arXiv subjects

M. Shaposhnikov

Publications and source records attributed to M. Shaposhnikov.

52 records · Page 3Linked to original sources

arXiv1997

High-T QCD and dimensional reduction: measuring the Debye mass

We study the high-temperature phase of SU(2) and SU(3) QCD using lattice simulations of an effective 3-dimensional SU(N) + adjoint Higgs -theory, obtained through dimensional reduction. We investigate the phase diagram of the 3D theory, and find that the high-T QCD phase corresponds to the metastable symmetric phase of the 3D theory. We measure the Debye screening mass m_D with gauge invariant operators; in particular we determine the O(g^2) and O(g^3) corrections to m_D. The corrections are seen to be large, modifying the standard power-counting hierarchy in high temperature QCD.

hep-lat↗

arXiv1997

Non-perturbative Debye mass in finite T QCD

Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.

hep-ph↗

arXiv1997

Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

In the standard model there are charges with abelian anomaly only (e.g. right-handed electron number) which are effectively conserved in the early universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the GUT scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields ($\sim 10^{22}$ gauss at $T\sim 100$ GeV with typical inhomogeneity scale $ \sim \frac{ 10^6}{T}$) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through non-linear mechanisms. Previously derived bounds on exotic $B-L$ violating operators may also be evaded.

astro-ph↗

arXiv1997

3d SU(N) + adjoint Higgs theory and finite temperature QCD

We study to what extent the three-dimensional SU(N)+adjoint Higgs theory can be used as an effective theory for finite temperature SU(N) gauge theory, with N=2,3. The parameters of the 3d theory are computed in 2-loop perturbation theory in terms of T/Lambda_MSbar,N,N_f. The perturbative effective potential of the 3d theory is computed to two loops for N=2. While the Z(N) symmetry probably driving the 4d confinement-deconfinement phase transition (for N_f=0) is not explicit in the effective Lagrangian, it is partly reinstated by radiative effects in the 3d theory. Lattice simulations in the 3d theory are carried out for N=2, and the static screening masses relevant for the high-temperature phase of the 4d theory are measured. In particular, we measure non-perturbatively the O(g^2 T) correction to the Debye screening mass. We find that non-perturbative effects are much larger in the SU(2) + adjoint Higgs theory than in the SU(2) + fundamental Higgs theory.

hep-ph↗

arXiv1996

A Non-Perturbative Analysis of the Finite T Phase Transition in SU(2)xU(1) Electroweak Theory

The continuum 3d SU(2)$\times$U(1)+Higgs theory is an effective theory for a large class of 4d high-temperature gauge theories, including the minimal standard model and some of its supersymmetric extensions. We study the effects of the U(1) subgroup using lattice Monte Carlo techniques. When $g'^2/g^2$ is increased from the zero corresponding to pure SU(2)+Higgs theory, the phase transition gets stronger. However, the increase in the strength is close to what is expected perturbatively, and the qualitative features of the phase diagram remain the same as for $g'^2=0$. In particular, the first order transition still disappears for $m_H>m_{H,c}$. We measure the photon mass and mixing angle, and find that the mass vanishes in both phases within the statistical errors.

hep-lat↗

arXiv1996

Is There a Hot Electroweak Phase Transition at $m_H\gsim m_W$?

We provide non-perturbative evidence for the fact that there is no hot electroweak phase transition at large Higgs masses, $m_H = 95$, 120 and 180 GeV. This means that the line of first order phase transitions separating the symmetric and broken phases at small $m_H$ has an end point $m_{H,c}$. In the minimal standard electroweak theory 70 GeV $<m_{H,c}<$ 95 GeV and most likely $m_{H,c} \approx 80$ GeV. If the electroweak theory is weakly coupled and the Higgs boson is found to be heavier than the critical value (which depends on the theory in question), cosmological remnants from the electroweak epoch are improbable.

hep-ph↗

arXiv1995

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 ($V\to\infty, a\to 0$) 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 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.

hep-lat↗

arXiv1995

Results from 3D Electroweak Phase Transition Simulations

We study the phase transition in SU(2)-Higgs model on the lattice using the 3D dimensionally reduced formalism. The 3D formalism enables us to obtain highly accurate Monte Carlo results, which we extrapolate both to the infinite volume and to the continuum limit. Our formalism also provides for a well-determined and unique way to relate the results to the perturbation theory. We measure the critical temperature, latent heat and interface tension for Higgs masses up to 70 GeV.

hep-lat↗

arXiv1995

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 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)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.

