Hunting for B + → K + τ + τ - imprints on the B + → K + μ + μ - dimuon spectrum

Abstract

We investigate the possibility of indirectly constraining the $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}$ decay rate using precise data on the $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ dimuon spectrum. To this end, we estimate the distortion of the spectrum induced by the $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}\to K^{+}{\mu }^{+}{\mu }^{-}$ re-scattering process, and propose a method to simultaneously constrain this (non-standard) contribution and the long-distance effects associated to hadronic intermediate states. The latter are constrained using the analytic properties of the amplitude combined with data and perturbative calculations. Finally, we estimate the sensitivity expected at the LHCb experiment with present and future datasets. We find that constraints on the branching fraction of $O\left({10}^{-3}\right)$ , competitive with current direct bounds, can be achieved with the current dataset, while bounds of $O\left({10}^{-4}\right)$ could be obtained with the LHCb upgrade-II luminosity.

Fig. 1

Diagrammatic representations of the long-distance contributions to $C_9^{\mu ,\mathrm{eff}}$. The left-hand side depicts the exchange of a single vector resonance. The graph on the right-hand side shows the contribution from two-particle intermediate states

Fig. 2

Real (solid) and imaginary (dashed) parts of the normalised hadronic two-particle contributions to $Y_{c\overline{c}}(q^2)$, as defined in Eq. (16)

Fig. 3

Example pseudodata expected from the full run II dataset collected by the LHCb experiment assuming the SM. The distribution expected if the $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}$ branching fraction were present at the current experimental limit of $2.25\times {10}^{-3}$ is overlaid