Sum rules for the baryon20, baryon20′ and meson 16-plet coupling constants in broken SU (4) and SU (3) symmetry

Sum rules for the coupling constants for D (20), B (20′) and P (16) are given taking into account first order breaking of SU (4) and SU (3) symmetries. The D (20) and B (20′) contain the usual 3/2⁺ baryon decuplet and 1/2⁺ baryon octet of SU (3), while the P (16) contains the usual pseudoscalar octet of pions, etc. These sum rules generalize the decuplet → octet + octet sum rules of broken SU (3 to a broken SU (4) symmetry scheme, in particular the charm SU (4) for hadrons. It is pointed out that, of the many sum rules, it may be possible to check some of them experimentally (see Section 5) and thus provide a test for an underlying SU (4 symmetry for strong interactions.     

ΔB = −ΔL, neutron →e−π+, e−K+, μ−π+ and μ−K+ decay modes in SU(2)L × SU(2)R × SU(4)col or SO(10)

It is stressed that within the simplest model SU(4) of color, unifying quarks with leptons, where B  L is a gauge symmetry, a spontaneous breaking of this symmetry leads naturally to baryonlepton decays like n→e^?k⁺, e^?K⁺, μ^?π⁺, μ^?K⁺ [in constant to SU(5) where B  L is not gauged]. Our mechanism is crucially tied to the presence of the Higgs multiplet (2, 2, 15) of SU(2) × SU(2) × SU(4), which is needed to account for the observed quarklepton mass ratios.     

Parity violating non-leptonic decays of hyperons and of charmed baryons in SU (8)

The parity violating non-leptonic decays of hyperons and of charmed baryons are discussed in the framework of SU (8) symmetry. Several relations in addition to the ones obtained earlier by using SU (4) symmetry and20″-dominance, are obtained. The assumption of20″-dominance at the SU (4) level is no longer required for explaining the non-leptonic decays of 1/2⁺ baryons.     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

Transition magnetic moments of J~P=3/2~+ decuplet to J~P=1/2~+ octet baryons in the chiral constituent quark model

In light of the developments of the chiral constituent quark model(χ~(CQM)) in studying low energy hadronic matrix elements of the ground-state baryons, we extend this model to investigate their transition properties.The magnetic moments of transitions from the J~P=3/2~+ decuplet to J~P=1/2~+ octet baryons are calculated with explicit valence quark spin, sea quark spin and sea quark orbital angular momentum contributions. Since the experimental data is available for only a few transitions, we compare our results with the results of other available models. The implications of other complicated effects such as chiral symmetry breaking and SU(3) symmetry breaking arising due to confinement of quarks are also discussed.     

A study of SU(3) × SU(2) × U(1) × U(1) as an intermediate energy subgroup of SO(10)

We analyze several patterns of symmetry breaking of SO(10) where SU(3)_c × SU(2) × U(1) × U(1) is an intermediate energy subgroup. Using constraints from the renormalization group and data from neutral-current experiments we show that if the only Higgs used in the low-energy breaking of the theory are those which can give mass to fermions then the possibility of a low intermediate mass scale is ruled out.     

Towards a finite N = 2 susy GUT

We consider finite, N = 2 supersymmetric GUTs based on gauge groups SU(n) and SO(n). As an example, we discuss a semirealistic model based on SO(12). We argue that in finite, N = 2 supersymmetric GUTs, gauge symmetry breaking should occur dynamically. We present a heuristic picture in which this is induced by soft, finiteness preserving SUSY breaking terms. The bound states formed cause a very rapid evolution of the SO(12) coupling constant and break SO(12) into SU(4)×SU(3)_C×U(1).     

Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model

Ward-Takahashi identities with composite fields are utilized to inverstigate (2+1) dimensional model with SU(2) four-fermion couplings.When SU(2) chiral symmetry is both explicitly and dynamically broken,fermion mass is dynamically generated and mass spectra of the bound states are obtained The properties of vector and axial-vector currents are discussed.It turns out that the bound state π_α acquires a mass and the axial-vector current is partially conserved,and the Goldberger-Treimab relation is approximately valid in the case of small fermion current masses.     

