We extend the 5D gauge-higgs scenario to the soft-wall framework where the IR brane is replaced by a smoothly decaying warp factor. The electroweak symmetry of the Standard Model is embedded in a larger symmetry group whose gauge bosons propagate in the bulk of a warped fifth dimension. This gauge symmetry is partly broken by UV boundary conditions and by a condensate of a bulk scalar field. The Higgs boson lives partly in the 5th component of the gauge field, and partly in the the bulk scalar. The Higgs potential is not UV sensitive if the condensate vanishes fast enough in the UV region. The soft-wall realization opens new possibilities for the spectrum and the couplings of the Kaluza-Klein resonances. We study two particular soft-wall backgrounds: one with resonances whose masses follow the linear Regge trajectory, and another with a continuum above a mass gap. We find that constraints on the Kaluza-Klein scale from electroweak precision tests are less severe than in analogous models with the IR brane. For the linear spectrum the typical constraint on the lightest resonance mass is 2 TeV, while the continuum is allowed to start below 1 TeV.
We present an entirely analytic, leading log order determination of the friction an electroweak bubble wall feels during a first order electroweak phase transition. The friction is dominated by W bosons, and gives a wall velocity parametrically ~ alpha_w, and numerically small, ~ .01 -- 0.1 depending on the Higgs mass.
Electroweak Baryogenesis from Collapsing Domain Walls
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Argonne National Laboratory（阿贡国家实验室）；University of Oklahoma（俄克拉荷马大学）；The Hong Kong University of Science and Technology（香港科技大学）
In models of thick wall electroweak baryogenesis a common assumption is that the plasma interacting with the expanding Higgs bubble wall during the electroweak phase transition is in kinetic equilibrium (or close to it). We point out that, in addition to the requirement of low wall velocity, kinetic equilibrium requires that the change in the momentum of the particles due to the force exerted by the wall should be much less than that due to scattering as the plasma passes through the wall. We investigate whether this condition is satisfied for charginos and neutralinos participating in thick w…
The bubble wall velocity is essential for the phase transition dynamics in the early universe and its cosmological implications, such as the energy budget of phase transition gravitational wave and electroweak baryogenesis. One key factor to determine the wall velocity is the collision term that quantifies the interactions between the massive particles in the plasma and the bubble wall. We improve the calculations of the collision term beyond the leading-log approximation, and further obtain more precise bubble wall velocity for a representative effective model.
The electroweak baryogenesis depends on the profile of the CP-violating bubble wall created at the first order phase transition. We attempt to determine it by solving the coupled equations of motion for the moduli and phases of the two Higgs doublets at the transition temperature. A variety of CP-violating bubble walls are classified by boundary conditions. We point out that a sufficiently small explicit CP violation gives nonperturbative effects to yield the baryon asymmetry of the universe.
We calculate the velocity and thickness of a bubble wall at the electroweak phase transition in the Minimal Standard Model. We model the wall with semiclassical equations of motion and show that friction arises from the deviation of massive particle populations from thermal equilibrium. We treat these with Boltzmann equations in a fluid approximation in the background of the wall. Our analysis improves on the previous work by using the two loop effective potential, accounting for particle transport, and determining the wall thickness dynamically. We find that the wall is significantly thicker …
We compute the wall velocity in the MSSM. We therefore generalize the SM equations of motion for bubble walls moving through a hot plasma at the electroweak phase transition and calculate the friction terms which describe the viscosity of the plasma. We give the general expressions and apply them to a simple model where stops, tops and W bosons contribute to the friction. In a wide range of parameters including those which fulfil the requirements of baryogenesis we find a wall velocity of order v = 0.05-0.1 much below the SM value.
We investigate the motion of fermions in the presence of an electro\-weak phase transition bubble wall. We derive and solve the Dirac equation for such fer\-mions, and compute the transmission and reflection coefficients for fermions traveling from the symmetric to the asymmetric phases separated by the domain wall.
