Can supersymmetry breaking lead to electroweak symmetry breaking via formation of scalar bound states?

The recent discovery of the putative 125 GeV Higgs boson has motivated a number of attempts to reconcile its relatively large mass with the predictions of the minimal supersymmetric standard model (MSSM). Some approaches invoked large trilinear supersymmetry breaking terms _At$A_t$ between stops and one of the elementary Higgs fields. We consider the possibility that electroweak symmetry breaking may be triggered by supersymmetry breaking with a large _At$A_t$, large enough to generate a composite field with the same quantum numbers as the Higgs boson and with a non-vanishing vacuum expectation value. In the resulting vacuum, the usual relation between the gauge couplings and the Higgs self-coupling does not apply, and there is no reason to expect the same upper bound on the mass of the lightest Higgs boson. In a simple model where the bound state is assumed to have no mixing with the other fields, we calculate the critical coupling _At$A_t$ necessary for symmetry breaking using the lowest-order Bethe–Salpeter (BS) equation. Study of the BS equation is complicated by the structure of its lowest-order kernel, which is a crossed box graph, but we find an accurate approximation to its solution. In a realistic model, the mixing of the bound state with the fundamental Higgs boson creates a symmetry-breaking seesaw. We outline the steps toward a realistic model.     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

Compactification and spontaneous symmetry breaking in the λϕ4 theory with Kaluza-Klein background

We obtain a one-loop effective action for the ⁴ theory in the space M₄×S_N.We study the questions of compactification and spontaneous symmetry breaking due to the one-loop effective action of the ⁴ theory. We show how the vacuum quantum effects of the scalar field induce the 4-dimensional Einstein-Cartan theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 9–14, September, 1988.The author is grateful to I. L. Bukhbinder, I. V. Tyutin, A. A. Tseitlin, and B. L. Spokoinyi for useful discussions.     

Stability of the scalar potential and symmetry breaking in the economical 3-3-1 model

A detailed study of the criteria for stability of the scalar potential and the proper electroweak symmetry breaking pattern in the economical 3-3-1 model, is presented. 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. A new theorem related to the stability of the potential is stated. As a consequence of this study, the consistency of the economical 3-3-1 model emerges.     

Density functional theory of transition metal phthalocyanines,II: electronic structure of MnPc and FePc—symmetry and symmetry breaking

We present a two-part systematic density functional theory (DFT) study of the electronic structure of selected transition metal phthalocyanines. We use a semi-local generalized gradient approximation (GGA) functional, as well as several hybrid exchange-correlation functionals, and compare the results to experimental photoemission data. Here, we study the intermediate spin systems MnPc and FePc. We show that DFT calculations of these systems are extremely sensitive to the choice of functional and basis set with respect to the obtained electronic configuration and to symmetry breaking. Interestingly, all simulated spectra are in good agreement with experiment despite the differences in the underlying electronic configurations.     

Lattice (Φ 4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ ⁴)₄ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredm _h ² is proportional to its “renormalized” self-couplingλ _R is not valid outside perturbation theory: the appropriate continuum limit hasm _h finite and vanishingλ _R . A Monte Carlo lattice computation of theλ(Φ ⁴)₄ effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλ _R ) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ ⁴)₄ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.     

New bounds on the number of bound states for Schrödinger operators

We consider the Schrödinger operatorH = – +V(|x|) onR ³. Letn denote the number of bound states with angular momentum (not counting the 2 + 1 degeneracy). We prove the following bounds onn . LetV 0 and d/dr r ^1-2p (-V)^{1 –p} 0 for somep [1/2, 1) then

Spontaneous breaking of chiral symmetry, and eventually of parity, in a σ-model with two Mexican hats

A σ-model with two linked Mexican hats is discussed. This scenario could be realized in low-energy QCD when the ground state and the first excited (pseudo)scalar mesons are included, and where not only in the subspace of the ground states, but also in that of the first excited states, a Mexican hat potential is present. This possibility can change some basic features of a low-energy hadronic theory of QCD. It is also shown that spontaneous breaking of parity can occur in the vacuum for some parameter choice of the model.     

Landau gauge without δ-constraints and the question of spontaneous symmetry breaking in the lattice U(1)-Higgs model

A new method is proposed that allows in compact abelian lattice gauge theories to investigate expectations in the Landau gauge analytically (and probably also numerically) without using δ-constraints. As an application it is shown that in the U(1)-Higgs model in the Landau gauge there is no spontaneous symmetry breaking in the confinement subregion of the Higgs-confinement phase.     

The symmetry of donor–bound electron wavefunctions in quantum wells

In order to investigate the symmetry (i.e. sphericity) of donor–bound electron wavefunctions in quantum wells, we have invoked a two-parameter trial wavefunction. One parameter is the Bohr radius λ, whilst the other is the eccentricity parameter ζ. The latter incorporates the effect of the quantum well (QW) on the carrier motion in the growth (i.e. the z) direction. Working within the envelope function approximation it is shown that the donor wavefunction has the form of a prolate spheroid. However, calculations of the ratio λ/ζ shows that it is the value of λ which determines the essential symmetry of the wavefunction.     

