Low-mass parity restoration, weak-interaction phenomenology, and grand unification

Abstract

The question of low-energy restoration of parity is examined using a left-right-asymmetric model implied by the gauge group $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{B\ensuremath{-}L}$ with ${g}_{L}g{g}_{R}$, both from a phenomenological point of view and also exploiting the possibility that such an asymmetry may be a consequence of two-stage symmetry breaking of $\mathrm{SU}{(2)}_{R}$ allowed in the SU(16) grand unification scheme. We carry out all the charged- and neutral-current tests with somewhat increased errors of the measured values of neutral-current parameters. The phenomenological asymmetric model passes all the tests permitting $1\ensuremath{\le}{(\frac{{g}_{L}}{{g}_{R}})}^{2}\ensuremath{\le}2$ and $0.23\ensuremath{\le}{{sin}^{2}\ensuremath{\theta}}_{W}\ensuremath{\le}0.29$, where the case $\frac{{g}_{L}}{{g}_{R}}=1$ corresponds to the symmetric model investigated by Rizzo and Senjanovic. Whereas low-energy parity restoration and low-mass gauge bosons may be possible in the symmetric model, the phenomenological asymmetric model allows a low-mass right-handed charged gauge boson (86-230 GeV) and a low-mass neutral boson (190-455 GeV), in addition to the two gauge bosons of first generation, but no parity restoration. It is shown that all the results of analysis of the phenomenological asymmetric model for the case of no mixing between the left- and right-handed charged gauge bosons still hold true in the case where the left-right asymmetry arises out of two-stage symmetry breaking of $\mathrm{SU}{(2)}_{R}$ allowed by SU(16) g\ifmmode \acute{r}\else \'{r}\fi{}and unification, but only with the replacement of the charged right-handed boson by a heavier one (g ${10}^{4}$ GeV). The SU(16) interpretation of left-right asymmetry and the available charged- and neutral-current data allows the observation of the second neutral boson together with the two gauge bosons of first generation, but no restoration of parity at ISABELLE energies. However, the parity restoration, if any, may be possible at energies \ensuremath{\gtrsim}${10}^{4}$ GeV. Several other observable distinctions of the asymmetric model from the standard one and the symmetric model with respect to the allowed regions and upper bounds on the allowed values of ${{sin}^{2}\ensuremath{\theta}}_{W}$ and the zeros of the neutral-current parameters and the variation of the second-neutral-$Z$-boson mass as functions of ${{sin}^{2}\ensuremath{\theta}}_{W}$ are pointed out. One of the particularly new features observed in this analysis is that for a large but fixed value of the coupling-constant ratio, the second-neutral-$Z$-boson mass increases with ${{sin}^{2}\ensuremath{\theta}}_{W}$.