Dynamical electroweak symmetry breaking via fermion condensates inSU(5) model

TheSU(4) symmetry scheme, used in a previous paper for the study of the 2v double decay, is applied to the study of the 0v double decay. Differences and similarities between the 2 processes are emphasized. The sensitivity to short-range correlations is discussed.     

Spontaneous U（1） symmetry breaking and Bose-Einstein condensation

Based on Bogoliubov's truncated Hamiltonian H_B for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a₀+\lambda^*a₀⁺) to H_B, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.     

Relation between the Lee-Wick and Nambu-Jona-Lasinio models of chiral symmetry breaking

The connection between the sigma model of Lee and Wick and the Nambu-Jona-Lasinio (NJL) model is discussed. It is shown that the sigma field potential of the linear Lee-Wick model is identical in form with the variation of the vacuum energy of the NJL system with the baryonic scalar densityn _s. The sigma field is proportional ton _s. Furthermore, the coupling constant and mass of thisσ field are fully determined by the NJL model version of the Goldberger-Treiman relation. It is shown further that the restoration of chiral symmetry with increasing baryonic density always occurs via a second order transition in the NJL model, while it is necessarily of first order in the associated linear Lee-Wick model.     

The symmetry breaking patternSU(5)→SU(3)×U(1) including one loop radiative corrections

We derive conditions on the Higgs parameters of the minimalSU(5) model under which the phenomenologically desired symmetry breaking patternSU(5)→SU(3)×U(1) persists at the one loop level.     

Description of interaction in theSU (2) L ⊗U (1) model with dynamical symmetry breaking

Expressions for the total cross sections of elementary interaction processes between the primary fermion scalar fields and the scalar fields generated by dynamical symmetry breaking are derived within the framework of the globalSU (2) _L ?U (1)-invariant four-fermion model by means of lowest-approximation loop expansions of the propagators for the indicated fields.     

Chiral symmetry and supersymmetry in the Nambu-Jona-Lasinio model

The connection between chiral symmetry and supersymmetry is investigated in the context of a supersymmetric extension of the Nambu-Jona-Lasinio model. A supersymmetric gap equation is found and it is shown that no solution exists which breaks chiral symmetry. A simple physical argument for this phenomenon is given and possible implications for the dynamics of composite models are discussed.     

U(1)-invariant current forms

Let λ : U(1) → GL (V) be a linear representation. Lagrangians defined on J¹(T*M × V)whose universal current form is gauge invariant, are described in terms of gauge invariant Lagrangians and invariant functions on V. A characterization of gauge invariant Lagrangians depending on matter fields only, that is, L : J¹V → ?, is also obtained.     

Radiative gauge symmetry breaking in supersymmetric flipped SU(5)

The radiative breaking of the SU(5)×U(1) symmetry in the flipped SU(5) model recently proposed by Antoniadis et al. is studied using renormalization group techniques. It is shown that gaugino masses can only be the dominant source of supersymmetry breaking at the Planck scale if the U(1) gaugino mass M₁ is at least 10 times larger than the SU(5) gaugino mass M₅. If M₁≅M₅ at the Planck scale, non-vanishing trilinear soft breaking terms (“A-terms”) are needed already at the Planck scale. In both cases consequences for the sparticle spectrum at the weak scale are discussed.     

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.     

SU(3) × SU(3) symmetry breaking in a simple model

A field-theoretical model, due to Lévy, is studied. It contains a triplet of quarks and a pseudoscalar and a scalar meson nonet. The original SU(3) × SU(3) symmetry is broken by terms linear in the scalar meson fields. A renormalization and regularization procedure is defined in order to remove the ultra-violet divergences. The possibility of a spontaneous breakdown of the symmetry is described and the Goldstone theorem is verified in the one-loop approximation.     

Spontaneous chiral symmetry breaking for a U(N) gauge theory on a lattice

We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.     

Spontaneous symmetry breaking in O(10)

We consider the most general renormalizable O(10) invariant potential for a $\text{45 + 16 +}\text{16}$ representation of Higgs fields. We show that O(10) can be spontaneously broken down to SU(5), SU(4) × U(1) or SU(3) × SU(2) × U(1), this last case being, of course, the most appealing.     

Dynamical SU(3) symmetry breaking in the linear baryonic string model

A dynamical mechanism responsible for breaking of the SU(3) symmetry among various states from the s-u-d sector is proposed. In the case when SU(3) is dynamically maximally broken we obtain Λ_α - Λ_γ degeneracy and reproduce also other prominent features of the leading strange baryon trajectories.     

Simple kinetic model of symmetry breaking

We consider a dynamical system described by a set of random variablesN| _i(t) and depending on a parameterR controlling its stability. IfR < R _c the system is stable and theN _i have some symmetry properties in the statistical sense (i.e., with respect to time averaging). IfR > R _c the system is unstable and the nonlinear dynamics of theN _i may lead to an asymptotic stationary state which does not possess the symmetries of the stable system. We show that the dynamics of symmetry breaking resembles a phase transition in the limit of many variables.