hep-ph↗

arXiv1994

3d physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis

We discuss a framework relying on both perturbative and non-perturbative lattice computations which will be able to reliably determine the parameters of the EW phase transition. A motivation for the use of 3d effective theory in the lattice simulations, rather than the complete 4d one, is provided. We introduce and compute on the 2-loop level a number of gauge-invariant order parameters -- condensates, which can be measured with high accuracy in MC simulations. The relation between MSbar and lattice condensates is found, together with the relation between lattice couplings and continuum parameters (the constant physics curves). These relations are exact in the continuum limit.

hep-lat↗

arXiv1994

The Electroweak Phase Transition at $m_H \simeq m_W$

We study the finite temperature electroweak transition with non-perturbative lattice Monte Carlo simulations. We find that it is of first order, at least for Higgs masses up to 80 GeV. The critical temperature of the phase transition is found to be smaller than that determined by a 2-loop renormalization group improved effective potential. The jump of the order parameter at the critical temperature is considerably larger than the perturbative value. By comparing lattice data and perturbation theory, we demonstrate that the latter, for the computation of the vacuum expectation value of the Higgs field $v(T)$ in the broken phase at given temperature, converges quite well, provided $v(T)/T>1$. An upper bound on the Higgs mass necessary for electroweak baryogenesis in the light of the lattice data is briefly discussed.

hep-ph↗

arXiv1994

3D Physics and the Electroweak Phase Transition: Perturbation Theory

We develop a method for the construction of the effective potential at high temperatures based on the effective field theory approach and renormalization group. It allows one to sum up the leading logarithms in all orders of perturbation theory. The method reproduces the known one-loop and two-loop results in a very simple and economic way and clarifies the issue of the convergence of the perturbation theory. We also discuss the assumptions being made for the determination of the critical temperature of the electroweak phase transition, and analyse different perturbative uncertainties in its determination. These results are then used for the non-perturbative lattice Monte Carlo simulations of the EW phase transition in forthcoming paper.

hep-ph↗

arXiv1993

The Finite Temperature Phase Transition in the Lattice SU(2)-Higgs Model

We study the finite temperature transition of SU(2)-Higgs model with lattice Monte Carlo techniques. We use dimensional reduction to transform the original 4-dimensional SU(2)-gauge + fundamental Higgs theory to an effective 3-dimensional SU(2) + adjoint Higgs + fundamental Higgs model. The simulations were performed with Higgs masses of 35 and 80 GeV; in both cases we observe a stronger first order transition than the perturbation theory predicts, indicating that the dynamics of the transition strongly depend on non-perturbative effects.

hep-lat↗

arXiv1993

Strong Sphalerons and Electroweak Baryogenesis

We analyze the spontaneous baryogenesis and charge transport mechanisms suggested by Cohen, Kaplan and Nelson for baryon asymmetry generation in extended versions of electroweak theory. We find that accounting for non-perturbative chirality-breaking transitions due to strong sphalerons reduces the baryonic asymmetry by the factor $(m_t/πT)^2$ or $α_W$, provided those processes are in thermal equilibrium.

hep-ph↗

arXiv1993

On Non-Perturbative Effects at the High-Temperature Electroweak Phase Transition

It is argued that confining effects in 3-dimensional non-Abelian gauge theories (high-temperature limit of 4-dimensional ones) imply the existence of the condensates of the gauge and Higgs fields in 3-d vacuum. This non-perturbative effect can decrease the energy of the phase with unbroken symmetry and may result in the creation of a barrier separating the broken and unbroken phases. Thus the high-temperature phase transitions in gauge theories can be stronger first order than is expected from perturbation theory. The applications of these results to electroweak baryogenesis are briefly discussed.

hep-ph↗

arXiv1993

A Lattice Monte Carlo Study of the Hot Electroweak Phase Transition

We study the finite temperature electroweak phase transition with lattice perturbation theory and Monte Carlo techniques. Dimensional reduction is used to approximate the full four-dimensional SU(2) + a fundamental doublet Higgs theory by an effective three-dimensional SU(2) + adjoint Higgs + fundamental Higgs theory with coefficients depending on temperature via screening masses and mass counterterms. Fermions contribute to the effective theory only via the $N_F$ and $m_{\rm top}$ dependence of the coefficients. For sufficiently small lattices ($N^3 < 30^3$ for $m_H$ = 35 GeV) the study of the one-loop lattice effective potential shows the existence of the {\em second} order phase transition even for the small Higgs masses. At the same time, a clear signal of a {\em first order} phase transition is seen on the lattice simulations with a transition temperature close to but less than the value determined from the perturbative calculations. This indicates that the dynamics of the first order electroweak phase transition depends strongly on non-perturbative effects and is not exclusively related to the so-called $ϕ^3$ term in the effective potential.

hep-ph↗