Scalar Vacuum Expectation Values Research Articles

SCALAR MODULI, WALL CROSSING AND PHENOMENOLOGICAL PREDICTIONS

We present the scalar moduli stabilization from the perspective of the real intrinsic geometry. In this paper, we describe the physical nature of the vacuum moduli fluctuations of an arbitrary Fayet configuration. For finitely many Abelian scalar fields, we show that the framework of the real intrinsic geometry investigates the mixing between the marginal and threshold vacua. Interestingly, we find that the phenomena of wall crossing and the search of the stable vacuum configurations, pertaining to D-term and F-term scalar moduli, can be accomplished for the Abelian charges. For given vacuum expectation values of the moduli scalars, we provide phenomenological aspects of the vacuum fluctuations and phase transitions in the supersymmetry breaking configurations.

Dynamical symmetry breaking in models with strong Yukawa interactions

Dynamical symmetry breaking in models with strong Yukawa interactionsThe primary aim of this paper is to explore the possibility of spontaneous symmetry breaking by strong Yukawa dynamics. Technically, the symmetry is assumed to be broken by formation of symmetry-breaking parts of both the scalar and the fermion propagators, rather than by the scalar vacuum expectation values. The idea is first introduced on an example of a toy model with the underlying symmetry being an Abelian one and later applied to a realistic model of electroweak interaction. In addition, the paper also deals with some more general, model-independent issues, applicable not only to the discussed model of strong Yukawa dynamics, but to a wider class of models with dynamical mass generation. First of these issues is the problem of fermion flavor mixing in the presence of fermion self-energies with a general momentum dependence. It is in particular shown how to define the Cabibbo-Kobayashi-Maskawa matrix in such models and argued that it can come out in principle non-unitary. Second issue is the problem of calculating the gauge boson masses when the symmetry is broken by fermion self-energies. On top of deriving the formula for the gauge boson mass matrix we also find corrections to the related Pagels-Stokar formula.

CAN MASSLESS AND LIGHT YUKAWAONS BE HARMLESS?

In the so-called yukawaon model, where the effective Yukawa coupling constants [Formula: see text] are given by vacuum expectation values (VEV's) of gauge singlet scalars (yukawaons) Yf with 3×3 components, i.e. [Formula: see text], massless (and light) scalars appear because a global flavor symmetry is assumed. In order to demonstrate whether such massless scalars in the yukawaon model are harmless or not, yukawaon masses are explicitly estimated, as an example, in the charged lepton sector.

Thermodynamics of dilaton-axion black holes

Considering a generalized action for the Einstein-Maxwell theory in four dimensions coupled to scalar and pseudoscalar fields, the thermodynamic properties of asymptotically flat black hole solutions in such a background are investigated. Bekenstein-Hawking area-entropy law is verified for these class of black holes. From the property of specific heat, it is shown that such black holes can be stable for a certain choice of the parameters like charge, mass, and the scalar vacuum expectation value. The possibility of a black hole phase transition is discussed in this context.

MASSLESS LIMIT OF GRAVITATIONAL HIGGS MECHANISM

In gravitational Higgs mechanism graviton components acquire mass via spontaneous diffeomorphism breaking by scalar vacuum expectation values. We point out that in the massless limit the resulting theory is not Einstein–Hilbert gravity (EHG) but constrained gravity (CG). Consequently, massive solutions in the massless limit must be compared to those in CG (as opposed to EHG). We discuss spherically symmetric solutions in this context. The Schwarzschild solution in EHG can be coordinate-transformed such that it is also a solution in CG. The resulting solutions are non-perturbative in the asymptotic regime, and are reproduced in the massless limit of asymptotic massive solutions, hence no van Dam–Veltman–Zakharov discontinuity. We point out that higher curvature terms must be included to obtain non-singular spherically symmetric massive solutions and discuss a suitable framework.

Massive gravity in Minkowski space via the gravitational Higgs mechanism

In the gravitational Higgs mechanism graviton components acquire mass in the process of spontaneous breaking of diffeomorphisms (via scalar vacuum expectation values). Recently, the gravitational Higgs mechanism was discussed in the context of obtaining massive gravity directly in four dimensions. We discuss a setup, with all diffeomorphisms spontaneously broken by scalars, where the gravitational Higgs mechanism results in massive gravity in Minkowski space with no nonunitary propagating modes. This is achieved by including higher derivative terms in the scalar sector. Decoupling the nonunitary mode (trace of the graviton) then requires tuning a single parameter, namely, the cosmological constant. We also discuss a setup where only spatial diffeomorphisms are broken. In this case we obtain massive gravity in Minkowski space with only transverse modes propagating, so the mode count is the same as for a massless graviton.

