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Electroweak Phase Transition and Baryogenesis
Abstract
I review the status of the strength of the electroweak phase transition, and electroweak baryogenesis in the Minimal Supersymmetric Standard Model (work done with K. Kainulainen and M. Joyce). The emphasis is on new brane-inspired ideas about electroweak baryogenesis, and improvements in the semiclassical treatment of CP violation at a first order electroweak phase transition.
... In the SM, the bound (1) was believed to be satisfied only for very light Higgs bosons [12] [13] [14] [15] [16]. However, this was before the mass of the top quark was known. ...
... In the literature the reader can also find attempts to gain information using gauge-gravity type duality [81, 82, 83]. The order of the electroweak phase transition (EWPT) depends on the underlying type of strong dynamics and plays an important role for baryogenesis [11, 84]. The technicolor chiral phase transition at finite temperature is mapped onto the electroweak one. ...
We unveil the temperature-dependent electroweak phase transition in new extensions of the Standard Model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly-conformal dynamics achieved by the means of multiple matter representations. In particular, we focus on the low energy effective theory introduced to describe Ultra Minimal Walking Technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify regions of parameter space which yield a strong first order transition. A striking feature of the model is the existence of a second phase transition associated to the electroweak-singlet sector. The interplay between these two transitions leads to an extremely rich phase diagram. Comment: 38 RevTeX pages, 9 figures
... There exists many proposals for baryogenesis of this sort; for reviews see, e.g., [8][9][10]. One popular mechanism is to introduce new physics around the electroweak scale and achieve baryogenesis at the electroweak phase transition, e.g., see [11][12][13][14]. As we have yet to see any new physics at the LHC, which is probing this energy regime, it is important to consider the possibility that baryogenesis is associated with much higher energies. ...
We propose a mechanism by which the inflaton can generate baryogenesis, by
taking the inflaton to be a complex scalar field with a weakly broken global
symmetry and present a new version of the Affleck-Dine mechanism. The smallness
of the breaking is motivated both by technical naturalness and a requirement
for inflation. We study inflation driven by a quadratic potential for
simplicity and discuss generalizations to other potentials. We compute the
inflationary dynamics and find that a conserved particle number is obtained
towards the end of inflation. We then explain in detail the later decay to
baryons. We present two promising embeddings in particle physics: (i) using
high dimension operators for a gauge singlet; we find this leads to the
observed asymmetry for decay controlled by the ~GUT scale and this is precisely
the regime where the EFT applies. (ii) using a colored inflaton, which requires
small couplings. We also point out two observational consequences: a possible
large scale dipole in the baryon density, and a striking prediction of
isocurvature fluctuations whose amplitude is found to be just below current
limits and potentially detectable in future data.
... For example, first order electroweak phase transitions are associated with strong gravitational wave signals due to the corresponding bubble nucleations in the vacuum [37, 42]. Similarly various models of electroweak baryogenesis requires such thin bubble walls occurring during the first order phase transition [37, 38, 39, 40]. It is very unlikely to have such an effect for the second order transition [41]. ...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2009. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Cataloged from student submitted PDF version of thesis. Includes bibliographical references (p. 67-75). In this thesis, we are investigating cosmological implications of hidden sector models which involve scalar fields that do not interact with the Standard Model gauge interactions, but couple directly to the Higgs field. We particularly focus on their relic particle density as a candidate for dark matter. For the case of hidden sector without a gauge field we have improved the accuracy of the bounds on the coupling constant and give bounds on the Lagrangian parameters. Models with Abelian and non-Abelian gauge fields are also studied with relic density bounds, BBN and galactic dynamics constraints. Several discussions on phase transitions and alternative dark matter candidates are included. by Serkan Cabi. Ph.D.
... They also allow a stronger first order phase transition [5]. In spite of these improvements with respect to the SM, the minimal supersymmetric model (MSSM) is severely constrained from experimental bounds on the chargino properties [6] leaving only a small corner of parameter space for the MSSM as a viable candidate for baryogenesis. Further possibilities to accommodate an explanation for the generation of baryon number during the EWPT include non-minimal supersymmetric models which, nonetheless, all share the unappealing feature of containing an even larger set of parameters than the already extensive number contained in the MSSM. ...
The origin of the matter-antimatter asymmetry of the universe remains one of the outstanding questions yet to be answered by modern cosmology and also one of only a handful of problems where the need of a larger number of degrees of freedom than those contained in the standard model (SM) is better illustrated. An appealing scenario for the generation of baryon number is the electroweak phase transition that took place when the temperature of the universe was about 100 GeV. Though in the minimal version of the SM, and without considering the interaction of the SM particles with additional degrees of freedom, this scenario has been ruled out given the current bounds for the Higgs mass, this still remains an open possibility in supersymmetric extensions of the SM. In recent years it has also been realized that large scale magnetic fields could be of primordial origin. A natural question is what effect, if any, these fields could have played during the electroweak phase transition in connection to the generation of baryon number. Prior to the electroweak symmetry breaking, the magnetic modes able to propagate for large distances belonged to the U(1) group of hypercharge and hence receive the name of hypermagnetic fields. In this contribution, we summarize recent work aimed to explore the effects that these fields could have introduced during a first order electroweak phase transition. In particular, we show how these fields induce a CP asymmetric scattering of fermions off the true vacuum bubbles nucleated during the phase transition. The segregated axial charge acts as a seed for the generation of baryon number. We conclude by mentioning possible research venues to further explore the effects of large scale magnetic fields for the generation of the baryon asymmetry.
