A signal of new physics from measuring CP violation in $B_{d,s} \to μ^+ μ^-$

We analyze the possibility of observing CP violating effects in $B^0_{d,s} \to \mu^+ \mu^-$ decays in future B factory. The CP violating obervables are defined by taking into account the mixing of the neutral mesons, $B^0_{d,s}$ and $\bar{B}^0_{d,s}$. It is shown that in the approximation of $|\frac{q}{p}|$=1 the CP violation vanishes in SM. In a 2HDM with CP violating phases and MSSM the CP asymmetries depend on the parameters of models and can be as large as 40% for $B^0_d$ and 3% for $B^0_s$. An observation of CP asymmetry in the decay $B^0_d\to \mu^+\mu^-$ would unambiguously signal the existence of new physics.