Signatures of doubly charged Higgs in theSU(3)L⊗U(1)Nmodel at the CERN LHC

The scalar sector of the simplest version of the 3-3-1 electroweak model is constructed with three Higgs triplets only. We show that a relation involving two of the constants of the model, two vacuum expectation values of the neutral scalars, and the mass of the doubly charged Higgs boson leads to important information concerning the signals of this scalar particle.

Leptogenesis from Split Fermions

We present a new type of leptogenesis mechanism based on a two-scalar split-fermions framework. At high temperatures the bulk scalar vacuum expectation values (VEVs) vanish and lepton number is strongly violated. Below some temperature, $T_c$, the scalars develop extra dimension dependent VEVs. This transition is assumed to proceed via a first order phase transition. In the broken phase the fermions are localized and lepton number violation is negligible. The lepton-bulk scalar Yukawa couplings contain sizable CP phases which induce lepton production near the interface between the two phases. We provide a qualitative estimation of the resultant baryon asymmetry which agrees with current observation. The neutrino flavor parameters are accounted for by the above model with an additional approximate U(1) symmetry.

Fermions on an interval: Quark and lepton masses without a Higgs

We consider fermions on an extra dimensional interval. We find the boundary conditions at the ends of the interval that are consistent with the variational principle, and explain which ones arise in various physical circumstances. We apply these results to higgsless models of electroweak symmetry breaking, where electroweak symmetry is not broken by a scalar vacuum expectation value, but rather by the boundary conditions of the gauge fields. We show that it is possible to find a set of boundary conditions for bulk fermions that would give a realistic fermion mass spectrum without the presence of a Higgs scalar, and present some sample fermion mass spectra for the standard model quarks and leptons as well as their resonances.

Possibility of optical unification in heterotic strings

Recently J. Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual MSSM unification below the string scale is extrapolated from the running of gauge couplings upward from M_Z^o when an intermediate scale desert is assumed. In this letter we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the NAHE set of basis vectors. This class is of particular interest for optical unification, because it provides a standard hypercharge embedding within SO(10), giving the standard k_Y = 5/3 hypercharge level, which was shown necessary for optical unification. We present a NAHE model for which the set of exotic SU(3)_C triplet/anti-triplet pairs, SU(2)_L doublets, and non-Abelian singlets with hypercharge offers the possibility of optical unification. Whether this model can realize optical unification is conditional upon these exotics not receiving Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum expectation values is non-perturbatively chosen to cancel the FI D-term, xi, generated by the anomalous U(1)-breaking Green-Schwarz-Dine-Seiberg-Wittten mechanism. A study of perturbative flat directions and their phenomenological implications for this model is underway. This paper is a product of the NFS Research Experiences for Undergraduates and the NSF High School Summer Science Research programs at Baylor University.

UA(1) SYMMETRY BREAKING AND THE SCALAR SECTOR OF QCD

It is shown that most of the unusual properties of the lowest lying scalar (and pseudoscalar) mesons can be understood, at the qualitative and quantitative level, on the basis of the breakdown of the UA(1) symmetry coupled to the vacuum expectation values of scalars by the spontaneous breaking of chiral symmetry.

Effects of the scale-dependent vacuum expectation values in the renormalisation group analysis of neutrino masses

The contribution of scale-dependent vacuum expectation values (VEVs) of Higgs scalars, which gives significant effects in the evolution of fundamental fermion masses in the Minimal Supersymmetric Standard Model (MSSM), is now considered in the derivation of the one-loop analytic expression for the evolution of the left-handed Majorana neutrino masses with energies. The inclusion of such effect of the running VEV increases the stability of the neutrino masses under quantum corrections and leads to a mild decrease of neutrino masses with higher energies.

Comment on “Majoron emitting neutrinoless double beta decay in the electroweak chiral gauge extensions”

We point out that if the majoron-like scheme is implemented within a 331 model, there must exist at least three different mass scales for the scalar vacuum expectation values in the model.

New formulas and predictions for running masses at higher scales in MSSM

Including contributions of scale-dependent vacuum expectation values of Higgs scalars, we derive new one-loop formulas analytically for running quark-lepton masses at higher scales in MSSM. Apart from the gauge-coupling dependence being different from earlier formulas, the third-generation- Yukawa-coupling effects are absent in the masses of the first two generations. While predicting the masses and $\tan\beta$ numerically, we also include two-loop effects.

