Theoretical analysis of $B^0 \to \phi \ell^+ \ell^-$ annihilation-type decay

In the Standard Model (SM), the $b \to s$ and $b \to d$ flavor-changing neutral currents (FCNC), being loop-induced, are standard experimental channels for testing the SM precisely and searching for possible physics beyond the SM. Purely annihilation decays of $B$-mesons are of significant interest as they are extremely suppressed in the SM and New Physics effects can increase substantially their decay widths. Radiative and semileptonic decays with the $\phi$-meson production, being a subject of experimental searches at the LHC and KEKB, are typical examples of annihilation-type processes. In the paper, the annihilation-type semileptonic $B^0 \to \phi \ell^+ \ell^-$ decay, where $\ell$ is a charged lepton, will be discussed, and SM theoretical predictions without including contribution from $\omega$-$\phi$ mixing for the branching fraction based on the effective electroweak Hamiltonian approach will be given. The dependence of the branching fraction on the choice of models of the $B$-meson distibution amplitude included in the branching fraction by means of the first inverse moments is investigated. The total branching fraction of the decay $Br\sim 10^{-12}$ is three orders of magnitude less than the limit obtained by the LHCb collaboration, however, there are mechanisms for increasing this value that require further research.