We analyze Higgs condensate bubble expansion during a first-order electroweak phase transition in the early Universe. The interaction of particles with the bubble wall can be accompanied by the emission of multiple soft gauge bosons. When computed at fixed order in perturbation theory, this process exhibits large logarithmic enhancements which must be resummed to all orders when the wall velocity is large. We perform this resummation both analytically and numerically at leading logarithmic accuracy. The numerical simulation is achieved by means of a particle shower in the broken phase of the e…
A spherical domain wall around a small black hole is formed by the Hawking radiation from the black hole in the symmetry-broken-phase of the field theory, e.g., the Standard Model (SM) and the Grand Unified Theory (GUT) which have a property of the phase transition. We have obtained two types of the spherical domain wall; (a) thermalized wall which is formed by the local heating up near black hole and symmetry restore locally and (b) dynamical wall which is formed by the balance between the pressure from the Hawking radiation and the pressure from the wall tensions. The electroweak wall is for…
We compute the net electric current generated during a first order electroweak phase transition when fermions transit from the false to the true vacuum. This current is generated by the CP-violating fermion interaction with the Higgs during the phase transition and is quantified in terms of a CP-violating phase in the bubble wall separating the symmetric from the symmetry-broken phases. We comment on the seed magnetic field that this current is able to generate and it is possible implications for magnetogenesis in the early universe during the electroweak phase transition.
By treating CP-violating interaction as a perturbative term, we solve the Dirac equation in the background of electroweak bubble wall (the distorted wave Born approximation). We obtain the transmission and reflection coefficients for a chiral fermion incident from the symmetric-phase region and for the one from the broken-phase region respectively. There hold the respective sets of unitarity relations and also reciprocity relations among them. These relations enable us to rigorously derive quantum-number flux through the bubble wall, which is the first order quantity of the CP violation. The f…
In unconstrained thermal equilibrium a local potential for total or fermionic hypercharge does not bias electroweak anomalous processes. We consider two proposed mechanisms for electroweak baryogenesis in this light. In `spontaneous' baryogenesis, which was argued to apply in the `adiabatic' limit of thick, slow walls, a non-zero result was obtained by setting globally conserved charges to be zero {\it locally}. We show that this is a poor approximation unless the walls are very thick. For more realistic wall thicknesses the local equilibrium approached as the wall velocity $v_w\rightarrow 0$ …
A general prescription to solve the Dirac equation in the presence of CP-violating electroweak bubble wall is presented. The profile of the bubble wall is not specified except that the wall height is $m_0$ and zero deep in the broken- and the symmetric-phase regions, respectively, where $m_0$ is a fermion mass given by the Higgs-vacuum-expectation value and the Yukawa coupling. The CP-violating effects are evaluated by regarding CP-violating part of the bubble wall as a perturbation to CP-conserving solutions. The basic quantity, $R_{R\rightarrow L}-\bar R_{R\rightarrow L}$, which would contri…
Baryogenesis at the electroweak scale depends on divers but identifiable details of bubble wall dynamics and the particle physics. We show that inclusion of the dynamics of relative phase in two-Higgs-doublet model (2HDM) enhances the adiabatic order of the mechanism proposed by McLerran-Shaposhnikov-Turok-Voloshin where the scalar-scalar-vector triangle diagram with top quark in the loop gives rise to a significant contribution to the effective chemical potential biasing the Chern-Simons number. We also show that in 2HDM with less stringent constraints on Yukawa couplings than those imposed b…
We consider electroweak baryogenesis mediated by embedded domain walls. Embedded domain walls originating from a symmetry breaking phase transition are stabilized by thermal plasma effects, so that the electroweak symmetry is unbroken in their cores. For this reason, the cosmological evolution of such domain walls can generate a sufficiently large baryon asymmetry, irrespective of the order of the electroweak phase transition. For embedded domain walls, the condition that the energy of the universe not be dominated by the energy of the domain walls is relaxed significantly, and it is shown to …
In any scenario of the electroweak baryogenesis, the profile of the CP violating bubble wall, created at the first-order phase transition, plays an essential role. We attempt to determine it by solving the equations of motion for the scalars in the two-Higgs-doublet model at the transition temperature. According to the parameters in the potential, we found three solutions. Two of them smoothly connect the CP-violating broken phase and the symmetric phase, while the other connects CP-conserving vacua but violates CP in the intermediate region. We also estimate the chiral charge flux, which will…
We study the CP-violating bubble wall by solving the coupled equations of motion derived from the two-Higgs-doublet model for the moduli $ρ_i$ and phases $θ_ i$ of the two scalars $(i=1,2)$ at the transition temperature. We find a solution that the CP-violating phase $θ\equivθ_1-θ_2$ connecting the CP-conserving vacua strongly violates CP in the intermediate region while the moduli largely deviate from the kink shape there. We estimate the chiral charge flux through the wall surface, which may be efficient enough to produce the baryon asymmetry by the sphaleron process.
