Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space–time scaling, with critical exponent z=2$z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.     

Effect of the renormalization group on the symmetry breaking patterns of SU(n) Higgs potentials

As a first step toward the study of the effects of radiative corrections on spontaneously broken potentials we consider the renormalization group equations for those parameters which determine the shape of the potential and the symmetry breaking patterns. As examples we consider the Higgs potential for a single scalar field and for the adjoint represention of SU(n). In the latter case we also obtain some results at the classical level - a new proof of the Michel conjecture, the Higgs mass spectrum and an explicit expression for the parameter that determines the symmetry breaking pattern.     

Effective potentials in the Lifshitz scalar field theory

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling z=2, and the mass and the coupling constants renormalization are performed whereas the finite counterterm is just needed for the highest order of the coupling because of the mild UV divergence. Finally, we investigate whether the critical temperature for the symmetry breaking can exist or not in this approximation.     

Dynamical Symmetry Breaking for Weinberg-Salam Model and Restoration at Finite Temperature

In this paper, we utilize Nambu-Jona-Lasinio (NJL) mechanism to discuss the dynamical symmetry breaking for Weinberg-Salam model. In the NJL mechanism the symmetry breaking not only is determined by the potential ofscalar field V(φ) but also has important relation with condensate of the fermion pair (φφ). We find that the coefficient of quadric term of scalar field μ² ≥ 0 can still cause symmetry breaking by virtue of (φφ) ≠ 0, and the vacuum expected value of scalar field obeys (φ) = (φφ), i.e., the order parameter which causes phase transition is the condensate of fermion pair (φφ). We also discuss the restoration problem of SU(2) × U(1) gauge symmetry breaking by the NJL mechanism at high temperatures.     

Dirac neutrino masses from generalized supersymmetry breaking

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the standard model with a generalized supersymmetry breaking sector. If the superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order.     

Schrödinger picture formalism of Φ6 theory

The static effective potential for a scalar field with Φ⁶ interaction is calculated using the effective action in Schrödinger picture formalism. It is found that the effective potential obtained is same as the Gaussian effective potential as far as static case is concerned. Equivalence with the CJT formalism can also be established. As in CJT formalism after renormalization an unrenormalized mass term persists. Nonzero turning points are obtained both for positive and negativeλ. Results are analysed numerically. Graphical analysis indicates a behaviour similar to that obtained for CJT formalism at zero temperature.     

Increasing vacuum solutions in induced gravitation

It is shown that a solution of the form R(ν)=0 (R is the space-time curvature) exists for a vacuum solution (the field fluctuations are assumed zero, and only the ground state with the minimum effective potential energy remains) in the initial stage with consideration of the effect of spontaneous symmetry breaking for a scalar field with the “wrong sign” of the mass term and the conformal factor. For a spherically symmetric metric in vacuum, a solution increasing as a square of the distance and proportional to the square of the Higgs boson mass exists. A. A. Fridman Theoretical Physics Laboratory. Translated from Izvestiya Vysshikh Uchebhykh Zavedenii, Fizika, No. 4, pp. 34–38, April, 2000.     

Exact Solutions of the Klein–Gordon Equation with Position-Dependent Mass for Mixed Vector and Scalar Kink-Like Potentials

The relativistic problem of spinless particles with position-dependent mass subject to kink-like potentials (~tanh αx) is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Klein–Gordon equation with the vector and scalar kink-like potential coupling, and obtain the bound state solutions in the closed form. It is found that in the presence of position-dependent mass there exists the symmetry that the discrete positive energy spectra and negative energy spectra are symmetric about zero energy for the case of a mixed vector and scalar kink-like potential coupling, and in the presence of constant mass this symmetry only appears for the cases of a pure scalar kink-like potential coupling or massless particles.     

Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.     

