Spontaneous breaking of globalB−Lsymmetry and matter-antimatter oscillations in grand unified theories

Abstract

We explore the consequences of the hypothesis that $B\ensuremath{-}L$ symmetry, which is exact in the standard model based on the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(3)}_{c}$ gauge group and its extension to the minimal SU(5) theory, is a spontaneously broken global symmetry. This results in possibly observable rates for $\ensuremath{\Delta}(B\ensuremath{-}L)=0$, $\ensuremath{\Delta}B=2$ hydrogen-antihydrogen transitions and double proton decay $\mathrm{pp}\ensuremath{\rightarrow}{e}^{+}{e}^{+}({\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+})$ and $\ensuremath{\Delta}(B\ensuremath{-}L)\ensuremath{\ne}0$, $\ensuremath{\Delta}B=2$ neutron-antineutron mixing and $p+n\ensuremath{\rightarrow}\ensuremath{\pi}'\mathrm{s}$; furthermore, a relation between the transition times ${\ensuremath{\tau}}_{\mathrm{H}\ensuremath{-}\overline{\mathrm{H}}}$, ${\ensuremath{\tau}}_{n\ensuremath{-}\overline{n}}$, Majorana neutrino mass, and the mass of a doubly charged Higgs particle ${\ensuremath{\Delta}}^{++}$ emerges. At the level of $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(3)}_{c}$, for ${\ensuremath{\tau}}_{n\ensuremath{-}\overline{n}}\ensuremath{\simeq}{10}^{7}$ sec and ${m}_{{\ensuremath{\Delta}}^{++}}\ensuremath{\simeq}20$ GeV, we predict ${\ensuremath{\tau}}_{\mathrm{H}\ensuremath{-}\overline{\mathrm{H}}}\ensuremath{\simeq}{10}^{3}$ yr and ${\ensuremath{\tau}}_{\mathrm{pp}}\ensuremath{\simeq}{10}^{31}$ yr, both of which are experimentally testable numbers. The embedding of our model in SU(5) is discussed in detail, with the analysis of ${\ensuremath{\tau}}_{p}$ and ${{sin}^{2}\ensuremath{\theta}}_{W}$ besides matter oscillations.