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.     

Can the SU(5) running be neglected in the minimal N = 1 Sugra model?

The radiative breaking of the electroweak symmetry is analysed in the minimal N = 1 supergravity model when the running of the parameters between the Planck and the grand unification scales is considered. The SU(5) running opens up the parameter space of the SU(2) × U(1) breaking solutions, and in particular all the values ߊ₀| > 3 are allowed. The SU(5) running will modify the structure of the low-energy mass spectra and will lead to the possibility of having realistic ones for very small values of the gravitino mass m_3/2. Indeed, if the SU(5) evolution is considered, no lower bound on m_3/2 is needed to obtain acceptable spectra.     

The kinematic and symmetry structure of e+e−→hadron pairs

The kinematic singularity and constraint free amplitudes for e⁺e^?→two particles which can have arbitrary spins are obtained in a simple closed form. The relationships of these amplitudes with the usual multipole form factors are given. It is noted that SU(6)_W and tests of ideas based on the Melosh transformation are liberated from their γN and πN arena and can be confronted with arbitrary targets and axcitations. The matrix elements or arbitrary meson pairs are then derived, rates are computed for pseudoscalar and vector meson production, and some tests of symmetry breaking mechanisms proposed. Extension to SU(4)[SU(8)_W] broken in the masses enables estimates of charmed particle production rates to be obtained. General features of πR final states suggest that scaling violation at small x may be connected with threshold phenomena as channels open up. A subtle difference between space-like and time-like regions is highted.     

THE SYMMETRY BREAKING OF THE SUPERSTRING-INSPIRED MODEL

By considering the one-loop radiative corrections,we discussed the symmetry breaking of a specific superstringinspired model based on the gauge group SU(3)_C×SU(2)_L×SU(2)_R×U(1)^′×U(1)^′′ We discussed phenomenologically the neutrino mass problem,and the value of the soft breaking parameters A,m and M at the scale Mx were given.     

THE CHIRAL SU(2)L SU(2)R σ-MODEL WITH MASSIVE π MESONS

The chiral SU(2)_L SU(2)_R σ-Model with both spontaneous and dynamical symmetry breaking is investigated and massive π mesons are obtained.The physical mechanism of how π mesons acquire mass is discussed.     

Adjoint representation admixture to weak nonleptonic decays in SU(4) and SU(8)

In order to remove some of the unsatisfactory features of the GIM model, we consider15-admixture in SU(4). ΔC=±ΔS decays remain unaffected. Lee-Sugawara sum-rule is obtained.15-admixture is extended then to63-admixture in SU(8). The most general Hamiltonian (H _w∼63⊕720⊕1232) in SU(8) is found to give Lee-Sugawara relation and Σ₊ ⁺=0 forS-wave decays of uncharmed baryons. Decay amplitude relations for ΔC=−1, ΔS=0 mode are obtained.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

Light singlet particles and their cosmological consequences in witten-type supersymmetric models

In a class of supersymmetric gauge models which generate a large mass scale from a supersymmetry breaking mass scale M through loop corrections, there exists generally a very light scalar particle which transforms like a singlet under SU(3)_c × SU(2)_L with no U(1) charge. Cosmological constraints on such a particle are so severe that an upper bound is set on possible values of supersymmetry breaking scale in this class of models as M ? 500 TeV provided that the large mass scale is 10¹⁵ GeV and the mass of the light scalar particle is generated in one-loop order. This bound holds even if the goldstino is not absorbed into the gravitino.     

SUSY GUT with automatic doublet-triplet hierarchy

A mechanism is suggested to resolve the problem of doublet-triplet hierarchy in the SU(5) SUSY GUT. In this mechanism, which we call “GIFT” (“Goldstones instead of fine tuning”), the doublets are pseudo-Goldstone bosons of a certain broken global symmetry of the superpotential. With supergravity as the source of SUSY breaking we show that the SU(2)_L×U(1)_Y→U(1)_em breaking as well as the mass of the lightest Higgs boson are due to the radiative corrections.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

SU(5) Higgs problem with adjoint + vector representations

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with $\text{5}$ and $\text{24}$ higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.