... Coming to the main topic of this paper, the order of the electroweak phase transition (EWPT) depends on the underlying type of strong dynamics and plays an important role for baryogenesis [14, 61]. The technicolor chiral phase transition at finite temperature is mapped onto the electroweak one. ...
We examine the temperature-dependent electroweak phase transition in extensions of the Standard Model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly-conformal dynamics. In particular, we focus on the low energy effective theory used to describe Minimal Walking Technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify significant regions of parameter space which yield a sufficiently strong first order transition for electroweak baryogenesis. The composite particle spectrum corresponding to these regions can be produced and studied at the Large Hadron Collider experiment. We note the possible emergence of a second phase transition at lower temperatures. This occurs when the underlying technicolor theory possesses a nontrivial center symmetry.
A successful baryogenesis mechanism is proposed in the cosmological framework of Brans-Dicke modified gravity. Primordial black holes with small mass are produced at the end of the Brans-Dicke field domination era. The Hawking radiation reheats a spherical region around every black hole to a high temperature and the electroweak symmetry is restored there. A domain wall is formed separating the region with the symmetric vacuum from the asymmetric region where electroweak baryogenesis takes place. First order phase transition is not needed. In Brans-Dicke cosmologies black hole accretion can be strong enough to lead to black holes domination which extends the lifetime of black holes and therefore baryogenesis. The analysis of the whole scenario, finally, results in the observed baryon number which can be achieved for a CP-violation angle that is predicted by observationally accepted Two-Higgs Doublet Models. The advantage of our proposed scenario is that naturally provides both black hole domination and more efficient baryogenesis for smaller CP violating angles compared to the same mechanism applied in a FRW cosmological background.
A novel cosmological scenario, capable to generate the observed baryon number at the electroweak scale for very small CP violating angles, is presented. The proposed mechanism can be applied in conventional FRW cosmology, but becomes extremely efficient due to accretion in the context of early cosmic expansion with high energy modifications. Assuming that our universe is a Randall-Sundrum brane, baryon asymmetry can easily be produced by Hawking radiation of very small primordial black holes. The Hawking radiation reheats a spherical region around every black hole to a high temperature and the electroweak symmetry is restored there. A domain wall is formed separating the region with the symmetric vacuum from the asymmetric region where electroweak baryogenesis takes place. First order phase transition is not needed. The black holes's lifetime is prolonged due to accretion, resulting to strong efficiency of the baryon producing mechanism. The allowed by the mechanism black hole mass range includes masses that are energetically favoured to be produced from interactions around the higher dimensional Planck scale.(AUTHORS IN ALPHABETICAL ORDER AFTER AGREEMENT)
In this letter we show that the inflaton can generate the cosmological baryon
asymmetry. We take the inflaton to be a complex scalar field with a weakly
broken global symmetry and develop a new variant on the Affleck-Dine mechanism.
We show that a conserved particle number can be produced in the latter stage of
inflation, which can later decay to baryons. We present promising embeddings in
particle physics, including the use of high dimension operators or using a
colored inflaton. We also point out observational consequences, including a
prediction of isocurvature fluctuations, whose amplitude is just below current
limits, and a possible large scale dipole.
The main motivation for this thesis is the physics of the very early universe and of heavy ion collisions. These two fields are described using quantum field theory. In order to do calculations in (quantum) field theory one often makes use of perturbation theory and/or the imaginary time formalism. However, if one wants to describe nonequilibrium processes such as phase transitions or thermalization, in which nonperturbative effects play a role, new approximation methods are needed. Commonly used nonperturbative real-time approximation schemes include the large-n, the Hartree and the classical approximations. They all have their limitations: the related large-n and Hartree include quantum corrections, but fail to properly describe thermalization, due to the lack of direct scattering. The classical approximation does include scattering and leads to (classical) thermalization, but has problems with the Rayleigh Jeans divergencies and cannot describe quantum thermalization. More recently, approximations based on an expansion of the 2PI effective action or on a truncation of the Schwinger-Dyson equations, both including direct scattering, have been shown to lead to thermalization. These methods give good results, but the treatment of inhomogeneous systems seems numerically too demanding. In this thesis an approximation is introduced and studied, which tries to improve on both the classical and the Hartree approximation. In the Hartree approximation the initial density matrix is taken to be Gaussian, leading to the absence of direct scattering terms. In the classical approximation one usually writes the initial density matrix as an ensemble average over initial conditions. By expanding a general density matrix on a (over complete) basis of Gaussian density matrices, one can use the Hartree or Gaussian approximation to calculate the dynamics in each of the `realizations' and take an ensemble average to allow for more general initial density matrices. At the same time these `realizations' can be inhomogeneous (i.e. space dependent), leading to indirect scattering and thus removing the principal obstruction for thermalization. The thesis examines this approximation in a simple scalar theory in 1+1 dimensions. In the first chapters it studies if the model thermalizes starting from some out of equilibrium initial condition. Starting at low momenta the system indeed thermalizes. However this process only slowly proceeds to higher momenta, and a full quantum thermal distribution is never found. Deviations start to emerge and the system evolves towards a classical distribution, caused by the fact that the Hartree equations of motion can be derived from a Hamiltonian. Timescales for both processes, thermalization and the flow to classical behaviour are derived and studied in both phases of the theory. Because of the numerical task involved, further approximations are also investigated, especially to allow for the extension to 3+1 dimensions. The final chapter studies the topological defects present in the theory, kinks and antikinks. It makes a comparison between the classical theory and the Hartree approximation. As initial conditions both semi-stationary and colliding configurations are studied. Some important differences between the classical and quantum theory are found.
