Symmetry Breaking In Model Research Articles

Gravitational waves from phase transitions at the electroweak scale and beyond

If there was a first-order phase transition in the early universe, there should be an associated stochastic background of gravitational waves. In this paper, we point out that the characteristic frequency of the spectrum due to phase transitions which took place in the temperature range $100\text{ }\text{ }\mathrm{GeV}--{10}^{7}\text{ }\text{ }\mathrm{GeV}$ is precisely in the window that will be probed by the second generation of space-based interferometers such as the big bang observer (BBO). Taking into account the astrophysical foreground, we determine the type of phase transitions which could be detected either at LISA, LIGO or BBO, in terms of the amount of supercooling and the duration of the phase transition that are needed. Those two quantities can be calculated for any given effective scalar potential describing the phase transition. In particular, the new models of electroweak symmetry-breaking which have been proposed in the last few years typically have a different Higgs potential from the standard model. They could lead to a gravitational wave signature in the milli-Hertz frequency, which is precisely the peak sensitivity of LISA. We also show that the signal coming from phase transitions taking place at $T\ensuremath{\sim}1--100\text{ }\text{ }\mathrm{TeV}$ could entirely screen the relic gravitational wave signal expected from standard inflationary models.

Van Hove Singularity and Spontaneous Fermi Surface Symmetry Breaking in Sr3Ru2O7

The most salient features observed around a metamagnetic transition in Sr3Ru2O7 are well captured in a simple model for spontaneous Fermi surface symmetry breaking under a magnetic field, without invoking a putative quantum critical point. The Fermi surface symmetry breaking happens in both a majority and a minority spin band but with a different magnitude of the order parameter, when either band is tuned close to van Hove filling by the magnetic field. The transition is second order for high temperature T and changes into first order for low T. The first order transition is accompanied by a metamagnetic transition. The uniform magnetic susceptibility and the specific heat coefficient show strong T dependence, especially a log T divergence at van Hove filling. The Fermi surface instability then cuts off such non-Fermi liquid behavior and gives rise to a cusp in the susceptibility and a specific heat jump at the transition temperature.

Improved Higgs naturalness with or without supersymmetry

Many models of electroweak symmetry-breaking with an extended Higgs sector exhibit improved naturalness, wherein the new physics scale, at which quadratic divergences of Higgs mass parameters due to top quark loops are cut off, can be pushed beyond the reach of the Large Hadron Collider without unnatural fine tuning. Such models include examples where the new physics is supersymmetry, implying that supersymmetry may still solve the hierarchy problem, even if it eludes detection at the LHC.

Global topologicalk-defects

We consider global topological defects in symmetry-breaking models with a noncanonical kinetic term. Apart from a mass parameter entering the potential, one additional dimensional parameter arises in such models---a kinetic mass. The properties of defects in these models are quite different from standard global domain walls, vortices, and monopoles, if their kinetic mass scale is smaller than their symmetry-breaking scale. In particular, depending on the concrete form of the kinetic term, the typical size of such a defect can be either much larger or much smaller than the size of a standard defect with the same potential term. The characteristic mass of a nonstandard defect, which might have been formed during a phase transition in the early universe, depends on both the temperature of a phase transition and the kinetic mass.

Causality, analyticity and an IR obstruction to UV completion

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentz-invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the "wrong" signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

A custodial symmetry for Zbb¯

We show that a subgroup of the custodial symmetry O(3) that protects �ρ from radiative corrections can also protect the Zbcoupling. This allows one to build models of electroweak symmetry breaking, such as Higgsless, Little Higgs or 5D composite Higgs models, that are safe from corrections to Z → bb. We show that when this symmetry protects Zbit cannot simultaneously protect Ztand W t ¯. Therefore one can expect to measure sizable deviations from the SM predictions of these couplings at future collider experiments. We also show under what circumstances ZbRR can receive corrections in the right direction to explain the anomaly in the LEP/SLD forward-backward asymmetry A b B.

The auxiliary field method in quantum mechanical four-fermi models: a study towards chiral condensation in QED

A study for checking the validity of the auxiliary field method (AFM) is made in quantum mechanical four-fermi models which act as prototypes of models for chiral symmetry breaking in quantum electrodynamics. It has been shown that AFM, defined by an insertion of Gaussian identity to path integral formulae and by the loop expansion, becomes more accurate when taking higher order terms into account under the bosonic model with a quartic coupling in 0- and 1-dimensions as well as the model with a four-fermi interaction in 0-dimension. The case is also confirmed in terms of two models with the four-fermi interaction among N species in 1-dimension (the quantum mechanical four-fermi models): higher order corrections lead us towards the exact energy of the ground state for a whole region including the weak as well as the strong coupling. It is found that the second model belongs to a ‘WKB exact class’ that has no higher order corrections other than the lowest correction. Discussions are also made for unreliability on the continuous time representation of path integration and for a new model of QED as a suitable probe for chiral symmetry breaking.

