Higgs scalars and vacuum instability inSU(2)L⊗SU(2)R⊗U(1)

Abstract

The ${\mathrm{SU}(2)}_{L}\ensuremath{\bigotimes}{\mathrm{SU}(2)}_{R}\ensuremath{\bigotimes}\mathrm{U}(1)$ model of weak and electromagnetic interactions requires a minimum of two Higgs multiplets, $\ensuremath{\Phi}$ and $P$, to have the residual electromagnetic U (1) symmetry after the spontaneous symmetry breaking. With this minimum number of Higgs multiplets, we study the existence of a metastable vacuum and the corresponding limits on the masses of Higgs bosons using the effective potential in the one-loop approximation. Demanding that this model have the same neutrino neutral-current interactions as those of the Weinberg-Salam model and using the available phenomenological information, we get the minimum value for the sum of the squares of masses, ${M}_{\ifmmode\pm\else\textpm\fi{}}$, of two of the neutral Higgs bosons in terms of a parameter which involves the mixing of $\ensuremath{\Phi}$ and $P$, assuming a stable asymmetric vacuum exists. Under the assumption that the ${(\mathrm{mass})}^{2}$ matrix of the Higgs bosons is diagonal, we obtain ${(M_{+}^{}{}_{}{}^{2}+M_{\ensuremath{-}}^{}{}_{}{}^{2})}^{\frac{1}{2}}>11.4$ Gev. No limit can be placed on the other Higgs bosons with the presently available information.