Theoretical analysis of the leptonic decays B →ℓℓℓ ν ¯ ℓ: Identical leptons in the final state

We study the effects of identical leptons in the final state of the B+→ℓ+ℓ-ℓ+ν¯ℓ decay. The amplitude of the process is described by the same form factors as the amplitude of the B→ℓℓℓ′ν¯ℓ′ decay for nonidentical leptons in the final state. However, the differential distributions are strongly different, as the B+→ℓ+ℓ-ℓ+ν¯ℓ amplitude contains both the direct (Ma) and exchange (Mb) diagrams. We calculate a number of the differential distributions. In particular, we propose an interesting observable that can be readily measured experimentally: the differential distribution over the invariant mass of the pair of leptons of the same charge, ℓ+ℓ+. The good news is that the interference between Ma and Mb, dBab is found to be at the level of less than 1% in all considered differential distributions and therefore can be neglected in the full kinematical region of this decay.