Impact of Hadronic Resonances on $B\to K^{(*)}\tau^+\tau^-$ decays
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 $B\to K^{(*)}\tau^+\tau^-$ 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 $B\to K^{(*)}\mu^+\mu^-$ 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 $R(D^{(*)})$ and $B\to K^{(*)}\nu\nu$ 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.