Mikhail E. Shaposhnikov

Electroweak baryon number non-conservation in the early universe and in high-energy collisions

We review recent progress in the study of the anomalous baryon number non-conservation at high temperatures and in high energy collisions. Recent results on high temperature phase transitions are described, and applications to electroweak baryogenesis are considered. The current status of the problem of electroweak instanton-like processes at high energies is outlined. This paper is written on the occasion of Sakharov’s 75th anniversary and will appear in the memorial volume of Uspekhi (Usp. Fiz. Nauk, volume 166, No 5, May 1996).

Supersymmetric Q balls as dark matter

Supersymmetric extensions of the standard model generically contain stable non-topological solitons, Q-balls, which carry baryon or lepton number. We show that large Q-balls can be copiously produced in the early universe, can survive until the present time, and can contribute to dark matter.

The statistical theory of anomalous fermion number non-conservation

Abstract We present a non-equilibrium method for studying anomalous B -non-conservation in the electroweak theory at finite temperature. We derive formally the equation of B -evolution advocated previously on physical grounds. The kinetic coefficient in it is quite generally expressed through a thermodynamic average. This expression allows for an estimate of higher order corrections and is applicable both below and above the phase transition temperature.

Generic rules for high temperature dimensional reduction and their application to the standard model

We formulate the rules for dimensional reduction of a generic finite temperature gauge theory to a simpler three-dimensional effective bosonic theory in terms of a matching of Greens functions in the full and the effective theory, and present a computation of a generic set of 1- and 2-loop graphs needed for the application of these rules. As a concrete application we determine the explicit mapping of the physical parameters of the standard electroweak theory to a three-dimensional SU(2)xU(1) gauge-Higgs theory. We argue that this three-dimensional theory has a universal character and appears as an effective theory for many extensions of the Standard Model.We formulate the rules for dimensional reduction of a generic finite temperature gauge theory to a simpler three-dimensional effective bosonic theory in terms of a matching of Green’s functions in the full and the effective theory, and present a computation of a generic set of 1- and 2-loop graphs needed for the application of these rules. As a concrete application we determine the explicit mapping of the physical parameters of the standard electroweak theory to a three-dimensional SU(2)×U(1) gauge-Higgs theory. We argue that this three-dimensional theory has a universal character and appears as an effective theory for many extensions of the Standard Model.

THE ELECTROWEAK PHASE TRANSITION: A NON-PERTURBATIVE ANALYSIS

We study on the lattice the 3d SU(2)+Higgs model, which is an effective theory of a large class of 4d high temperature gauge theories. Using the exact constant physics curve, continuum (

The nuMSM, inflation, and dark matter

V\to\infty, a\to 0

Localizing Gravity on a String-Like Defect in Six Dimensions

) results for the properties of the phase transition (critical temperature, latent heat, interface tension) are given. The 3-loop correction to the effective potential of the scalar field is determined. The masses of scalar and vector excitations are determined and found to be larger in the symmetric than in the broken phase. The vector mass is considerably larger than the scalar one, which suggests a further simplification to a scalar effective theory at large Higgs masses. The use of consistent 1-loop relations between 3d parameters and 4d physics permits one to convert the 3d simulation results to quantitatively accurate numbers for different physical theories, such as the Standard Model -- excluding possible nonperturbative effects of the U(1) subgroup -- for Higgs masses up to about 70 GeV. The applications of our results to cosmology are discussed.We study on the lattice the 3d SU(2)+Higgs model, which is an effective theory of a large class of 4d high temperature gauge theories. Using the exact constant physics curve, continuum (V → ∞, a → 0) results for the properties of the phase transition (critical temperature, latent heat, interface tension) are given. The 3-loop correction to the effective potential of the scalar field is determined. The masses of scalar and vector excitations are determined and found to be larger in the symmetric than in the broken phase. The vector mass is considerably larger than the scalar one, which suggests a further simplification to a scalar effective theory at large mH. The use of consistent 1-loop relations between 3d parameters and 4d physics permits one to convert the 3d simulation results to quantitatively accurate numbers for different physical theories, such as the Standard Model – excluding possible nonperturbative effects of the U(1) subgroup – for Higgs masses up to about 70 GeV. The applications of our results to cosmology are discussed.

Is There a Hot Electroweak Phase Transition at mH > ∼ mW?

We show how to enlarge theMSM (the minimal extension of the standard model by three right- handed neutrinos) to incorporate inflation and provide a common source for electroweak symmetry breaking and for right-handed neutrino masses. In addition to inflation, the resulting theory can explain simultaneously dark matter and the baryon asymmetry of the Universe; it is consistent with experiments on neutrino oscillations and with all astrophysical and cosmological constraints on sterile neutrino as a dark matter candidate. The mass of inflaton can be much smaller than the electroweak scale.

3D physics and the electroweak phase transition: Perturbation theory

We present a metric solution in six dimensions, where gravity is localized on a four-dimensional singular stringlike defect. The corrections to four-dimensional gravity from the bulk continuum modes are suppressed by O(1/r(3)). No tuning of the bulk cosmological constant to the brane tension is required in order to cancel the four-dimensional cosmological constant.

A possible symmetry of the νMSM

We provide non-perturbative evidence for the fact that there is no hot electroweak phase transition at large Higgs masses,