We unveil the temperature-dependent electroweak phase transition in new extensions of the standard model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly conformal dynamics achieved by the means of multiple matter representations. In particular, we focus on the low energy effective theory introduced to describe ultra minimal walking technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify regions of parameter space, which yield a strong first-order transition. A striking feature of the model is the existence of a second phase transition associated to the electroweak-singlet sector. The interplay between these two transitions leads to an extremely rich phase diagram.
We study resonant CP violation in the Higgsstrahlung process e{sup +}eâ»âH{sub 1,2,3}(Zâe{sup +}eâ»,μ{sup +}μâ») and subsequent decays H{sub 1,2,3}âbb,Ïâ»Ï{sup +}, in the minimal supersymmetric extension of the standard model (MSSM) with Higgs-sector CP violation induced by radiative corrections. At a high-energy e{sup +}eâ» linear collider, the recoil-mass method enables one to determine the invariant mass of a fermion pair produced by Higgs decays with a precision as good as 1 GeV. Assuming an integrated luminosity of 100 fbâ»Â¹, we show that the production line shape of a coupled system of neutral Higgs bosons decaying into bb quarks is sensitive to the CP-violating parameters. When the Higgs bosons decay into Ïâ»Ï{sup +}, two CP asymmetries can be defined using the longitudinal and transverse polarizations of the Ï leptons. Taking into account the constraints from electric dipole moments, we find that these CP asymmetries can be as large as 80%, in a trimixing scenario where all three neutral Higgs states of the MSSM are nearly degenerate and mix significantly.
A commonly accepted mechanism of generating baryon asymmetry in the minimal supersymmetric standard model (MSSM) depends on the CP violating relative phase between the gaugino mass and the Higgsino μ term. The direct constraint on this phase comes from the limit of electric dipole moments (EDM’s) of various light fermions. To avoid such a constraint, a scheme which assumes that the first two generation sfermions are very heavy is usually evoked to suppress the one-loop EDM contributions. We point out that under such a scheme the most severe constraint may come from a new contribution to the electric dipole moment of the electron, the neutron, or atoms via the chargino sector at the two-loop level. As a result, the allowed parameter space for baryogenesis in the MSSM is severely constrained, independent of the masses of the first two generation sfermions.
This report emphasizes the comparison between supersymmetric models and experiments. A minimal theoretical introduction is included as a guide to the interpretation of results. The existing constraints from low energy measurements, accelerator searches (LEP, Tevatron and HERA) and non-accelerator searches for neutralinos are presented. Prospects for upgrades of these facilities and for the LHC and linear collider are summarized. Most discussions are made in the framework of the minimal supersymmetric standard model inspired by supergravity (MSUGRA). But alternatives such as gauge mediated supersymmetry breaking (GMSB), anomaly mediated supersymmetry breaking (AMSB), models with R-parity violation and even alternatives to supersymmetry are also briefly considered.
We briefly review the issues related to electroweak baryogenesis in minimal supersymmetric standard model (MSSM). The constraints from electric dipole moments of electron and neutron are emphasized.
We build on existing calculations of the wall velocity of the expanding
bubbles of the broken symmetry phase in a first-order electroweak phase
transition within the light stop scenario (LSS) of the MSSM. We carry out the
analysis using the 2-loop thermal potential for values of the Higgs mass
consistent with present experimental bounds. Our approach relies on describing
the interaction between the bubble and the hot plasma by a single friction
parameter, which we fix by matching to an existing 1-loop computation and
extrapolate it to our regime of interest. For a sufficiently strong phase
transition (in which washout of the newly-created baryon asymmetry is
prevented) we obtain values of the wall velocity, v_w~0.05, far below the speed
of sound in the medium, and not very much deviating from the previous 1-loop
calculation. We also find that the phase transition is about 10% stronger than
suggested by simply evaluating the thermal potential at the critical
temperature.
We introduce the topic of dynamical breaking of the electroweak symmetry and its link to unparticle physics and cosmology. The knowledge of the phase diagram of strongly coupled theories plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we present the state-of-the-art of the phase diagram for SU, Sp and SO gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We summarize several analytic methods used recently to acquire information about these gauge theories. We also provide new results for the phase diagram of the generalized Bars-Yankielowicz and Georgi-Glashow chiral gauge theories. These theories have been used for constructing grand unified models and have been the template for models of extended technicolor interactions. To gain information on the phase diagram of chiral gauge theories we will introduce a novel all orders beta function for chiral gauge theories. This permits the first unified study of all non-supersymmetric gauge theories with fermionic matter representation both chiral and non-chiral. To the best of our knowledge the phase diagram of these complex models appears here for the first time. We will introduce recent extensions of the SM featuring minimal conformal gauge theories known as minimal walking models. Finally we will discuss the electroweak phase transition at nonzero temperature for models of dynamical electroweak symmetry breaking. Comment: 207 pages. Several figures. Lectures presented at the 49th Cracow School of Theoretical Physics. New results are reported for the phases of chiral gauge theories. Comments and corrections are encouraged and welcome
We study the production and decay of a coupled system of mixed neutral MSSM Higgs bosons in exclusive double-diffractive processes at the LHC, including non-vanishing CP phases in the soft supersymmetry-breaking gaugino masses and third-generation trilinear squark couplings. The three neutral Higgs bosons are naturally nearly degenerate, for large values of \tan\beta, when the charged Higgs boson weighs around 150 GeV. Large mixing between all three neutral Higgs bosons is possible when CP is violated, a three-way mixing scenario which we also term tri-mixing. A resolution in the Higgs mass of \sim 1 GeV, which may be achievable using the missing-mass method, would allow one to distinguish nearly degenerate Higgs bosons by studying the production lineshape. Measurements of the polarizations of the tau leptons coming from the Higgs-boson decays could offer a direct and observable signal of CP violation in the Higgs sector.