Spectral Observables for Two- and Three-Fold Symmetry Breaking

We investigate the spectral statistics of a random matrix model for symmetry breaking. It is pointed out that the spectral rigidity distinguishes more clearly the breaking of two- and three-fold symmetries than does the nearest-neighbour spacing distribution.

Electroweak symmetry breaking

In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories. Preprint MSU-041021

An effective Higgsless theory: Satisfying electroweak constraints and a heavy top quark

The main challenge faced by Higgsless models of electroweak symmetry breaking is to reconcile the experimental constraints imposed by the precision electroweak data and the top quark phenomenology with the unitarity constraints imposed by longitudinal gauge boson scattering amplitudes. In this paper we expand on previous work, giving details of how delocalized fermions can be used to adjust the $S$ parameter to zero, while keeping the $T$ and $U$ parameters naturally suppressed. We also show that it is possible to obtain the top quark mass, without affecting the delay of unitarity violation of the $W^+ W^-\to W^+W^-$ scattering amplitude, by separating the mass scales of the fermion sector ($1/R_f$) from that of the gauge sector ($1/R_g$). The fermion sector scale $1/R_f$ is only weakly constrained by unitarity of the $t\bar{t}\to W^+ W^-$ scattering amplitude; thus the ratio $R_g/R_f$ can be quite large, and the top mass can be easily achieved. Anomalous right-handed couplings involving the third generation quarks also avoid constraints from experimental data if $1/R_f$ is sufficiently large.

Boundary localized symmetry breaking and topological defects

We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking is not localized. This new structure can lead to corrections to the mass scale of the defects which is not captured by a simple effective theory obtained by integrating out the extra dimension. We also consider the Higgsless model of symmetry breaking and show that no finite energy defects appear in some situations where they might have been expected.

Associate Higgs and gauge boson production at hadron colliders in a model with vector resonances

Motivated by new models of dynamical electroweak symmetry breaking that predict a light composite Higgs boson, we build an effective Lagrangian which describes the standard model (with a light Higgs) and vector resonances. We compute the cross section for the associate production of a Higgs and a gauge boson. For some values of model parameters we find that the cross section is significantly enhanced with respect to the standard model. This enhancement is similar at the LHC (large hadron collider) and the Tevatron for the same range of resonance mass.

Fermion condensate model of electroweak interactions

A new dynamical symmetry breaking model of electroweak interactions is proposed based on interacting fermions. Two fermions of different SU_{L}(2) representations form a symmetry breaking condensate and generate the lepton and quark masses. The weak gauge bosons get their usual standard model masses from a gauge invariant Lagrangian of a doublet scalar field composed of the new fermion fields. The new fermion fields become massive by condensation. It is shown that the new charged fermions are produced at the next linear colliders in large number. The model is a low energy one which cannot be renormalized perturbatively. For the parameters of the model unitarity constraints are presented.

Solitons and soliton–antisoliton pairs of a goldstone model in 3 + 1 dimensions

We study finite energy static solutions to a global symmetry breaking model in 3+1 dimensions described by an isovector scalar field. The basic features of two different types of configurations are discussed, one of them corresponding to axially symmetric multisolitons with topological charge $n$, and the other one to unstable soliton-antisoliton pairs with zero topological charge.

A new mechanism for light composite Higgs bosons

Repeated symmetry-breaking and restoration phase transitions occur as one traverses the parameter space of interactions competing to align the vacuum. This phenomenon, augmented with a topcolor-like interaction, can make a composite Higgs boson's mass and vacuum expectation value naturally much less than its underlying structure scale, without introducing new symmetries and their associated TeV-scale particles. We illustrate it by reconstructing a simple light composite Higgs model of electroweak symmetry breaking proposed by Georgi and Kaplan.

General analysis of single top production and W helicity in top decay

We provide a framework for the analysis of the W boson helicity in the decay of the top quark that is based on a general effective tbW coupling. Four independent coupling coefficients can be uniquely determined by the fractions of longitudinal and transverse W boson polarizations as well as the single top production rates for the t-channel and the s-channel processes. The knowledge of these coefficients can be used to discriminate models of electroweak symmetry breaking.

