A unified theory of weak interactions
A gauge model for the weak interactions of the leptons (ve, e, μ, νμ) and the quarks (qp, qn,qλ,qp′) 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 angleϑc itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑc = ±π/8, | tanϑc | = √2 − 1 (an alternative solution | tanϑc | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑc; 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 | tanϑc | 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 | tanϑc | = 0.4.
Volume 94, 2020
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