We review the experimental evidence for a net baryon density in cosmology, and the theoretical mechanism for producing it, called leptogenesis, which relies on the creation of a lepton asymmetry at an intermediate step. The naturality of this mechanism and its possible relations with neutrino oscillations are outlined.
Although the origin of matter-antimatter asymmetry remains unknown, continuing advances in theory and improved experimental limits have ruled out some scenarios for baryogenesis, for example the sphaleron baryogenesis at the electroweak phase transition in the standard model. At the same time, the success of cosmological inflation and the prospects for discovering supersymmetry at the LHC have put some other models in sharper focus. We review the current state of our understanding of baryogenesis with the emphasis on those scenarios that we consider most plausible.
We summarize basic features associated to dynamical breaking of the
electroweak symmetry. The knowledge of the phase diagram of strongly coupled
theories as function of the number of colors, flavors and matter representation
plays a fundamental role when trying to construct viable extensions of the
standard model (SM). Therefore we will report on the status of the phase
diagram for SU(N) gauge theories with fermionic matter transforming according
to arbitrary representations of the underlying gauge group. We will discuss how
the phase diagram can be used to construct unparticle models. We will then
review Minimal Walking Technicolor (MWT) and other extensions, such as
partially gauged and split technicolor. MWT is a sufficiently general, symmetry
wise, model to be considered as a benchmark for any model aiming at breaking
the electroweak symmetry dynamically. The unification of the standard model
gauge couplings will be revisited within technicolor extensions of the SM. A
number of appendices are added to review some basic methods and to provide
useful details. In one of the appendices we will show how to gain information
on the spectrum of strongly coupled theories relevant for new extensions of the
SM by introducing and using alternative large N limits.
We present a novel scenario for baryogenesis in a hybrid inflation model at the electroweak scale, in which the standard model Higgs field triggers the end of inflation. One of the conditions for successful baryogenesis, the departure from thermal equilibrium, is naturally achieved at the stage of preheating after inflation. The inflaton oscillations induce large occupation numbers for long-wavelength configurations of the Higgs and gauge fields, which leads to a large rate of sphaleron transitions. We estimate this rate during the first stages of reheating and evaluate the amount of baryons produced due to a particular type of higher-dimensional CP violating operator. The universe thermalizes through fermion interactions, at a temperature below critical, Trh≲100 GeV, preventing the wash-out of the produced baryon asymmetry. Numerical simulations in 1+1 dimensions support our theoretical analyses.
this paper we will assume that the supersymmetry breaking terms have CP-violating phases and see whether these phases can account for sufficient baryogenesis without violating the electric dipole moment bounds. In the MSSM, the requirement of a sufficiently first order phase transition places upper limits on the Higgs and stop (supersymmetric partners of the top) masses [33] which are barely consistent with experimental constraints--there are speculations that these bounds could be relaxed slightly by higher order and nonperturbative effects [34]
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 are not washed out after the resonance. Comment: 5 pages, RevTeX, 8 figures, included with epsf
We propose a new alternative for baryogenesis which resolves a number of the problems associated with GUT and electroweak scenarios, and which may allow baryogenesis even in modest extensions of the standard model. If the universe never reheats above the electroweak scale following inflation, GUT baryon production does not occur and at the same time thermal sphalerons, gravitinos and monopoles are not produced in abundance. Nevertheless, non-thermal production of sphaleron configurations via preheating could generate the observed baryon asymmetry of the universe. Comment: 4 pages, revtex, submitted to PRL
We investigate the possibility of preheating in hybrid inflation. This scenario involves at least two scalar fields, the inflaton field , and the symmetry breaking field . We found that the behavior of these fields after inflation, as well as the possibility of preheating (particle production due to parametric resonance), depends crucially on the ratio of the coupling constant (self-interaction of the field ) to the coupling constant (interaction of and ). For , the oscillations of the field soon after inflation become very small, and all the energy is concentrated in the oscillating field . For both fields and oscillate in a rather chaotic way, but eventually their motion stabilizes, and parametric resonance with production of particles becomes possible. For the oscillations of the field soon after inflation become very small, and all the energy is concentrated in the oscillating field . Preheating can be efficient if the effective masses of the fields and are much greater than the Hubble constant, or if these fields are coupled to other light scalar (or vector) fields . In the recently proposed hybrid models with a second stage of inflation after the phase transition, both preheating and usual reheating are inefficient. Therefore for a very long time the universe remains in a state with vanishing pressure. As a result, density contrasts generated during the phase transition in these models can grow and collapse to form primordial black holes. Under certain conditions, most of the energy density after inflation will be stored in small black holes, which will later evaporate and reheat the universe. Comment: 15 pages, 11 figures, new results illustrating a possibility of an efficient preheating are added
We perform a systematic gradient expansion on kinetic equations and derive the CP-violating semiclassical force for fermions propagating in presence of a CP-violating wall at a first order electroweak phase transition. The force appears at order h-bar in the flow term of the kinetic equation and agrees with the semiclassical force used for baryogenesis computations. In particular we consider the force for charginos in both the MSSM and NMSSM. We then study the continuity equations for the vector and axial vector currents and stress the role of the latter as the one containing baryogenesis sources. We also show that there is no CP-violating force for bosons to order h-bar in gradient expansion. Comment: 32 pages, the version published in JHEP
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 are led to Boltzmann transport equations for the difference of left-handed particles and their CP conjugates. This asymmetry is finally transformed into a baryon asymmetry by out of equilibrium sphaleron transitions in the symmetric phase. We solve the transport equations and find a baryon asymmetry depending mostly on the CP violating phases and the wall velocity. Comment: Discussion slightly improved, refs. corrected, acknowledgement added
In many inflationary models, a large amount of energy is transferred rapidly to the long-wavelength matter fields during a period of preheating after inflation. We study how this changes the dynamics of the electroweak phase transition if inflation ends at the electroweak scale. We simulate a classical SU(2)xU(1)+Higgs model with initial conditions in which the energy is concentrated in the long-wavelength Higgs modes. With a suitable initial energy density, the electroweak symmetry is restored non-thermally but broken again when the fields thermalize. During this symmetry restoration, baryon number is violated, and we measure its time evolution, pointing out that it is highly non-Brownian. This makes it difficult to estimate the generated baryon asymmetry. Comment: 22 pages, 6 figures. Parts of the text rewritten, one new figure added, some references added. Final version
We compute the wall velocity in the MSSM with W, tops and stops contributing 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_w=O(0.01) much below the SM value.
