The recently discovered narrow peaks (theψ-particles) in e⁺e⁻ system at 3.105 and 3.695 GeV are interpreted as hadrons in a broken SU₄ symmetry scheme. A new additional additive quantum number, parachargeZ, is combined with the usual SU₃ quantum numbers in the group SU₄. Theψ (3.1) is assigned to a near ideally mixed15⊕1 multiplet of vector mesons (containing theρ) as theI=Y=0, charge conjugationC=−combination ofZ=±1.members. Theψ (3.7) is assigned correspondingly to another mixed15⊕1 multiplet containing theρ′ (1600). The hadronic electromagnetic interactions are modified by the addition of (non-minimal) anomalous pieces that can changeZ. The decays of theψ-particles are discussed. New enlarged SU₄ multiplets of other hadrons are proposed. Tests of our scheme are put forward. The most crucial test will be the observation of two rather broad resonances in e⁺ e⁻ collisions with masses around 4.2 GeV and 5.1 GeV. Another prediction is the presence of energetic photons in the decays of theψ-particles. Important results concerning the recently observed phenomena in the process e⁺e⁻→hadrons follow in this scheme.

A universal theory of weak interaction is constructed by exploiting an analogy inherent between the four leptons and the four quarks of the paracharge scheme proposed recently to deal with theψ-particles. The leptons (ν_e,ν_μ,e_L,μ_L) are assigned to the representation (1/2, 1/2) and the quarks (p, n_W)_L and (χ,λ_W)_L to the representations (1/2, 0) and (0, 1/2), respectively, of the groupO₄ (L stands for the left-handed projections and W for the Cabibbo rotated orthogonal combinations ofn andλ). Universality is ensured by embedding the above (weak)O₄ into thesimple groupO₅ and gauging the latter. In the final effective weak interaction, besides the conventionalV-A charged-current part, a (V-A)neutral current interaction (consistent with the present data) is naturally present. The neutral current has a$$\bar \nu _\mu \nu _\mu $$ term but no$$\bar \nu _e \nu _e $$ term, thus providing a crucial test of the theory.

A systematic semiquantitative account of all aspects of the strong and electromagnetic interactions of all the newly discovered hadronic states (theψ’s, theχ’s, etc.) is presented within the framework of the paracharge scheme. Extensions of ideas familiar from the SU₃ classification scheme to SU₄ are shown to provide an understanding of the new states seen in the decays ofψ (3.1) andψ′ (3.7), including their masses and gross decay characteristics. The decays ofψ (3.1) andψ′ (3.7) themselves are studied in some detail. Since these are of electromagnetic origin in the scheme, their electromagnetic mixing with the resonance at 4.15 GeV (theP-state of the scheme) is important. Once this is taken into account, the resulting picture is in excellent agreement with available data.

A comprehensive discussion of the unitarity bounds on inclusive angular distributions, given the elastic amplitudes and the integrated inelastic cross section, is presented. The role played by the latter constraint in improving the bound is studied in detail. Calculations are made forπ^±p →p (inclusive) at 6 GeV/c.

An SU₃ gauge model of weak interactions, which generates the Cabibbo suppression spontaneously and consistently, is presented. Out of the eight currents, a triplet couples to relatively light gauge bosons and satisfies the commutation relations of the SU₂-universality algebra of Gell-Mann. The other five couple to necessarily very massive gauge bosons. The leptons have a realistic mass spectrum and the (bare) quarks are massless. The theory as it stands does not encompass charm and cannot suppress strangeness changing neutral currents; both these deficiencies require a larger gauge group for their correction.

A master scaling law is proposed for arbitrary distributions in arbitrary hadronic processes of which all experimentally established scaling laws (and a host of others, easily deduced as occasion demands) are special cases.

A gauge model for the weak interactions of the leptons (v_e, e, μ, ν_μ) and the quarks (q_p, q_n,qλ,q_p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW^±) and two neutrals are necessarily heavier than the third (W⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless.

The dominant charged weak currents coupling toW^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions.

The Cabibbo angleϑ_c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ_c = ±π/8, | tanϑ_c | = √2 − 1 (an alternative solution | tanϑ_c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ_c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ_c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ_c | = 0.4.

It is proved that the groupG=SU(n) has a decompositionG=FCF whereF is a maximal abelian subgroup andC is an (n − 1)² parameter subset of matrices. The result is applied to the problem of absorbing the maximum possible number of phases in the mass-diagonalising matrix of the charged weak current into the quark fields; i.e., of determining the exact number of CP-violating phases for arbitrary number of generations. The inadequacies of the usual way of solving this problem are discussed. Then=3 case is worked out in detail as an example of the constructive procedure furnished by the proof of the decomposition theorem.

In radiative decays of charged leptons induced by non-degenerate neutrino masses and consequent lepton flavour-mixing, the dominant suppression factor at the 1-loop level is (Σ m_a²)/m_W²,m_a being the mass of theath neutrino. We show that this suppression factor is presentin all orders in a class of models including the standard model.