The fate of the U(1) goldstone boson

In the framework of a manifestly covariant formulation of (non-Abelian) gauge theories, we analyse what the gauge invariance (BRS invariance) implies for the problem of the Goldstone boson associated with the conserved U(1) axial vector current. Based on the symmetry consideration of gauge invariance only, it is shown that the Goldstone boson does not appear as a physical particle at all, if and only if the Faddeev-Popov (FP) ghost forms a massless bound state with the gauge boson in a pseudoscalar channel. This decoupling of the Goldstone boson from the physical sector is not caused by the Goldstone dipole proposed by Kogut and Susskind, but by a Goldstone quartet including the FP ghost bound state. This decoupling mechanism by the Goldstone quartet can be shown to become equivalent to that of the Goldstone dipole, only in a special case, i.e., the Schwinger model which is an Abelian theory in two dimensions. In the Abelian gauge theory in four dimensions, the chiral U(1) Goldstone boson necessarily appears as a physical particle.     

On the character of chiral symmetry breaking and fermion vacuum structure in QED<Subscript>3</Subscript>

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED₃ is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED₃, complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.     

On a unified theory of electromagnetism and weak interaction

A unified theory of weak and electromagnetic interaction has been developed on the basis of the assumption that the charge and mass of a lepton is of dynamical origin. According to this model, the spontaneous breakdown of symmetry generates the photon as a Goldstone boson.     

Tensor Interaction Effect in Dibaryon

The gluon and Goldstone boson induced tensor interaction effect on the dibaryon mass and the D-wave decay width has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease quickly as the increasing of the channel strangeness. The K and η meson tensor contribution is negligible in this model. No six-quark state in the light flavor world can become a bound one by the help of these tensor interactions except the deuteron. The partial D-wave decay width of IJ^p=\frac{1}{2}2⁺ NΩ state to spin 0, 1 ΛΞ final state is 20.7 keV and 63.1 keV respectively. It is a very narrow dibaryon resonance and might be detected in the relativistic heavy ion reaction by the existing RHIC detectors through the reconstruction of the ΛΞ vertex mass and the future COMPAS detector at CERN and FAIR project in Germany.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Dynamical symmetry breaking in the sea of the nucleon

We derive the nonanalytic chiral behavior of the flavor asymmetry d - u. Such behavior is a unique characteristic of Goldstone boson loops in chiral theories, including QCD, and establishes the unambiguous role played by the Goldstone boson cloud in the sea of the proton. Generalizing the results to the SU(3) sector, we show that strange chiral loops require that the s - s distribution be nonzero.     

A microscopic theory of the lambda transition

Starting with a microscopic hamiltonian for a many-boson system with a hardcore interaction, the grand potential of the system, which contains the order-parameter of the lambda transition as one of the thermodynamical variables, is derived by making use of the finite temperature loop expansion. The divergence difficulty caused by the hardcore interaction is circumvented by the conventional field theoretic perturbational renormalization such that the chemical potential is renormalized instead of the conventional mass renormalization. The grand potential obtained consists of the superfluid part and the finite temperature elementary excitation part. The elementary excitation energy spectrum shows the Goldstone boson mode, namely, the photon, for the zero external field. A non-vanishing external field destroys such a Goldstone boson mode by causing an energy gap at zero momentum. The chemical potential and the critical temperature are also obtained for the weak coupling case. It is shown how the Bose-Einstein condensation is affected by the hardcore interaction.     

A complete Lagrangian formulation of superconductivity

We present here a complete Lagrangian formulation of superconductivity. Only the boson degrees of freedom are explicitly introduced. The BCS solution is obtained as classical approximation. The physical interpretation of the Goldstone boson comes up naturally from this theory.     

Enlarged Peccei-Quinn symmetry and limits from the supernova

We construct a model generalizing the invisible axion model of Dine, Fischler and Srednicki to three scalar doublets and two scalar singlets. By imposing two U(1) symmetries rather than the single Peccei-Quinn symmetry of the DFS model, we arrive at a physical particle spectrum containing both a light axion and a massless Goldstone boson. The axion couplings are as usual suppressed by a large VEV, which is bounded below by SN1987a emission limits and above by cosmological arguments. The VEV in the Goldstone boson couplings is bounded below by SN1987a emission and subsequent conversion into gamma rays via the galactic magnetic field, but the cosmological upper bound cannot be applied to this massless boson.     

Spontaneously broken supergauge symmetries and goldstone spinors

We present a model with a spontaneously broken supergauge symmetry which results in the appearance of a massless Goldstone spinor. The model combines supergauge invariance with ordinary gauge invariance. After the breaking the gauge boson acquires a mass as a result of the Higgs mechanism.     