We re-examine the generation of the baryon asymmetry in the minimal supersymmetric standard model (MSSM) during the electroweak phase transition. We find that the dominant source for baryogenesis arises from the chargino sector. The CP-violation comes from the complex phase in the mu parameter, which provides CP-odd contributions to the particle dispersion relations. This leads to different accelerations for particles and antiparticles in the wall region which, combined with diffusion, leads to the separation of Higgsinos and their antiparticles in the front of the wall. These asymmetries get transported to produce perturbations in the left-handed chiral quarks, which then drive sphaleron interactions to create the baryon asymmetry. We present a complete derivation of the semiclassical WKB formalism, including the chargino dispersion relations and a self-consistent derivation of the diffusion equations starting from semiclassical Boltzmann equations for WKB-excitations. We stress the advantages of treating the transport equations in terms of the manifestly gauge invariant physical energy and kinetic momentum, rather than in the gauge variant canonical variables used in previous treatments. We show that a large enough baryon asymmetry can be created for the phase of the complex mu parameter as small as ~ 0.001, which is consistent with bounds from the neutron electric dipole moment. Comment: 54 pages, 3 figures
We examine the evolution of a 3-brane that separates two regions of a
4+1
dimensional bulk space-time with potentially different cosmological constants. We have included a term in the brane action for the scalar curvature. When one or both of the regions has a zero cosmological constant, we find solutions for which the cosmology on the brane has the same time-dependence as a standard radiation-dominated universe, but which depends on a mass parameter in the bulk metric rather than the radiation density on the brane. When a non-zero cosmological constant is present in both bulk regions, it is possible to obtain a standard Robertson-Walker evolution. We then extract the effective theory of gravity in the weak-field limit seen by an observer on the brane in each of these scenarios.
During hybrid inflation, the slowly-rolling inflaton field has a significant coupling to the trigger field which is responsible for most of the potential. Barring a fine-tuned accidental cancellation, this coupling induces a minimal one-loop contribution to the inflaton potential. The requirement that this contribution be not too large constrains a wide class of hybrid inflation models. Assuming that the inflaton perturbation generates structure in the Universe, the inflaton field and/or the trigger field after inflation have to be bigger than 109GeV. This and other results make hybrid inflation at or below the TeV scale problematical. (There is no problem with hybrid inflation at the high energy scales normally considered.) `New' and thermal inflation seem to be viable alternatives for inflation at or below the TeV scale, including the case that quantum gravity is at the TeV scale. In any case, supersymmetry is needed required during inflation, in order to protect a scalar mass.
We derive the corrections to the Friedmann equation of order rho2 in the Randall-Sundrum (RS) model, where two 3-branes bound a slice of five-dimensional Anti-deSitter space. The effects of radion stabilization by the Goldberger-Wise mechanism are taken into account. Surprisingly, we find that an inflaton on either brane will experience no order rho2 corrections in the Hubble rate H due to its own energy density, although an observer on the opposite brane does see such a correction. Thus there is no enhancement of the slow-roll condition unless inflation is simultaneously driven by inflatons on both branes. Similarly, during radiation domination, the rho2 correction to H on a given brane vanishes unless there is nonvanishing energy density on the opposite brane. During the electroweak phase transition the correction can be large, but is has the wrong sign for causing sphalerons to go out of thermal equilibrium, so it cannot help electroweak baryogenesis. We discuss the differences between our results and exact solutions in RS-II cosmology.
Certain inflation models undergo pre-heating, in which inflaton oscillations can drive parametric resonance instabilities. We discuss several phenomena stemming from such instabilities, especially in weak-scale models; generically, these involve energizing a resonant system so that it can evade tunneling by crossing barriers classically. One possibility is a spontaneous change of phase from a lower-energy vacuum state to one of higher energy, as exemplified by an asymmetric double-well potential with different masses in each well. If the lower well is in resonance with oscillations of the potential, a system can be driven resonantly to the upper well and stay there (except for tunneling) if the upper well is not resonant. Another example occurs in hybrid inflation models where the Higgs field is resonant; the Higgs oscillations can be transferred to electroweak (EW) gauge potentials, leading to rapid transitions over sphaleron barriers and consequent B+L violation. Given an appropriate CP-violating seed, we find that preheating can drive a time-varying condensate of Chern-Simons number over large spatial scales; this condensate evolves by oscillation as well as decay into modes with shorter spatial gradients, eventually ending up as a condensate of sphalerons. We study these examples numerically and to some extent analytically. The emphasis in the present paper is on the generic mechanisms, and not on specific preheating models; these will be discussed in a later paper.
