisible width, the observed dark matter relic abundance and the latest dark matter direct detection limits. We found that the magnitude of t…
Within the $SP(2,R)$ symmetry, the Two-time model (2T model) has six dimensions with two dimensions of time and the dilaton field that can be identified as inflaton in a warm inflation scenario with potential of the form $\simϕ^4$. From that consideration, we derive the range of parameters for the Higgs-Dilaton potential, the coupling constant between Higgs and Dialton ($α$) is larger than $0.0053$ and the mass of Dilaton is smaller than $10^{-7}$ GeV. Therefore, the 2T-model indirectly suggests that extra-dimension can also be a source of inflation.
New defects (Z-vortices and Nambu monopoles) are found to become thermodynamically relevant for the broken phase near to the (weakly first order) electroweak phase transition, and below the crossover for higher Higgs mass. The symmetric phase is characterized by vortex condensation (percolation). The percolation transition persists in the crossover region. The quasiclassical nature of the vortices is supported by correlations with Higgs field and gauge field energy. Sphalerons are shown to be related to monopolium bound states.
Motivated by the bulk mixing $ξR_5 H^{\dagger}H$ between a massive radion and a bulk scalar Higgs in warped extra dimensions, we construct an effective four dimensional action that---via the AdS/CFT correspondence---describes the most general mixing between the only light states in the theory, the dilaton and the Higgs. Due to conformal invariance, once the Higgs scalar is localized in the bulk of the extra-dimension the coupling between the dilaton and the Higgs kinetic term vanishes, implying a suppressed coupling between the dilaton and massive gauge bosons. We comment on the implications o…
We study a scenario in which the dilaton, a pseudo-Goldstone boson of the spontaneous breaking of conformal symmetry, provides a portal between dark matter and the visible sector. We consider the low-energy description of the theory in which the dilaton mixes with the Standard Model Higgs boson, thereby predicting a second scalar at or above the weak scale. We derive the collider and dark matter constraints on the corresponding parameter space and find that existing experimental data point towards the decoupling limit in which the CFT scale is well above the electroweak scale. Moreover, the th…
We study a holographic model dual to walking/conformal technicolor (W/C TC) deforming a hard-wall type of bottom-up setup by including effects from techni-gluon condensation. We calculate masses of (techni-) $ρ$ meson, $a_1$ meson, and flavor/chiral-singlet scalar meson identified with techni-dilaton (TD)/conformal Higgs boson, as well as the $S$ parameter. It is shown that gluon contributions and large anomalous dimension tend to decrease specifically mass of the TD. In the typical model with $S \simeq 0.1$, we find $m_{\rm TD} \simeq 600$ GeV, while $m_ρ,m_{a_1} \simeq 4 {\rm TeV}$.
We introduce a new approach to the Higgs naturalness problem, where the value of the Higgs mass is tied to cosmic stability and the possibility of a large observable Universe. The Higgs mixes with the dilaton of a CFT sector whose true ground state has a large negative vacuum energy. If the Higgs VEV is non-zero and below $\mathcal{O}({\rm TeV})$, the CFT also admits a second metastable vacuum, where the expansion history of the Universe is conventional. As a result, only Hubble patches with unnaturally small values of the Higgs mass support inflation and post-inflationary expansion, while all…
We consider the possibility that the new particle that has been observed at 125 GeV is not the Standard Model (SM) Higgs, but instead the dilaton associated with an approximate conformal symmetry that has been spontaneously broken. We focus on dilatons that arise from theories of technicolor, or from theories of the Higgs as a pseudo-Nambu-Goldstone boson (pNGB), that involve strong conformal dynamics in the ultraviolet. In the pNGB case, we are considering a framework where the Higgs particle is significantly heavier than the dilaton and has therefore not yet been observed. In each of the tec…
Confront a dilaton model with the LHC measurements
School of Physics Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Center for Future High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理前沿中心）
We investigate the Higgs-strahlung production process e^+ e^- \to Z h at the future Higgs factory such as TLEP by including radiative corrections in the Minimal Dilaton Model (MDM), which extends the SM by one singlet scalar called dilaton. We consider various theoretical and experimental constraints on the model, and perform fits to the Higgs data taken from ATLAS, CMS and CDF+D0. Then for the 1σsurviving samples, we calculate the MDM predictions on the inclusive production rate σ(e^+e^-\to Zh) at the 240-GeV Higgs factory, and also the signal rates of e^+e^-\to Zh with the Higgs boson decayi…
It is likely that the LHC will observe a color- and charge-neutral scalar whose decays are consistent with those of the Standard Model (SM) Higgs boson. The Higgs interpretation of such a discovery is not the only possibility. For example, electroweak symmetry breaking (EWSB) could be triggered by a spontaneously broken, nearly conformal sector. The spectrum of states at the electroweak scale would then contain a narrow scalar resonance, the pseudo-Goldstone boson of conformal symmetry breaking, with Higgs-like properties. If the conformal sector is strongly coupled, this pseudo-dilaton may be…
We study sphaleron solutions in the next-to-minimal supersymmetric standard model. We find that the boundary condition on the singlet field at the origin of the radial coordinate is of Neumann type, while the other boundary conditions are of Dirichlet type. The sphaleron energy takes almost the same value as in the MSSM for wide range of parameters, in spite of the negative contribution from the cubic term in the Higgs potential.
In the first scenario, we revise the upper bound of the cutoff scale of the dimension-six potential Higgs operator required for a successful electroweak baryogenesis in the case of a modified expansion history caused by the existence of a non-interacting scalar field at the time phase transition happens. The upper bound 860 GeV of the cutoff scale in the conventional case can be improved to 1 TeV in the modified expansion case under certain conditions. In the second scenario, we consider the Randall-Sundrum type II model. We show that the lower bound of the five-dimensional Planck scale in thi…
We show that introducing $R^2$-term makes the Higgs-inflation and Higgs-dilaton inflation consistent models: the strong coupling energy scales in scalar, gauge and gravity sectors all are lifted up to the Planck scale.
