Spontaneous CP violation and the B system

We investigate effects of spontaneous breakdown of CP in $B^0_{d,s}-\overline{B^0}_{d,s}$ systems in left-right symmetric models. Assuming that the left-right contribution to the $B^0-\overline{B^0}$ matrix element $M_{12}$ can be at most equal to the standard model one we obtain a new lower bound, $M_H\gsim 12$ TeV, on the flavour changing Higgs boson mass. Most importantly, the convention independent parameter $Re(\overline{\epsilon}_B),$ which measures the amount of $\Delta B=2$ CP violation, can be enhanced by a factor of four or more for $B^0_d$ and almost by two orders of magnitude for $B^0_s$ systems when compared with the Standard Model predictions. Therefore, interesting possibilities to observe indirect CP violation in the $B$ system are open in the planned facilities.