We discuss the generation of the baryon asymmetry by a strong first order electroweak phase transition in the early universe, particularly in the context of the MSSM. This requires a thorough numerical treatment of the bubble wall profile in the case of two Higgs fields. CP violating complex particle masses varying with the Higgs field in the wall are essential. Since in the MSSM there is no indication of spontaneous CP violation around the critical temperature (contrary to the NMSSM) we have to rely on standard explicit CP violation. Using the WKB approximation for particles in the plasma we …
In extensions of the Standard Model with extra scalars, the electroweak phase transition can be very strong, and the bubble walls can be highly relativistic. We revisit our previous argument that electroweak bubble walls can "run away," that is, achieve extreme ultrarelativistic velocities $γ\sim 10^{14}$. We show that, when particles cross the bubble wall, they can emit transition radiation. Wall-frame soft processes, though suppressed by a power of the coupling $α$, have a significance enhanced by the $γ$-factor of the wall, limiting wall velocities to $γ\sim 1/α$. Though the bubble walls ca…
We consider the dynamics of bubble growth in the Minimal Standard Model at the electroweak phase transition and determine the shape and the velocity of the phase boundary, or bubble wall. We show that in the semi-classical approximation the friction on the wall arises from the deviation of massive particle populations from thermal equilibrium. We treat these with Boltzmann equations in a fluid approximation. This approximation is reasonable for the top quarks and the light species while it underestimates the friction from the infrared $W$ bosons and Higgs particles. We use the two-loop finite …
By treating CP-violating interaction of the electroweak bubble wall as a perturbative term, chiral charge flux through the bubble wall is estimated. It is found that the absolute value of the flux $F_Q$ has a sharp peak at $m_0 \sim a \sim T$ with $F_Q/(u T^3) \sim 10^{-3}\, (Q_L-Q_R)\,Δθ$. Here $m_0$ is the fermion mass, $1/a$ is the wall thickness, $T$ is the temperature at which the bubbles are growing, $u$ is the wall velocity, $Q_{L(R)}$ is the chiral charge of the relevant left(right)-handed fermion and $Δθ$ is the measure of CP violation.
One mechanism for generating a baryon asymmetry at the electroweak phase transition involves propagation of particle asymmetries generated by reflection from the bubble walls into the unbroken phase. Hitherto attention has focussed on top quarks because of their large mass and thus effective scattering from bubble walls. In this paper we point out that leptons may be more efficient mediators of this type of electroweak baryogenesis, particularly for thicker bubble walls favored by perturbative calculations. We carry out an analytic calculation of each stage of the mechanism and conclude it pro…
We derive the kinetic equation for fermions and antifermions interacting with a planar Higgs bubble wall during the electroweak phase transition using the `evenisation' procedure and the Wigner formalism for a Lagrangian with the phase of the complex fermion mass rotated away. We obtain the energy, velocity and force for the particles in the presence of the Higgs bubble wall. Our results using both methods are in agreement. This indicates the robustness of evenisation as a method to study quantum corrections to the velocity and force for particles in the Higgs wall during the electroweak phase…
In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultra-relativistic, with the relativistic gamma factor gamma = (1-v_{wall}^2)^{-1/2} growing linearly with the wall's propagation distance. We provide a simple criterion for determining whether the bubble wall "runs away" in this way or if gamma approaches a terminal value.