Fermion propagators on a four-dimensional random-block lattice

Fermion propagators, composite boson propagators and the fermion condensate are calculated numerically on the four-dimensional random-block lattice, respectively. The ensemble-averaged fermion propagator agrees with the continuum propagator for distances greater than three average lattice spacings. The results on the fermion condensate show that the chiral symmetry of the doubled modes is broken in the continuum limit. The Goldstone boson arising from the broken symmetry is revealed by examining the composite pseudo-scalar propagator. The doubled fermion and the Goldstone boson both acquire masses of the order of inverse lattice spacing and thus decouple from the theory in the continuum limit.     

Fermions and bosons in a two-dimensional world

We derive the formal equivalence of a free massless two-dimensional theory and a free massless two-dimensional boson theory constructed from the bilinear products of the self-same fermion theory. The sense of this equivalence is investigated. Using a box normalization, it is found that the fermion states are Glauber coherent states of bosons, where the boson vacuum is the ground state of the charge sector corresponding to the given fermion state. The massless boson is the Goldstone boson and the degenerate vacua are the ground states of the various charge sectors. A complete operator identity between fermion and boson operators can be obtained, but to do this an additional boson operator must be introduced which cannot be defined in terms of bilinear products of the fermion operators. Doing this makes the charge spectrum continuous.     

Pair production of the Elementary Goldstone Higgs boson at the LHC

The Elementary Goldstone Higgs(EGH) model is a perturbative extension of the standard model(SM),which identifies the EGH boson as the observed Higgs boson. In this paper, we study pair production of the EGH boson via gluon fusion at the LHC and find that the resonant contribution of the heavy scalar is very small and the SM-like triangle diagram contribution is strongly suppressed. The total production cross section mainly comes from the box diagram contribution and its value can be significantly enhanced with respect to the SM prediction.     

On how to count Goldstone bosons

A generalization of Goldstone's theorem is presented which is valid for theories either with or without relativistic invariance. The central suggestion is that, under certain specified assumptions, all Goldstone bosons can be divided into two classes, termed type I and type II, in accordance with the behaviour of their dispersion laws. A Goldstone boson is a member of either the first or the second class according as its energy, in the limit of long wavelengths, is proportional to an odd or an even power of its momentum, respectively. The major result then is that, if each Goldstone boson of type I is counted once and that of type II is counted twice, the total number of “bosons” so obtained is always equal to or greater than the number of symmetry generators that are spontaneously broken. An immediate corollary is the familiar result that for relativistically invariant theories the number of Goldstone bosons can never be less than the number of spontaneously broken generators. Throughout the proof of the above result particular emphasis is placed on theories which are not Lorentz invariant.     

Goldstone Boson Normal Coordinates

The phenomenon of spontaneous symmetry breaking is well known. It is known to be accompanied with the appearance of the “Goldstone boson”. In this paper we construct the canonical coordinates of the Goldstone boson, for quantum spin systems with short range as well as long range interactions. Received: 2 February 2000 / Accepted: 11 September 2000     

A method of η′ decay product selection to detect partial chiral symmetry restoration

In case of chiral U _A(1) symmetry restoration the mass of the η′ boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced [1], The η′ decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einstein correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum [2). Preliminary results strongly support the mass decrease of the η′ boson [3–5]. In this paper we propose a method to select pions coming from η′ decays. We investigate the efficiency of the proposed kinematical cut in several collision systems and energies with several simulators. We prove that our method can be used in all investigeted collision systems.     

Decaying warm dark matter and neutrino masses

Neutrino masses may arise from spontaneous breaking of ungauged lepton number. Because of quantum gravity effects the associated Goldstone boson - the majoron - will pick up a mass. We determine the lifetime and mass required by cosmic microwave background observations so that the massive majoron provides the observed dark matter of the Universe. The majoron decaying dark matter scenario fits nicely in models where neutrino masses arise via the seesaw mechanism, and may lead to other possible cosmological implications.     

Natural electroweak breaking from a mirror symmetry

We present "twin Higgs models," simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.     

Tagging of $ \eta{^\prime}$ decay products to analyze chiral restoration

In case of chiral U _A(1) symmetry restoration the mass of the h￠ \eta{^\prime} boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross-section is heavily enhanced. The h￠ \eta{^\prime} decays (through one of its decay channels) into five low-momentum pions. These pions will not contribute to measured Bose-Einstein correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results on Bose-Einstein correlation functions support the mass decrease of the h￠ \eta{^\prime} boson. In this paper we propose a method to select pions originating from h￠ \eta{^\prime} decays. We investigate the efficiency of the proposed kinematical cut in several collision systems and energies with several simulators. We prove that our method can be used in all investigated collision systems.     

Neutrino masses and family symmetry

Neutrino masses in the 100 eV?1 MeV range are permitted if there is a spontaneously broken global family symmetry that allows the heavy neutrinos to decay by Goldstone boson emission with a cosmologically acceptable lifetime. The family symmetry may be either abelian or nonabelian; we present models illustrating both possibilities. If the family symmetry is nonabelian, then the decay τ → μ + Goidstone boson or τ → e + oldstone boson may have an observable rate.