In this work we compute the CP-violating currents of the right-handed stops and higgsinos, induced by the presence of non-trivial vacuum expectation values of the Higgs fields within the context of the minimal supersymmetric extension of the Standard Model (MSSM) with explicit CP-violating phases. Using the Keldysh formalism, we perform the computation of the currents at finite temperature, in an expansion of derivatives of the Higgs fields. Contrary to previous works, we implement a resummation of the Higgs mass insertion effects to all orders in perturbation theory. While the components of the right-handed stop current become proportional to the difference (suppressed by Δβ), the higgsino currents, present contributions proportional to both . For large values of the charged Higgs mass and moderate values of the contribution to the source proportional to in the diffusion equations become sizeable, although it is suppressed by the higgsino number violating interaction rate . For small values of the wall velocity, , the total contribution leads to acceptable values of the baryon asymmetry for values of the CP-violating phases in the range . Finally, we comment on the relevance of the latest results of Higgs searches at LEP2 for the mechanism of electroweak baryogenesis within the MSSM.
We analyse the cosmology of a brane world model where a single brane carrying the standard model fields forms the boundary of a 5-dimensional AdS bulk (the Randall–Sundrum II scenario). We focus on the thermal radiation of bulk gravitons, the formation of the bulk black hole, and the holographic AdS/CFT definition of the RSII theory. Our detailed calculation of bulk radiation reduces previous estimates to a phenomenologically acceptable, although potentially visible level. In late cosmology, in which the Friedmann equation depends linearly on the energy density ρ, only about 1% of energy density is lost to the black hole or, equivalently, to the ‘dark radiation’ ( at nucleosynthesis). The preceding, unconventional ρ2 period can produce up to 10% dark radiation (). The AdS/CFT correspondence provides an equivalent description of late RSII cosmology. We show how the AdS/CFT formulation can reproduce the ρ2 correction to the standard treatment at low matter density. However, the 4-dimensional effective theory of CFT + gravity breaks down due to higher curvature terms for energy densities where ρ2 behaviour in the Friedmann equation is usually predicted. We emphasize that, in going beyond this energy density, the microscopic formulation of the theory becomes essential. For example, the pure AdS5 and string-motivated AdS5×S5 definitions differ in their cosmological implications.
We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, using a new method to compute the CP-violating asymmetry in the Higgsino flux reflected into the unbroken phase. The method is based on a Higgs insertion expansion. We find that the CP asymmetry at leading order is proportional to the change in tanβ in the bubble wall, which is at most of order 10−2, while at next-to-leading order this suppression factor disappears. This result may enhance the final baryon asymmetry generated during the electroweak phase transition for small Δβ(<10−3).
The Minimal Supersymmetric Standard Model can possess several CP-violating phases beyond the conventional Cabibbo-Kobayashi-Maskawa phase. We calculate the contribution of these phases to T-violating nuclear forces. These forces induce a Schiff moment in the 199Hg nucleus, which is strongly limited by experiments aimed at the detection of the electric dipole moment of the mercury atom. The result for dHg is found to be very sensitive to the CP-violating phases of the MSSM and the calculation carries far fewer QCD uncertainties than the corresponding calculation of the neutron EDM. In certain regions of the MSSM parameter space, the limit from the mercury EDM is stronger than previous constraints based on either the neutron or electron EDMs. We present combined constraints from the mercury and electron EDMs to limit both CP-violating phases of the MSSM. We also present limits in mSUGRA models with unified gaugino and scalar masses at the GUT scale.
We examine the cosmology of the two recently proposed scenarios for a five dimensional universe with localized gravity. We find that the scenario with a non-compact fifth dimension is potentially viable, while the scenario which might solve the hierarchy problem predicts a contracting universe, leading to a variety of cosmological problems.
We compute the three-dimensional effective action for the minimal supersymmetric standard model, which describes the light modes of the theory near the finite-temperature electroweak phase transition, keeping the one-loop corrections from the third generations quarks and squarks. Using the lattice results of Kajantie et al. for the phase transition in the same class of 3D models, we find that the strength of the phase transition is sufficient for electroweak baryogenesis, in much broader regions of parameter space than have been indicated by purely perturbative analyses. In particular we find that, while small values of tan β are favored, positive results persist even for arbitrarily large values of tan β if the mass of the A- boson is between 40 and 120 GeV, a region of parameters which has not been previously identified as being favorable for electroweak baryogenesis.
Electroweak baryogenesis is an interesting theoretical scenario, which demands physics beyond the Standard Model at energy scales of the order of the weak boson masses. It has been recently emphasized that, in the presence of light stops, the electroweak phase transition can be strongly first order, opening the window for electroweak baryogenesis in the MSSM. For the realization of this scenario, the Higgs boson must be light, at the reach of the LEP2 collider. In this article, we compute the baryon asymmetry assuming the presence of non-trivial CP-violating phases in the parameters associated with the left-right stop mixing term and the Higgsino mass μ. We conclude that a phase |sinΦμ| > 0.01 and Higgsino and gaugino mass parameters |μ| ≅ M2, and of the order of the electroweak scale, are necessary in order to generate the observed baryon asymmetry.
In the electroweak phase transition there arises the problem of baryon number washout by sphaleron transitions, which can be avoided if the phase transition is strongly enough first order. The minimal supersymmetric standard model has just two Higgs doublets H1 and H2, while the next to minimal model, NMSSM, has an additional singlet, N, this latter giving rise to the helpful feature that the Higgs potential contains a tree level trilinear field term. We use the tunneling criterion for the existence of a first order electroweak phase change. A quantitative statistical analysis indicates that with parameters of the NMSSM satisfying the experimental constraints a strong first order phase change occurs in about 50% of cases.
