Theoretical analysis of the leptonic decays B → lll(ν)over bar>l: Identical leptons in the final state

We study the effects of identical leptons in the final state of the B+ -> l(+)l(-)l(+)(nu) over bar (l) decay. The amplitude of the process is described by the same form factors as the amplitude of the B -> lll'(nu) over bar (l)' decay for nonidentical leptons in the final state. However, the differential distributions are strongly different, as the B+ -> l(+)l(-)l(+)(nu) over bar (l) amplitude contains both the direct (M-a) and exchange (M-b) 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 M-a and M-b, dB(ab) 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.

Automated summary

We study the effects of identical leptons in the final state of B+ -> l(+)l(-)l(+)(nu) over bar (l) decay. We calculate a series of differential distributions and propose an interesting observable that can be measured experimentally. The interference between different diagrams can be neglected in the full kinematical region of this decay.