Weak Symmetry Breaking Research Articles

Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields

We discuss the Nöckel model of an open quantum dot, i.e. a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, there are embedded eigenvalues which turn into resonances if the symmetry is violated, either by applying a magnetic field or by deformation of the well. For a weak symmetry breaking we derive the perturbative expansion of these resonances. We also deduce a sufficient condition under which the discrete spectrum of such a system (without any symmetry) survives the presence of a strong magnetic field. It is satisfied, in particular, if the dot potential is purely attractive.

Chaos-assisted tunnelling in the absence of reflexion symmetry

It has been shown previously that a novel tunnelling behaviour, dubbed chaos-assisted tunnelling, can arise in bound, mixed phase space systems possessing reflection symmetries. As with the usual, direct tunnelling problem of a double well, even a very weak symmetry breaking typically quenches the ability of certain probability densities to tunnel resonantly back and forth. Experiments lacking exact reflexion symmetry will fail to exhibit tunnelling. We show here how chaos-assisted tunnelling can be re-established experimentally and distinguished from direct tunnelling through the variation of two external system parameters, and demonstrate the applicability of a generalized three-level model of the tunnelling process with the coupled quartic oscillators.

Self-organized critical random directed polymers

We uncover a nontrivial signature of the hierarchical structure of quasidegenerate random directed polymers (RDPs) at zero temperature in $(1+1)$-dimensional lattices. Using a cylindrical geometry with circumference $8<~W<~512$, we study the differences in configurations taken by RDPs forced to pass through points displaced successively by one unit lattice mesh. The transition between two successive configurations (interpreted as an avalanche) defines an area $S$. The distribution of moderately sized avalanches is found to be a power law $P(S)\mathrm{dS}\ensuremath{\sim}{S}^{\ensuremath{-}(1+\ensuremath{\mu})}\mathrm{dS}$. Using a hierarchical formulation based on the length scales ${W}^{2/3}$ (transverse excursion) and the distance ${W}^{(2/3)\ensuremath{\alpha}}$ between quasidegenerate ground states (with $0<\ensuremath{\alpha}<~1)$, we determine $\ensuremath{\mu}=$$\frac{2}{5}$, in excellent agreement with numerical simulations by a transfer matrix method. This power law is valid up to a maximum size ${S}_{5/3}\ensuremath{\sim}{W}^{5/3}$. There is another population of avalanches that for characteristic sizes beyond ${S}_{5/3},$ obeys $P(S)\mathrm{dS}\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}{(S/S}_{5/3}{)}^{3}]\mathrm{dS}$, also confirmed numerically. The first population corresponds to almost degenerate ground states, providing a direct evidence of ``weak replica symmetry breaking,'' while the second population is associated with different optimal states separated by the typical fluctuation ${W}^{2/3}$ of a single RDP.

Effect of a chiral impulse on the weak interaction induced handedness in a prebiotic medium.

Previously we have carried out simulation of the Weak Neutral Current and symmetry breaking transition bifurcation process addressing some of the issues raised by critics of the approach. We now include the effects of a chiral impulse on the transition and show that under certain cases this could greatly alter the transition time. Examples of a chiral impulse could be a nearby Supernova and an impulse of beta-emitters. We briefly discuss the possibility of these processes in the early solar system.

Supersymmetric models with a gauge singlet and non-universal soft terms from orbifold string theory

The particle spectrum of the supersymmetric extension of the standard model with a gauge singlet is studied. Soft supersymmetry breaking terms are explicitly chosen to be non-universal according to orbifold string theory. They depend on modular weights of chiral fields and on an angle θ specifying the supersymmetry breaking sector. Imposing radiative weak symmetry breaking and requiring that standard model Yukawa couplings should be allowed yield constraints on modular weights and almost specifies the angle θ. We then perform a numerical analysis of the low energy spectrum. It turns out that the spectrum is very constrained, revealing salient features such as light Higgses and neutralinos. The latter happen to be essentially gaugino-like.

Polymers in quenched random environment: Weak replica symmetry breaking

The case of polymers in strong quenched disorder is investigated. The disorder is modeled by a quenched random potential which is sampled by a flexible polymer chain. It is shown that the problem, originally formulated in terms of Edwards type path integrals, can be transformed into an effective field theory. Localized phases of the polymer, where the size of the chain is independent of its contour length, i.e. R2∝(1/Δ)2/(4−d), can be found by a weak breaking of the replica symmetry. Δ is a measure for the disorder. The same formalism predicts at d=4 an essential singularity R2 ∝exp(2π2/Δ) for vanishing disorder Δ→0.

Slave equations for spin models

We apply an accelerated Langevin algorithm to the simulation of continous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models.