During hybrid inflation, the slowly-rolling inflaton field has a significant coupling to the trigger field which is responsible for most of the potential. Barring a fine-tuned accidental cancellation, this coupling induces a minimal one-loop contribution to the inflaton potential. The requirement that this contribution be not too large constrains a wide class of hybrid inflation models. Assuming that the inflaton perturbation generates structure in the Universe, the inflaton field and/or the trigger field after inflation have to be bigger than . This and other results make hybrid inflation at or below the TeV scale problematical. (There is no problem with hybrid inflation at the high energy scales normally considered.) `New' and thermal inflation seem to be viable alternatives for inflation at or below the TeV scale, including the case that quantum gravity is at the TeV scale. In any case, supersymmetry is needed required during inflation, in order to protect a scalar mass.
We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, treating the particles in a WKB approximation in the bubble wall background. A set of diffusion equations for the particle species relevant to baryon generation, including source terms arising from the CP violation associated with the complex phase δ of the μ parameter, are derived from Boltzmann equations, and solved. The conclusion is that δ must be ≳0.1 to generate a baryon asymmetry consistent with nucleosynthesis. We compare our results to several other recent computations of the effect, arguing that some are overestimates.
We compute the tunneling probability from the symmetric phase to the true vacuum, in the first-order electroweak phase transition of the MSSM, and the corresponding Higgs profiles along the bubble wall. We use the resummed two-loop temperature-dependent effective potential, and pay particular attention to the light stop scenario, where the phase transition can be sufficiently strongly first-order not to wipe off any previously generated baryon asymmetry. We compute the bubble parameters which are relevant for the baryogenesis mechanism: the wall thickness and Δβ. The two-loop corrections provide important enhancement effects, with respect to the one-loop results, in the amount of baryon asymmetry.
We systematically analyze constraints on supersymmetric theories imposed by the experimental bounds on the electron, neutron, and mercury electric dipole moments. We critically reappraise the known mechanisms to suppress the EDMs and conclude that only the scenarios with approximate CP-symmetry or flavour-off-diagonal CP violation remain attractive after the addition of the mercury EDM constraint.
We perform an analysis of the behaviour of the electroweak phase transition in the Minimal Supersymmetric Standard Model, in the presence of light stops. We show that, in previously unexplored regions of parameter space, the order parameter v(T_c)/T_c can become significantly larger than one, for values of the Higgs and supersymmetric particle masses consistent with the present experimental bounds. This implies that baryon number can be efficiently generated at the electroweak phase transition. As a by-product of this study, we present an analysis of the problem of colour breaking minima at zero and finite temperature, and we use it to investigate the region of parameter space preferred by the best fit to the present precision electroweak measurement data, in which the left-handed stops are much heavier than the right-handed ones.
One of the most experimentally testable explanations for the origin of the baryon asymmetry of the Universe is that it was created during the electroweak phase transition, in the minimal supersymmetric standard model. Previous efforts have focused on the current for the difference of the two Higgsino fields, H1-H2, as the source of biasing sphalerons to create the baryon asymmetry. We point out that the current for the orthogonal linear combination, H1+H2, is larger by several orders of magnitude. Although this increases the efficiency of electroweak baryogenesis, we nevertheless find that large CP-violating angles > or = 0.15 are required to get a large enough baryon asymmetry.
Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.
We consider “brane universes”, where energy density is confined to four-dimensional hypersurfaces (three-branes) whereas one extra compact dimension is felt by gravity only. We show that the cosmology of such branes, when the bulk stress-energy tensor is neglected, is definitely different from standard cosmology and identify the reasons behind this difference. We give a new class of exact solutions with a constant five-dimensional radius and cosmologically evolving brane. We discuss various consequences.
We study through holography the compact Randall-Sundrum (RS) model at finite temperature. In the presence of radius stabilization, the system is described at low enough temperature by the RS solution. At high temperature it is described by the AdS-Schwarzschild solution with an event horizon replacing the TeV brane. We calculate the transition temperature T_c between the two phases and we find it to be somewhat smaller than the TeV scale. Assuming that the Universe starts out at T >> T_c and cools down by expansion, we study the rate of the transition to the RS phase. We find that the transition is very slow so that an inflationary phase at the weak scale begins. The subsequent evolution depends on the stabilization mechanism: in the simplest Goldberger-Wise case inflation goes on forever unless tight bounds are satisfied by the model parameters; in slightly less-minimal cases these bounds may be relaxed. Comment: 28 pages, 3 figures, discussion with more generic Goldberger-Wise potentials added and minor changes. Published JHEP version
It has recently been pointed out that global solutions of Einstein's equations for a 3-brane universe embedded in 4 spatial dimensions give rise to a Friedmann equation of the form H ~ rho on the brane, instead of the usual H ~ (rho)^{1/2}, which is inconsistent with cosmological observations. We remedy this problem by adding cosmological constants to the brane and the bulk, as in the recent scenario of Randall and Sundrum. Our observation allows for normal expansion during nucleosynthesis, but faster than normal expansion in the very early universe, which could be helpful for electroweak baryogenesis, for example. Comment: 4pp, latex, 1 figure; added and corrected references; revised incorrect argument about sign of action on brane; final version to be published in PRL
We propose a new higher-dimensional mechanism for solving the Hierarchy Problem. The Weak scale is generated from a large scale of order the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of AdS_5 spacetime). This mechanism relies on the existence of only a single additional dimension. We demonstrate a simple explicit example of this mechanism with two three-branes, one of which contains the Standard Model fields. The experimental consequences of this scenario are new and dramatic. There are fundamental spin-2 excitations with mass of weak scale order, which are coupled with weak scale as opposed to gravitational strength to the standard model particles. The phenomenology of these models is quite distinct from that of large extra dimension scenarios; none of the current constraints on theories with very large extra dimensions apply.