Confinement of atoms with Robin’s condition: Spontaneous symmetry breaking

The properties of the ground state of the hydrogen atom in a spherical vacuum cavity with general boundary “not going out” conditions (i.e., when the probability current through the boundary vanishes) are studied. It is shown that in contrast to the confinement of an atom by a potential barrier, in this case depending on the parameters of the cavity, the atom could be in stable equilibrium at the center of the cavity or shift towards its periphery: spontaneous breaking of spherical symmetry occurs. The phase diagram of the shift and the dependence of the shift value and the binding energy of the ground state of the atom on the cavity parameters are presented. At the same time, the deformation properties of the electron wave function (WF) for an asymmetric distortion are so nontrivial that a non-zero shift occurs even when an electron is repulsed from the cavity boundary.     

Absence of continuous symmetry breaking in a one-dimensional n−2 model

For a one-dimensional array ofS ^N–1 spins (N 2) with isotropic pair interactions (and more general systems) with J(j–i) obeying sup_n[n^–1 ₁ ⁿ j ²|J(j)|]<, we prove that every equilibrium state is invariant under the natural action ofSO(N). In particular, there is no long-range order of the conventional type. Included is the caseJ(n)=n ^–2.Research partially supported by U.S.N.S.F. Grant No. MCS-78-01885.S. Fairchild Scholar at Caltech. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544.     

Can the breaking of time-reversal symmetry remove degeneracies in quantum mechanics?

Reduction of spatial symmetry can remove the degeneracy of energy levels in quantum mechanics. The break of time-reversal symmetry by inclusion of a dissipative environment can have a similar effect. The corresponding time-evolution of position and momentum fluctuations can be described by a nonlinear differential equation that can lead to bifurcations and, thus, splitting of energy levels.     

Comment on reparametrization invariance of quark–lepton complementarity

We study the complementarity between quark and lepton mixing angles (QLC), the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4$\pi /4$. Experimentally in the standard PDG parametrization, two such relations exist approximately. These QLC relations are accidental which only manifest themselves in the PDG parametrization. We propose reparametrization invariant expressions for the complementarity relations in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that |_Vus/_Vud|+|_Ve2/_Ve1|+|_Vus/_Vud||_Ve2/_Ve1|=1$|V_{us}/V_{ud}|+|V_{e2}/V_{e1}|+|V_{us}/V_{ud}||V_{e2}/V_{e1}|=1$ and |_Vcb/_Vtb|+|_Vμ3/_Vτ3|+|_Vcb/_Vtb||_Vμ3/_Vτ3|=1$|V_{cb}/V_{tb}|+|V_{\mu 3}/V_{\tau 3}|+|V_{cb}/V_{tb}||V_{\mu 3}/V_{\tau 3}|=1$. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.     

Gate control of lattice-pseudospin currents in graphene on SW2: Effect of sublattice symmetry breaking and spin–orbit interaction

Strong spin–orbit interaction (SOI) in graphene grown on tungsten disulfide (SW₂) has been recently observed, leading to energy gap opening by SOI. Energy gap in graphene may also be induced by sublattice symmetry breaking (SSB) where energy level in A-sublattice is not equal to that in B-sublattice. SSB-gap may be produced by growing graphene on hexagonal boron nitride or silicon carbide. In this work, we investigate transport property in a SOI/SSB/SOI gapped graphene junction, focusing the effect of interplay of SOI and SSB. We find that, lattice-pseudospin polarization (L-PSP) can be controlled perfectly from +100% to −100% by gate voltage. This is due to the fact that in graphene grown on SW₂, the carriers carry lattice-pseudospin degree of freedom “up and down”. The SSB-gapped graphene exhibits pseudo-ferromagnetism to play the role of lattice-pseudospin filtering barrier. It is also found that the SOI and SSB-gaps in graphene may be measured by characteristic of L-PSP in the junction. The proposed controllable-lattice-pseudospin currents may be applicable for graphene-based pseudospintronics.     

A lower bound on Hartmann number for relaxed plasmas described byTaylor’s principle

A lower bound on Hartmann number for relaxed plasmas described by Taylor’s principle of minimum magnetic energy with fixed magnetic helicity is found analytically starting from first principles. Spontaneous filamentation occurs if the Hartmann number is below threshold. Comparison with both experiments and numerical computations is presented.     

A non-perturbative analysis of symmetry breaking in two-dimensional φ4 theory using periodic field methods

We describe the generalization of spherical field theory to other modal expansion methods. The main approach remains the same, to reduce a d-dimensional field theory into a set of coupled one-dimensional systems. The method we discuss here uses an expansion with respect to periodic-box modes. We apply the method to φ⁴ theory in two dimensions and compute the critical coupling and critical exponents. We compare with lattice results and predictions via universality and the two-dimensional Ising model.     

Analysis of the pseudoscalar partner of the Y(4660) and related bound states

In this article, we study the pseudoscalar bound state η _c ′f ₀(980) (irrespective of the hadro-charmonium and the molecular state) with the QCD sum rules. Considering the SU(3) symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states η _c ′σ(400?1200), η _b '''f ₀(980) and η _b '''σ(400?1200), and make reasonable predictions for their masses.     

Renormalizability of a quark–gluon model with soft BRST breaking in the infrared region

We prove the renormalizability of a quark–gluon model with soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.