First order phase transitions in the early universe naturally lead to the production of a stochastic background of gravitational waves and to the generation of a matter-antimatter asymmetry. The dynamics of the phase transition is affected by the density perturbations in the hot plasma. We address this topic by providing, for the first time, a full numerical solution to the linearized Boltzmann equation for the top quark species coupled to the Higgs field during a first order phase transition at the electroweak scale. Differently from the traditional approaches, our results do not depend on an…
We consider the baryon number generation by charge transport mechanism in the electroweak phase transition taking properly into account thermal fluxes through the wall separating true and false vacuum in the spatial space. We show that the diffusion from the true vacuum to the false one has a large diminishing effect on the baryon number unless the wall velocity is near to, but less than, the speed of sound in the medium and the ratio between the collision rate and wall thickness is about 0.3. The maximum net baryon density generated is $ρ_B/s\simeq 0.2\times 10^{-10}$, where $s$ is the entrop…
Standard electroweak baryogenesis in the context of a first order phase transition is effective in generating the baryon asymmetry of the universe if the broken phase bubbles expand at subsonic speed, so that CP asymmetric currents can diffuse in front of the wall. Here we present a new mechanism for electroweak baryogenesis which operates for supersonic bubble walls. It relies on the formation of small bubbles of the symmetric phase behind the bubble wall, in the broken phase, due to the heating of the plasma as the wall passes by. We apply the mechanism to a model in which the Higgs field is…
We propose a new scenario of the electroweak baryogenesis based on the properties of electroweak domain walls surrounding black holes in the Higgs phase vacuum of the extended Standard Model with 2-Higgs doublets. It is shown that there exists the electroweak domain walls and the symmetric regions surrounding black holes and that the Hawking radiation of the black holes can produce a non-zero baryon number density. The scenario can explain the origin of the baryon number in our universe even without the assumption of the existence of the first order electroweak phase transition.
It is widely believed that electroweak baryogenesis should be suppressed in strong phase transitions with fast-moving bubble walls, but this effect has never been quantitatively studied. We rederive fluid equations describing transport of particle asymmetries near the bubble wall without making the small-wall-velocity approximation. We show that the suppression of the baryon asymmetry is a smooth function of the wall speed and that there is no special behavior when crossing the sound speed barrier. Electroweak baryogenesis can thus be efficient also with strong detonations, generically associa…
The subsonic expansion of bubbles in a strongly first-order electroweak phase transition is a convenient scenario for electroweak baryogenesis. For most extensions of the Standard Model, stationary subsonic solutions (i.e., deflagrations) exist for the propagation of phase transition fronts. However, deflagrations are known to be hydrodynamically unstable for wall velocities below a certain critical value. We calculate this critical velocity for several extensions of the Standard Model and compare with an estimation of the wall velocity. In general, we find a region in parameter space which gi…
Models with singlet fields coupling to the Higgs can enable a strongly first order electroweak phase transition, of interest for baryogenesis and gravity waves. We improve on previous attempts to self-consistently solve for the bubble wall properties -- wall speed $v_w$ and shape -- in a highly predictive class of models with $Z_2$-symmetric singlet potentials. A new algorithm is implemented to determine $v_w$ and the wall profiles throughout the singlet parameter space in the case of subsonic walls, focusing on models with strong enough phase transitions to satisfy the sphaleron washout const…
Spontaneous Baryogenesis from Axions on Induced Electroweak Walls
Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICC), Universitat de Barcelona（巴塞罗那大学量子物理与天体物理系及宇宙科学研究所）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理系）
The limiting bubble wall velocity during a first-order electroweak phase transition is of interest in scenarios for electroweak baryogenesis. Khlebnikov has recently proposed an interesting method for computing this velocity based on the fluctuation-dissipation theorem. I demonstrate that at one-loop order this method is identical to simple, earlier techniques for computing the wall velocity based on computing the friction from particles reflecting off or transmitting through the wall in the ideal gas limit.