Singlet extensions of the Standard Model (SM) allow for a strongly first order electroweak phase transition, because of trilinear terms in the tree-level potential. We present a systematic procedure to study the parameter space of the Next-to-Minimal Supersymmetric SM (NMSSM). We find that this model is consistent with electroweak baryogenesis for a wide range of parameters, allowing Higgs masses up to at least 115 GeV.
We make generic remarks about baryogenesis in models where the scale of quantum gravity is much below the Planck scale. These correspond to M-theory vacua with a large volume for the internal space. Baryogenesis is a challenge, particularly for M_s \lappeq 10^5 GeV, because there is an upper bound on the reheat temperature of the Universe, and because certain baryon number violating operators must be suppressed. We discuss these constraints for different values of , and illustrate with a toy model the possibility of using horizontal family symmetries to circumvent them. Comment: 15 pages, latex, one figure. References added
We use the two loop effective potential to study the first order electroweak phase transition in the minimial supersymmetric standard model. A global search of the parameter space is made to identify parameters compatible with electroweak baryogenesis. We improve on previous such studies by fully incorporating squark and Higgs boson mixing, by using the latest experimental constraints, and by computing the latent heat and the sphaleron rate. We find the constraints tan beta > 2.1, top squark mass < 172 GeV, and Higgs mass < 107 GeV (becoming more or less restrictive if the heavy stop has mass less than or greater than 1 TeV). We also find that the change in tan beta in the bubble wall is rarely greater than 0.001, which severely constrains the mechanism of baryogenesis. Comment: 4 pages, 6 figures, revtex; published version, corrected conclusion about LEP2 sensitivity to relevant Higgs masses
We reanalyse the sphaleron bound of electroweak baryogenesis when allowing deviations to the Friedmann equation. These modifications are well motivated in the context of brane cosmology where they appear without being in conflict with major experimental constraints on four-dimensional gravity. While suppressed at the time of nucleosynthesis, these corrections can dominate at the time of the electroweak phase transition and in certain cases provide the amount of expansion needed to freeze out the baryon asymmetry without requiring a strongly first order phase transition. The sphaleron bound is substantially weakened and can even disappear so that the constraints on the higgs and stop masses do not apply anymore. Such modification of cosmology at early times therefore reopens the parameter space allowing electroweak baryogenesis which had been reduced substantially given the new bound on the higgs mass imposed by LEP. In contrast with previous attempts to turn around the sphaleron bound using alternative cosmologies, we are still considering that the electroweak phase transition takes place in a radiation dominated universe. The universe is expanding fast because of the modification of the Friedmann equation itself without the need for a scalar field and therefore evading the problem of the decay of this scalar field after the completion of the phase transition and the risk that its release of entropy dilutes the baryon asymmetry produced at the transition. Comment: 19 pages, 3 figures; v2: minor changes, remark added at end of section 5 and in caption of figure 1; v3: references added, version to be published
The baryon asymmetry of the universe may originate in the phase transition at the end of hybrid inflation, provided that the reheat temperature is low enough. I show that if the field that triggers the end of inflation is the electroweak Higgs field and CP is violated, the transition leads to baryon asymmetry even if no preheating or non-thermal symmetry restoration takes place. I estimate the strength of this effect and the constraints it imposes on the inflationary model.
We explore viable scenarios for parametric resonant amplification of electroweak (EW) gauge fields and Chern-Simons number during preheating, leading to baryogenesis at the electroweak (EW) scale. In this class of scenarios time-dependent classical EW gauge fields, essentially spatially-homogeneous on the horizon scales, carry Chern-Simons number which can be amplified by parametric resonance up to magnitudes at which unsuppressed topological transitions in the Higgs sector become possible. Baryon number non-conservation associated with the gauge sector and the highly non-equilibrium nature of preheating allow for efficient baryogenesis. The requisite large CP violation can arise either from the time dependence of a slowly varying Higgs field (spontaneous baryogenesis), or from a resonant amplification of CP violation induced in the gauge sector through loops. We identify several CP violating operators in the Standard Model and its minimal extensions that can facilitate efficient baryogenesis at preheating, and show how to overcome would-be exponential suppression of baryogenesis associated with tunneling barriers. Comment: 51 pages, 8 figues; minor corrections; references added
We consider the construction of inverted hybrid inflation models in which the vacuum energy during inflation is at the TeV scale, and the inflaton couples to the Higgs field. Such models are of interest in the context of some recently proposed models of electroweak baryogenesis. We demonstrate how constraints on these models arise from quantum corrections, and how self-consistent examples may be constructed, albeit at the expense of fine-tuning. We discuss two possible ways in which the baryon asymmetry of the universe may be produced in these models. One of them is based on preheating and a consequent non-thermal electroweak symmetry restoration and the other on the formation of Higgs winding configurations by the Kibble mechanism at the end of inflation. Comment: 21 pages, 5 figures. Minor changes, some references added. To appear in PRD
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
asymmetry through the weak sphaleron in the hot phase. This is worked out for
concrete parameters.
I review recent progress on the electroweak phase transition and baryogenesis, focusing on the minimal supersymmetric standard model as the source of new physics. Comment: 10 pp, 6 figures; plenary talk given at 6th Workshop on High Energy Physics Phenomenology, 4 Jan. 2000, Chennai, India. v.2: added references
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. Comment: 8 pages, no figures. Slight revision of introduction: published version (JHEP)
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