Fermion masses and mixings from higher dimensions

A systematic discussion of the structure of fermion mass matrices in terms of quantum numbers is presented. Small ratios between fermion masses and small mixing angles are related to a fine structure of scales around the unification scale. We argue that in higher dimensional models all small fermion masses should be explained from symmetry considerations since no free small Yukawa couplings are available. This leads to a scanning procedure selecting higher dimensional models consistent with realistic fermion mass patterns. We present a six-dimensional model admitting “compactifications” with only SU(3) c ×SU(2) L×U(1) γ gauge symmetry, a vanishing cosmological constant and three generations of quarks and leptons. The field equations have solutions with a gauge hierarchy for weak symmetry breaking for a large range of model parameters without the need of fine tuning. The weak scale M W is a free integration constant and the mechanism determining its order of magnitude is not yet identified. These solutions have a good chance to be classically stable. For one particular solution the largest fermion mass is the top quark mass which is of the same order as M W. At the next level the fermion masses m b, m τ and m c are supressed by a small ratio of symmetry breaking scales γ. For the mixing between the second and third generation one finds θ 23≈ m b/ m t≈ γ. The relation m b( M) = m τ ( M)(1+O γ)) is predicted. Corrections of order γ 2 quark and the muon with the relation m s (M) = 1 3 m μ(M) . This reproduces the qualitative order of magnitude m s/ m b ≈ m c/ m t. Unfortunately this particular solution fails by predicting maximal Cabibbo mixing and θ 13 ≈ γ. The model can be interpreted as a subgroup analysis for E 8 × E 8 superstrings. We also give a systematic discussion of higher dimensional scalar fields in non-trivial representations of the gauge group. We describe the higher dimensional Higgs effect which can lead to a stabilization of the ground state.

Aspects of the super-unification of strong, electroweak and gravitational interactions

We develop a strategy for extracting low-energy phenomenological four-dimensional physics from the superstring. We discuss supersymmetry and gauge symmetry breaking, emphasizing key ingredients in the construction of a realistic model based on Calabi-Yau compactification. The incorporation of a no-scale mechanism for the dynamical generation of the electroweak gauge hierarchy imposes a unique choice of the gauge group SU(3) × SU(2) × U(1) 2, an almost unique set of matter fields and of Yukawa couplings. Our phenomenological analysis of this model includes the derivation of bounds on the mass of the new neutral gauge boson from the Z 0 boson mass, low-energy neutral currents, and cosmology. We calculate the ratios of sparticle masses and give estimates of their magnitudes. These are based on detailed dynamical calculations demonstrating the feasibility of weak gauge symmetry breaking, made possible by radiative corrections to supersymmetry breaking initiated by a gaugino mass.

Fermion condensates and weak symmetry breaking in a superstring-based model.

We start with the gauge group SU(3)/sub C/ x SU(2)/sub L/ x U(1)/sub R/ x U(1)/sub N/ (equivalentG/sub 3211/), which is a rank-five subgroup of E/sub 6/. We include chiral-fermion-condensate terms in the effective four-dimensional Lagrangian derived from superstrings and discuss how this condensation can be responsible for weak symmetry breaking at a scale of 100 GeV. One experimental effect of the above will be the nonobservation of light Higgs scalars of the Salam-Weinberg model, although the other results of the same remain unchanged.

Scales in superstring models

We argue that supersymmetry breaking in the observable low energy sector of superstring models is triggered by gaugino masses m 1 2 which are proportional to the product of the gravitino mass and a non-vanishing F-term. The scales of global supersymmetry breaking m 1 2 , weak gauge symmetry breaking m W, grand unification m X, compactification m C and the gravitino mass m 3 2 are then determined by radiative corrections in a variant of the no-scale models proposed previously: m 1 2 , m W ∝ m P exp(− O(1)/α t ), m X , m C , m 3 2 ∝ m P . Key ingredients are an additional SU(3) C × SU(2) L × U(1) Y singlet field and an extra low energy U(1) gauge symmetry expected in supestring models.

Gravity-induced weak symmetry breaking and supergravity

We give here a review of the recent developments of grand unified theories based onN=1 supergravity. We start with a brief introduction of supersymmetry and supergravity multiplets, and then discuss the construction of an invariant Lagrangian. The phenomena of gravity-induced weak symmetry breaking via the super Higgs effect at the tree level, corresponding to the conventional SU(5) gauge group, are then considered. We then extend this idea to the larger group SO(10), showing two possible breaking chains given as (i) SO(10)×susy→SU(2) L ×U(1) R ×U(1) B-L ×SU(3) C (≡ G2113)×susy→U(1)em×SU(3) C (G LE ) predicting a secondZ-boson having mass lower than 1 TeV, and (ii) SO(10)×susy→SU(2) L ×SU(2) R ×SU(4)→(≡G224)×susy→ SU(2) L ×U(1) Y ×SU(3) C (≡ G213)×susy→U(1)em×SU(3) C . We also consider the radiative breaking of weak symmetry via renormalisation group effects, which predicts the top quark mass. Some experimental signatures of the supersymmetric particles are investigated and possible future outlook is discussed.

Possibility of dynamical symmetry restoration in the Gaussian overlap approximation.