Radiative corrections to theta term in the left-right supersymmetric models

We calculate the radiative correction to the theta term in the generic left-right supersymmetric model due to the Kobayashi-Maskawa source of CP-violation. We found that the value of θ is very sensitive to the relations between vacuum expectation values of bidoublet scalars 〈 φ 1〉 = diag( κ 1, κ′ 1 and 〈 φ 2〉 = diag( κ′ 2, κ 2). The minim value of θ in the model is found to be of order 10 −9 for κ 1 κ 2 ∼ 1 , κ′ 1 = κ′ 2 = 0 in agreement with the experimental constraint without an axion mechanism or fine tuning. In other regions of the parameter space, the radiatively induced θ gives unacceptably large contributions to the electric dipole moment of the neutron.

CP violation in multi-Higgs supersymmetric models

We consider supersymmetric extensions of the standard model with two pairs of Higgs doublets. We study the possibility of spontaneous CP violation in these scenarios and present a model where the origin of CP violation is soft, with all the complex phases in the Lagrangian derived from complex masses and vacuum expectation values (VEVs) of the Higgs fields. The main ingredient of the model is an approximate global symmetry, which determines the order of magnitude of Yukawa couplings and scalar VEVs. We assume that the terms violating this symmetry are suppressed by powers of the small parameter ϵ PQ = O( m b / m t ). The tree-level flavor-changing interactions are small due to a combination of this global symmetry and a flavor symmetry, but they can be the dominant source of CP violation. All CP-violating effects occur at order ϵ PQ 2 as the result of exchange of almost decoupled extra Higgs bosons and/or through the usual mechanisms with an almost real CKM matrix. On dimensional grounds, the model gives ϵ K ≈ ϵ PQ 2 and predicts for the neutron electric dipole moment (and possibly also for ϵ K 1) a suppression of order ϵ PQ 2 with respect to the values obtained in standard and minimal supersymmetric scenarios. The predicted CP asymmetries in B decays are generically too small to be seen in the near future. The mass of the lightest neutral scalar, the strong CP problem, and possible contributions to the Z decay into b quarks (the R b puzzle) are also briefly addressed in the framework of this model.

On the finite temperature effective potential in scalar QED with N flavors

The effective potential of scalar quantum electrodynamics with N flavors of complex scalar fields is studied, by performing a self-consistent 1 N expansion up to next to leading order in 1 N . Starting from the broken phase at zero temperature, the theory exhibits a phase transition to the symmetric phase at some finite temperature T c. We work in general covariant gauges and demonstrate the gauge invariance of both, the critical temperature T c and the minimization condition at any finite temperature T. Furthermore, the only minimum of the potential is at zero scalar vacuum expectation value for any temperature T ⩾ T c and varies continuously to nonzero values for temperatures below T c, implying the existence of a second-order phase transition.

SPONTANEOUS CP VIOLATION IN A TWO-GENERATION LEFT-RIGHT SYMMETRIC MODEL WITH TWO HIGGS BI-DOUBLETS

We discuss a two-generation left-right symmetric model with two Higgs bi-doublets and a discrete symmetry to show that spontaneous CP violation arises as a result of soft breaking of the discrete symmetry. The contributions to the CP violation parameter ε in the [Formula: see text] transition come from the box diagrams due to WL-WR exchanges as well as from the mixing of the real and imaginary parts of the flavor changing neutral Higgs at the tree level and both contributions depend on the relative phase difference between the vacuum expectation values (vevs) of the relevant neutral Higgs scalars. Other CP violating effects in the model are consistent with their experimental values for the appropriate choice of the model parameters. The extension of the model to the realistic case of three generations of fermions does not appreciably change the phenomenology of the model.

Unitarity constraints on CP nonconservation in Higgs-boson exchange.

Bounds are derived for the dimensionless factors that enter in the violation of {ital CP} invariance in Higgs-boson exchange. In particular, for the class of theories with two scalar SU(2){times}U(1) doublets (plus any other scalars whose expectation values do not break SU(2){times}U(1)), the magnitude of the parameter Im {ital Z}{sub 2}, which appears in the dominant neutral-Higgs-boson-exchange contribution to the neutron electric dipole moment, is bounded by 1/2({ital r}{sup 2}+{ital r}{sup 4}){sup 1/2}, where {ital r} is a ratio of the magnitudes of scalar vacuum expectation values. It is shown that this bound can actually be reached in realistic models.

Fine-tuning the rho parameter with new gauge bosons.

We explore the class of models containing a triplet Higgs-scalar representation as well as singlets and doublets under ${\mathrm{SU}(2)}_{L}$ in which the gauge group is also extended by (at least) an additional U(1) factor. In a large subclass of such models we show that the $\ensuremath{\rho}$ parameter, involving the lightest physical charged and neutral gauge bosons, can be fine-tuned to unity without the vanishing of any of the scalar vacuum expectation values. Two examples of such models, based on the groups ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{R}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{B\ensuremath{-}L}$ and ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$, are shown to be phenomenologically viable.