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.

In an attempt to explain the recent measurements on the radiative decays of the vector-mesons (V→Pγ), we study the consequences of introducing a small admixture of SU (3) singlet piece in the electromagnetic current. We find that this leads to an excellent fit of the theory with the new measurements on theV→Pγ decays. However, this addition adversely affects the fit of the leptonic decays of the vector mesons (V→e⁺e⁻) and of the radiative decay of the pion (π→2γ). We conclude that the overall fit to the available data does not favour a large (>10%) admixture of the SU(3) singlet. The decay rates have been calculated in the vectormeson dominance model. At the hadronic vertex (VVP), we assume asymptotic nonet symmetry. The electromagnetic couplings (V−γ) are the ones appropriate to vector-mixing.

Relations among the magnetic moments of charmed and uncharmed baryons are derived in the framework of SU(4) and SU(8) symmetries. The SU(3) resultμ (Σ^o)=−μ(Λ) is not present in SU(4), but is obtained in SU(8). Higher order effects are further considered to improve the situation.

Mass relations among charmed and uncharmed baryons belonging to20 and20′ multiplets of SU(4) are derived in the framework of SU(8) symmetry, Spin singlet mass breaking interaction is found to give unsatisfactory results. Second order effects and spin triplet mass breaking interactions are studied to improve the situation.

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.

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8)_w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ*₃⁺⁺ and Θ⁻ are also discussed. SU(8)_w symmetry predictsα$$(\Omega \bar k) = 0$$, which is consistent with the experimental value.

Assuming that the anomalous magnetic moment interaction has the formaT₁¹ +bT₂² +cT₄⁴ +sT_α^α in SU(4), which may arise due to symmetry breaking or some other dynamical effects, we have obtained the magnetic moments and the transition moments of the ordinary and charmed baryons.

We use the quark model considerations of Federman, Rubinstein and Talmi and the relation (m_ψ/m_ϕ)≃(m_ϒ/m_ψ)≃(m_ϒ/m_ϒ) to compute the masses of beautiful and tasty vector mesons.

Using the consistency requirements arising from the Coleman-Glashow null result for ‘tadpole’-type symmetry-breaking, we obtain a simple method of accounting for the SU(3) symmetry-breaking at theBBP-vertex, without introducing any new parameters. The results obtained are in excellent agreement with the available numbers. We extend the analysis to the charmed baryon couplings in order to accommodate SU(4)-breaking.

Employing non-relativistic quasinuclear coloured quark model, which provides a unified description of mesons and baryons, masses of charmed andb-quark hadrons are studied. Various mass splittings are estimated, and mass relations among them are obtained.

The baryon magnetic moments in quark-diquark model are studied and it is found that the diquark (spin 1 and 0) mixing which may arise as a result of quarkgluon interaction inside a hadron, leads to a good agreement of theory with experiment.

The consequences of the variable pressure bag model for the nonleptonic decays of hyperons and Ω⁻ are investigated. Though the order of magnitude and the relative sign for the various decay amplitudes are correctly reproduced, the overall results are small by a factor of 2 to 4, indicating that the theoretical predictions are strongly dependent on the model parameters.

Ground-state baryon magnetic moments and nucleon axial vector coupling are calculated usingqcd inspired configuration mixing and relativistic corrections. Unlike earlier attempts, we incorporate a natural mass scale for quarks, taken as one third the nucleon mass for up and down quarks, and the strange quark mass suggested by the Lipkin’s sum rule. In the parameter-free non-relativistic limit, we find a fairly good fit, which improves upon including relativistic corrections.

Recent developments in the theory of heavy quarks have increased the prospects for the study of non-perturbative QCD in the weak decays of heavy mesons and baryons and for the reliable determination of some of the parameters of the Standard Model. It has been made possible due to the discovery of a spin-flavour symmetry for heavy quarks which arises in QCD when quark mass is taken to infinity. Certain properties in hadrons containing a heavy quark then become independent of its mass and spin. These ideas have tremendous impact on the phenemenology of heavy hadrons. In particular, these symmetries give rise to restrictive relations among weak decay amplitudes and reduce the number of independent form factors. By relating various matrix elements and fixing normalization of some matrix elements, the heavy quark symmetry has enhanced our predictive ability, allowing in some cases to bypass the difficulties of understanding hadronic structure.