Revisiting 5D chiral symmetry breaking and holographic QCD models

We take a closer look at the recently discussed models of hadrons based on holographic ideas and chiral symmetry breaking in five dimensions. We study the two point correlator in detail and look at the field theoretic properties needed to be satisfied by the correlator. It is shown that the spectral density becomes negative, violating the basic requirements for the Kallen–Lehmann representation. We briefly discuss the implications of this violation of the positivity of the spectral density and also discuss possible origin of such a violation in these models. Put simply this means that such models are not physical descriptions of the hadron spectrum.

Publisher’s Note: Sleptonium at the linear collider and the slepton co-next-to-lightest supersymmetric particle scenario in gauge mediated symmetry breaking models [Phys. Rev. D72, 015005 (2005)

We discuss the possibility of formation and subsequent detection of a supersymmetric bound state composed of a slepton--antislepton pair at the next linear collider. The Green function method is used within a non-relativistic approximation to estimate the threshold production cross-section of the $2P$ bound state. The parameter space of Gauge Mediated Symmetry Breaking (GMSB) models allow a particular scenario in which a charged slepton ($\widetilde{e}_R, \widetilde{\mu}_R$ or $\widetilde{\tau}_1$) is the NLSP. Within this scenario the produced $2P$ bound-state decays, through a dipole transition, into the $1S$ ground-state with branching ratio $\approx 100% $ emitting a very soft ($\approx 1 $ MeV) photon which goes undetected. The spectroscopy of the $1S$-state shows that it decays into two photons with $Br \approx 0.5$ up to $m_{NLSP} \approx 1$ TeV. Thus NLSP sleptonium threshold production gives rise to the signal $e^+e^- \to 2P \to 1S + "soft \gamma " \to \gamma \gamma$ which when compared with the standard model two-photon process ($ e^+e^- \to \gamma \gamma$) has a statistical significance ($SS$=signal/noise) which, at an energy offset from threshold of E=20 GeV, goes from $SS=11$ to $SS=2$ when the mass of the NLSP ranges in the interval $[100,200]$ GeV.

Sleptonium at the linear collider and the slepton co-next-to-lightest supersymmetric particle scenario in gauge mediated symmetry breaking models

We discuss the possibility of formation and subsequent detection of a supersymmetric bound state composed of a slepton-antislepton pair at the next linear collider. The Green function method is used within a nonrelativistic approximation to estimate the threshold production cross section of the $2P$ bound state. The parameter space of gauge mediated symmetry breaking (GMSB) models allow a particular scenario in which a charged slepton (${\stackrel{\texttildelow{}}{e}}_{R},{\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$ or ${\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}$) is the next-to-lightest supersymmetric particle (NLSP). Within this scenario the produced $2P$ bound-state decays, through a dipole transition, into the $1S$ ground-state with branching ratio $\ensuremath{\approx}100%$ emitting a very soft ($\ensuremath{\approx}1\text{ }\text{ }\mathrm{MeV}$) photon which goes undetected. The spectroscopy of the $1S$-state shows that it decays into two photons with $\mathrm{Br}\ensuremath{\approx}0.5$ up to ${m}_{\mathrm{NLSP}}\ensuremath{\approx}1\text{ }\text{ }\mathrm{TeV}$. Thus NLSP sleptonium threshold production gives rise to the signal ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}2P\ensuremath{\rightarrow}1S+``\mathrm{soft}\text{ }\text{ }\ensuremath{\gamma}''\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ which when compared with the standard model two-photon process (${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ ) has a statistical significance ($SS=$signal/noise) which, at an energy offset from threshold of $E=20\text{ }\text{ }\mathrm{GeV}$, goes from $SS=11$ to $SS=2$ when the mass of the NLSP ranges in the interval $[100,200]\text{ }\text{ }\mathrm{GeV}$.

Chaos, solitons and fractals in hidden symmetry models

Abstract A spontaneous symmetry breaking (or hidden symmetry) model is reduced to a system nonlinear evolution equations integrable via an appropriate change of variables, by means of the asymptotic perturbation (AP) method, based on spatio-temporal rescaling and Fourier expansion. It is demonstrated the existence of coherent solutions as well as chaotic and fractal patterns, due to the possibility of selecting appropriately some arbitrary functions. Dromion, lump, breather, instanton and ring soliton solutions are derived and the interaction between these coherent solutions are completely elastic, because they pass through each other and preserve their shapes and velocities, the only change being a phase shift. Finally, one can construct lower dimensional chaotic patterns such as chaotic–chaotic patterns, periodic–chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution.