An empirical mass formula is tested for the basic fermion sequences of charged quarks and leptons. This relation is a generalization of Barut’s mass formula for the lepton sequence (e, μ, τ......). It is found that successful mass extrapolation to the third and possibly to other higher generations (N>2) can be obtained with the first and second generation masses as inputs, which predicts the top quark massm_t to be around 20 GeV. This also leads to the mass ratios between members of two different sequences (i) and (i′) corresponding to the same higher generations (N>2).

It is shown that a non-relativistic power-law potential model for the heavy quarks in the form V(r)=Ar^v+V₀, (A, ν>0) acquires relativistic consistency in generating Dirac bound states of $$Q\bar Q$$-system in agreement with the Schrödinger spectroscopy if the interaction is modelled by equally mixed scalar and vector parts as suggested by the phenomenology of fine-hyperfine splittings of heavy quarkonium systems in a non-relativistic perturbative approach.

Incorporating chiral-symmetry to the potential model of quarks with confining potentialU(r)=1/2 (1 +γ°)ar² with m_q=10 MeV anda=2.273 fm⁻³ that gives a reasonable quark-core contribution to μ_p, 〈r² 〉_p^1/2 andg_A, the quark-pion coupling constant for quarks in a nucleon is estimated.G_qqπ²/4π obtained between 0.4 and 0.5 is consistent with those extracted from experimental vector meson decay-width ratios by Suzuki and Bhaduri. The nucleon-pion coupling constantG_NNπ²/4π comes out to be of the order of 13.1 in reasonable agreement with the experimental value.

Incorporating the lowest-order pionic correction, the magnetic moments of the nucleon octet have been calculated in a chiral potential model. The potential, representing phenomenologically the nonperturbative gluon interactions including gluon self-couplings, is chosen with equally mixed scalar and vector parts in a power-law form. The results are in reasonable agreement with experiment.

Pion mass and its decay constant have been studied in a chiral symmetric potential model of independent quarks. The non-perturbative multi-gluon interaction which is responsible for quark confinement in a hadron is phenomenologically represented here by an effective potentialU(r) = 1/2(1 +γ⁰)(ar² +V₀). The residual interactions due to quark-pion coupling arising out of the chiral symmetry preservation and that due to quark-gluon coupling arising out of single-gluon exchange are treated as low order perturbations. The centre of mass correction is also taken into account appropriately. This leads to the$$(q\bar q) - pion$$ mass in consistency with that of the PCAC-pion and the pion decay constant in reasonable agreement with experiment.

Magnetic moments of decuplet baryons have been calculated in a relativistic independent quark model with a phenomenological potential in equally mixed scalar-vector harmonic form. Such a model has been successful in describing wide ranging hadronic phenomena in mesonic and baryonic sectors. Using the solutions of the constituent quark orbitals with the model parameters taken from its earlier applications, the magnetic moments of decuplet baryons Δ⁺⁺ and Ω⁻ have been obtained which are in good agreement with the available experimental data. However, the agreement is found to be much better when the magnetic moment ratios such as μ_δ++/μ_p and μ_Ω-/μ_Λ are considered. Model predictions for the magnetic moments of other decuplet baryons together with the charge radii have also been calculated which may be verified in future experiments.

We investigate the weak leptonic decays of light and heavy pseudoscalar mesons in a relativistic quark model of independent quarks. We perform a static calculation of the decay constantf_M purely on grounds of simplicity. In order to minimize the possible uncertainty in the static calculation, we estimate the ratios of the decay constants which are found to be in good agreement, in the heavy flavor sector, with the predictions of other models available in the literature and existing experimental data. However, there is a noticeable discrepancy in the current prediction for pion decay constant which demonstrates the inherent limitations of the static approximation in the study of non-strange light mesons.

Considering the nucleon as consisting entirely of its valence quarks confined independently in a scalar-vector harmonic potential; unpolarized structure functions F₁(x, μ²) and F₂(x, μ²) are derived in the Bjorken limit under certain simplifying assumptions; from which valence quark distribution functions u_v(x, μ²) and d_v(x, μ²) are appropriately extracted satisfying the normalization constraints. QCD-evolution of these input distributions from a model scale of μ²=0.07 GeV² to a higher Q² scale of Q₀²=15 GeV² yields xu_v(x, Q₀²) and xd_v(x, Q₀²) in good agreement with experimental data. The gluon and sea-quark distributions such as G(x, Q₀²) and q_s(x, Q₀²) are dynamically generated with a reasonable qualitative agreement with the available data; using the leading order renormalization group equations with appropriate valence-quark distributions as the input.