Top-Quark Condensate at Finite Temperature and Electroweak Symmetry Restoration

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value v of the effective Higgs field, we analyze the dependence on temperature T and chemical potential p of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the p-T criticality curve for symmetry restoration. We find out that the critical temperature T_c = 2υ for μ = 0 and the critical chemical potential μ_c = 2 π υ / √3 for T = 0. When μ = 0, the top-quark mass near T_c has the leading (T_c² - T²)^1/2 behavior with an extra factor dependent on temperature T and the momentum cutoff Λ. However, it is generally argued that the symmetry restoration at T ≥ T_c is still a second-order phase transition.     

Finite temperature Cornwall-Jackiw-Tomboulis formalism of Φ6 theory

The finite temperature effective potential for a scalar field with Φ⁶ interaction is calculated by extending the CJT formalism for composite operators. It is found that unrenormalized terms appear in the effective potential due to the presence of an unrenormalized mass term. Nonzero turning points are obtained both for positive and negativeλ. High temperature expansion is performed and the results are analysed numerically. Graphical analysis indicates symmetry restoration whenT→0.     

Do instantons like a colorful background?

We investigate chiral symmetry breaking and color symmetry breaking in QCD. The effective potential of the corresponding scalar condensates is discussed in the presence of non-perturbative contributions from the semiclassical one-instanton sector. We concentrate on a color singlet scalar background which can describe chiral condensation, as well as a color octet scalar background which can generate mass for the gluons. Whereas a non-vanishing singlet chiral field is favored by the instantons, we have found no indication for a preference of color octet backgrounds.     

Production of charged ρ meson in bottom hadron charmed decays and the effect of the finite width correction of the ρ meson

In the Standard Model, the Higgs potential allows only one minimum at tree level. But the open possibility that there might be two scalar doublets enriches the vacuum structure, allowing for the risk that we might now be in a metastable state, which we dub the panic vacuum. Current experiments at the LHC are probing the Higgs particle predicted as a result of the spontaneous symmetry breaking. Remarkably, in the two Higgs model with a softly broken U(1) symmetry, the LHC experiments already allow to exclude many panic vacuum solutions.     

Real-Time Thermal Field Theory Analyses of 2D Gross-Neveu Model

The discrete symmetry breaking and possible restoration at finite temperature T are analyzed in 20 Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass m is proven to, be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the meanfield approximation used in the auxiliary scalar field approach. Reproducing of the nonzero critical temperature T_c = 0.567m(O), m(0) is the dynamical fermion mass at T = 0, shows the equivalence between the real-time and the imaginary-time thermal. field theories in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the ln(T_c/T) behavior of m² at T ≤ T_c can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.     

Dynamically Broken Supergauge Symmetries

The dynamical breaking of the supergauge symmetries in the massless supergauge Wess Zumino model isdiscussed without adding the Fayet-Iliopoulos term to the Lagrangian. It is shown, in terms of the Nambu-Jona-Lasiniomechanism, that the supersymmetry breaking and the gauge symmetry breaking can be realized dynamically. It is alsoshown that the dynamical breaking moves the vacuum expectation values of two scalar fields away from zero. In order torestore the symmetry of the vacuum, one of the two scalar fields is translated and at the same time the mass spectrumis changed too.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

Scalar potential without cubic term in 3-3-1 models without exotic electric charges

A detailed study of the criteria for stability of the scalar potential, and the proper electroweak symmetry breaking pattern in some 3-3-1 models without exotic electric charges is presented. In this paper we concentrate in a scalar sector with three Higgs scalar triplets, with a potential that does not include the cubic term, due to the presence of a discrete symmetry. For the analysis we use, and improve, a method previously developed to study the scalar potential in the two-Higgs-doublet extension of the standard model. Our main result is to show the consistency of those 3-3-1 models without exotic electric charges.     

The effective potential and symmetry breaking in theO(N) xO(N) model

We compute the finite temperature effective potential in theO(N)xO(N) symmetric model for largeN in spacetime dimensionsd=4, 3, 2 and discuss the spontaneous symmetry breaking patterns. Ford=3 we find that the symmetry, if broken at zero temperature is restored at arbitrarily small nonzero temperature. Ford=4 the model is plagued by an intrinsic instability; in particular, there is no stable ground state at high temperature.