We analyze the symmetry-conserving-variational-dynamics and the time-dependent-generator-coordinate methods showing their equivalence for a large class of problems. The application to actual calculations involving the restoration of the rotational symmetry in nuclear dynamics is examined together with the Gaussian overlap hypothesis. It is shown that the range of validity of the combined approach is restricted to very weak symmetry breaking. The relative location of the method in the context of variational approximations to the dynamics is established as well as the various relations among different procedures.

Grand unification and supergravity in SO(10).

We extend the supergravity model to SO(10) gauge symmetry. There is a hierarchical structure with intermediate mass scale for SO(10)-symmetry breaking, along with a tree-level weak-symmetry breaking caused by a Polony-type potential in a manner parallel to SU(5)-symmetry breaking.

Effects of grand unification interactions on weak symmetry breaking in supergravity theories

Possible effects of grand unification interactions on SU(2) × U(1) breaking are investigated by explicitly considering a supersymmetric SU(5) model coupled to N = 1 supergravity. Some remarkable features concerning the effects of renormalization on the effective soft supersymmetry breaking terms of SU(5) in the GUT region M P − M G are clarified, which are relevant for determining the SU(3) × SU(2) × U(1) theory below M G. In particular, the (mass) 2 of the Higgs doublets, g H m g 2 and g H m g 2 , might become significantly small at M G (g H ⋍ g H ≈ 0.1) through the effect of SU(5) couplings such as Hø E H . Then, g H can rather easily become negative below M G, so as to realize SU(2) × U(1) breaking naturally even for the “diet” top quark case ( m t ≈ 40 GeV). On the other hand, if g H ⋍ g H ⋍ 1 at M G by neglecting the grand unification interactions, some careful tuning of μ 3 2/ m g 2 is required with an accuracy ⪅10 −2 to achieve SU(2) × U(1) breaking with “diet” top quark, though a mass term μ 3 2( H H) may be present.

The low-energy particle spectrum in the missing partner SU(5) model

In the “missing partner” SU(5) model coupled to N = 1 supergravity the “missing partner” mechanism does not only solve the second hierarchy problem but also leads to weak interaction gauge symmetry breaking for arbitrary top quark mass. In this scenario the lower limit on the proton lifetime can impose a severe constraint on the low-energy supersymmetric particle spectrum. Predictions of the model are accessible at present energy or in the near future.

Monopole-induced baryon number violation due to weak anomally

Abstract Magnetic monopoles may catalyze baryon number violation due to the weak 't Hooft anomaly, even if the boundary conditions at the monopole core conserve baryon number. We show, by analyzing a simple toy model, that this effect is unsuppressed by any power of the monopole size, weak symmetry breaking scale, or coupling constant, provided the radius of the monopole core is smaller than Eg2/mw2, E being the energy of the external fermions, g the coupling constant of the SU(2)weak group, and mw the SU(2)weak breaking scale. It is argued that this is a general feature of all monopoles (not necessarily 't Hooft-Polyakov monopoles). Possible suppression factors due to the presence of higher generation fermions are discussed.

Is supersymmetry found?

Monojet events seen recently by the UA1 collaboration at the CERN pp̄ collider may be due to squarks or gluinos with masses O(40) GeV. The thinness of the observed jets favours the squark interpretation. In this case, we predict that sleptons should have masses between 20 and 30 GeV and that the photino should have a mass between 5 and 10 GeV. Such masses are close to the experimental lower limits and sparticles could soon be detectable in e +e − → ( γ γ )γ experiments and W ± and Z 0 decay. We demonstrate that such light sparticle masses are consistent with models whose weak gauge symmetry breaking is driven by a t quark weighing O(40) GeV as recently reported, and even with no-scale models in which the supersymmetry breaking scale is also determined dynamically.

No-scale supergravity models with a planck mass gravitino

We construct phenomenological N = 1 supergravity models in which the gravitino may be fixed to have a mass O(10 19 GeV), whilst the weak interaction mass scale is determined by radiative corrections to be hierarchically smaller. Weak gauge symmetry breaking is driven by dynamically determined gaugino masses, and all the SUSY partners of standard model particles have masses O(100) GeV.

Weak-Symmetry Breaking in Locally Supersymmetric Grand Unified Theories

A possibility of the radiative breaking of the weak gauge symmetry is studied in the framework of grand unified theories coupled to the N = 1 supergravity. Some supersymmetry breaking mass parameters in the effective low energy theory, which do not emerge at the tree level from the spontaneous breakdown of the N = 1 supergravity, are found to become sizable when the loop effect of heavy particles is taken into account at the grand unification mass scale. These mass parameters, as well as those produced at the tree level, are considered as boundary values at the unification mass scale for the renormalization group equations. It is remarkably found that there isa possibility that the top quark can be as light as the present experimental lower bound in order for the radiative weak symmetry breaking to occur. It is further shown that gluinos acquire phenomenologically allowable masses even if the canonical kinetic term is assumed for the Yang-Mills supergravity coupling. Wiggsinos (i.e., mixed states of gauge and Higgs fermions) also obtain sizable masses.