If cosmic strings are present at the electroweak phase transition, they can act as seeds on which bubbles of true vacuum nucleate. We explore the nature of such a phase transition, in particular the wall velocity and thickness of the bubbles. {}From the viewpoint of electroweak baryogenesis, adiabatic conditions exist in the expanding bubble walls, and such models of baryogenesis can be successfully applied. In the present mechanism, the nature of the electroweak phase transition is insensitive to the other details of the model, thus reducing the uncertainties in the estimate of net baryon asy…
We describe a new effect which produces baryons at a first order electroweak phase transition. It operates when there is a CP-violating field present on propagating bubble walls. The novel aspect is that it involves a purely classical force, which alters the motion of particles across the wall and through diffusion creates a chiral asymmetry in front of the wall. We develop a technique for computing the baryon asymmetry using the Boltzmann equation, and a fluid approximation which allows us to model strong scattering effects. The final formula for the baryon asymmetry has a remarkably simple f…
We perform large-scale real-time simulations of a bubble wall sweeping through an out-of-equilibrium plasma. The scenario we have in mind is the electroweak phase transition, which may be first order in extensions of the Standard Model, and produce such bubbles. The process may be responsible for baryogenesis and can generate a background of primordial cosmological gravitational waves. We study thermodynamic features of the plasma near the advancing wall, the generation of Chern-Simons number/Higgs winding number and consider the potential for CP-violation at the wall generating a baryon asymm…
The cosmological electroweak phase transition can be strongly first order in extended particle physics models. To accurately predict the speed and shape of the bubble walls during such a transition, Boltzmann equations for the CP-even fluid perturbations must be solved. We point out that the equations usually adopted lead to unphysical behavior of the perturbations, for walls traveling close to or above the speed of sound in the plasma. This is an artifact that can be overcome by more carefully truncating the full Boltzmann equation. We present an improved set of fluid equations, suitable for …
The baryogenesis is reanalyzed based on the model by A.G.Cohen et al., in which the lepton number, generated by the neutrinos' scattering from the bubble walls appearing in the development of the electroweak phase transition, is converted to the baryon number excess through the sphaleron transition. A formula obtained in this paper on the lepton number production rate is correct for the both thin and thick walls within the linear approximation. Investigation on the time-development of the first order phase transition is simulated, including the temporal change of the wall velocity as well as t…
We re-evaluate the status of supersonic electroweak baryogenesis using a generalized fluid Ansatz for the non-equilibrium distribution functions. Instead of truncating the expansion to first order in momentum, we allow for higher order terms as well, including up to 21 fluctuations. The collision terms are computed analytically at leading-log accuracy. We also point out inconsistencies in the standard treatments of transport in electroweak baryogenesis, arguing that one cannot do without specifying an Ansatz for the distribution function. We present the first analysis of baryogenesis using the…
We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, $0.1\lesssim v_w\lesssim 0.6$. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermi…
We discuss the implementation of bulk fermions in soft wall models. The introduction of a position dependent bulk mass allows for a well defined Kaluza-Klein expansion for bulk fermions. The realization of flavor and the contribution to electroweak precision observables are shown to be very similar to the hard wall case. The bounds from electroweak precision test are however milder with gauge boson Kaluza-Klein modes as light as $\sim 1.5$ TeV compatible with current experimental bounds.
