Impact of Hadronic Resonances on $B\to K^{(\ast )}{\tau }^{+}{\tau }^{-}$ decays

Abstract

Neutral-current semileptonic $B$ decays are plagued by hadronic resonances across the dilepton invariant-mass squared spectrum, $q^2$. For light leptons, $\ell =e,\mu$, these resonances can be avoided with suitable $q^2$ cuts. This strategy is less straightforward for $\tau$ modes, where missing energy from the $\tau$ decay makes $q^2$ difficult to reconstruct. In fact, while Belle II is able to discriminate between different regions in $q^2$ due to its clean environment, this is not directly possible in a hadronic one. Therefore, the interpretation of $b\to s{\tau }^{+}{\tau }^{-}$ measurements from e.g. LHCb, CMS requires the description of these resonant effects. In this article, we adopt a different strategy by including the resonant contributions (in particular from $\psi (2S)$) into our predictions for $B\to K^{(\ast )}{\tau }^{+}{\tau }^{-}$ decays, instead of avoiding them. We provide predictions for different initial kinematic points ($4m_{\tau }^2,14.18$GeV${}^2$ and $15$GeV${}^2$) that can be convenient for LHCb, CMS and Belle II. For this, we use a data-driven approach based on the LHCb measurements of $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$ decays. Including the resonances and integrating over the full $q^2$ range substantially enhances the Standard Model predictions. However, for sufficiently large New Physics, motivated by the current tensions in $R(D^{(\ast )})$ and $B\to K^{(\ast )}\nu \nu$ decays, the short-distance contribution becomes comparable to or even exceeds the resonant one. This highlights two advantages of this strategy: it exploits the additional phase space associated with the resonant regions to probe large New Physics contributions, and it enables the use of hadron-collider data, where the resonances cannot be resolved. We further quantify how including or neglecting the resonances affects the total branching ratio as a function of New Physics contributions and, equivalently, of the experimental precision.

Comments: 10 pages, 4 figures, 3 appendices