We study bulk fermions in models with warped extra dimensions in the presence of a soft wall. Fermions can acquire a position dependent bulk Dirac mass that shields them from the deep infrared, allowing for a systematic expansion in which electroweak symmetry breaking effects are treated perturbatively. Using this expansion, we analyze properties of bulk fermions in the soft wall background. These properties include the realization of non-trivial boundary conditions that simulate the ones commonly used in hard wall models, the analysis of the flavor structure of the model and the implications …
Topological defects can act as local impurities that seed cosmological phase transitions. In this paper we study the case of domain walls, and how they can affect the electroweak phase transition in the Standard Model extended with a $Z_2$-odd scalar singlet. When the transition is two-step, the early breaking of the $Z_2$ symmetry implies the formation of domain walls which can then act as nucleation sites for the second step. We develop a method based on dimensional reduction to calculate the rate of the catalyzed phase transition within the 3d theory on the domain wall surface. By compariso…
We derive the kinetic equation for fermions and antifermions interacting with a planar Higgs bubble wall during the electroweak phase transition using the `evenisation' procedure. Equations of motion in a relativistic quantum theory do not mirror classical relations unless one uses evenised operators. We give a brief introduction to evenisation and then use the evenised Heisenberg equations of motion to obtain the velocity and force for the particles in the presence of the Higgs bubble wall. Keeping quantum contributions to $O(\hbar)$ in the equations of motion we obtain the semi-classical for…
We study the scattering of fermions off a finite width kink wall during the electroweak phase transition in the presence of a background hypermagnetic field. We derive and solve the Dirac equation for such fermions and compute the reflection and transmission coefficients for the case when the fermions move from the symmetric to the broken symmetry phase. We show that the chiral nature of the fermion coupling with the background field in the symmetric phase generates an axial asymmetry in the scattering processes. We discuss possible implications of such axial charge segregation for baryon numb…
I present applications of a master formula for next-to-next-to-leading order soft and virtual QCD corrections to various electroweak, Higgs, and supersymmetric processes. They include Drell-Yan and charged Higgs production, single-top production in flavor-changing neutral-current processes, and squark and gluino production.
The soft function relevant for the production of an electroweak boson (photon, W, Z or H) with large transverse momentum at a hadron collider is computed at next-to-next-to-leading order. This is the first two-loop computation of a soft function involving three light-cone directions. With the result, the threshold resummation for these processes can now be performed at next-to-next-to-next-to-leading logarithmic accuracy.
Utilizing results on the cosmology of anomalous discrete symmetries we show that models of spontaneous CP violation can in principle avoid the domain wall problem first pointed out by Zel'dovich, Kobzarev and Okun. A small but nonzero $θ_{QCD}$ explicitly breaks CP and can lift the degeneracy of the two CP conjugate vacua through nonperturbative effects so that the domain walls become unstable, but survive to cosmologically interesting epochs. We explore the viability of spontaneous CP violation in the context of two Higgs models, and find that the invisible axion solution of the strong CP pro…
The Next to Minimal Supersymmetric Standard Model (NMSSM), proposed as a solution of the mu problem of the Minimal Supersymmetric Standard Model, has a discrete Z_{3} symmetry which is spontaneously broken at the electroweak phase transition, resulting in a cosmological domain wall problem. In most cases this domain wall problem cannot be solved by explicit Z_{3} breaking without introducing supergravity tadpole corrections which destabilize the weak scale hierarchy. Here we consider the possibility of solving the domain wall problem of the NMSSM via spontaneous discrete symmetry breaking occu…
Electroweak baryogenesis depends on the profile of the bubble wall created in the first-order phase transition. It is pointed out that CP violation in the Higgs sector of the MSSM could become large enough to explain the baryon asymmetry. We confirm this by solving the equations of motion for the Higgs fields with the effective potential at the transition temperature. That is, we present an example such that the transitional CP violation is realized and show the possibility that the baryon asymmetry of the universe may be produced, if marginally, by the $τ$ lepton interacting with the wall, wh…
SUSY models with a gauge singlet easily allow for a strong first order electroweak phase transition (EWPT) if the vevs of the singlet and Higgs fields are of comparable size. We discuss the profile of the stationary expanding bubble wall and CP-violation in the effective potential, in particular transitional CP-violation inside the bubble wall during the EWPT. The dispersion relations for charginos contain CP-violating terms in the WKB approximation. These enter as source terms in the Boltzmann equations for the (particle--antiparticle) chemical potentials and fuel the creation of a baryon asy…
By treating CP-violating interaction as a perturbative term, we solved in a previous paper the Dirac equation in the background of electroweak bubble wall, and obtained the transmission and reflection coefficients for a chiral fermion incident from the symmetric-phase region. We give the transmission and reflection coefficients under the other boundary condition, that is, the case of the fermion incident from the broken-phase region. There hold the respective sets of unitarity relations and also reciprocity relations among them. These relations enable us to obtain a simple form of quantum-numb…
