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arXiv · 2603.17900

$K \pi$ scattering as a step towards $B \to K^* \ell^+ \ell^-$ from Lattice QCD

Felix Erben·Matthew Black·Peter Boyle·Matteo Di Carlo·Vera Gülpers·Maxwell T. Hansen·Nelson Pitanga Lachini·Rajnandini Mukherjee·Antonin Portelli·J. Tobias Tsang
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Abstract

Rare $b\to s\ell^+\ell^-$ decays provide some of the most sensitive tests of the Standard Model and require precise and systematically improvable hadronic input from lattice QCD. For the phenomenologically important channel $B\to K^*\ell^+\ell^-$ this entails a first-principles treatment of a resonant $K\pi$ final state together with controlled heavy-quark dynamics. We present the status of a new exploratory lattice calculation that combines a variational determination of finite-volume $K\pi$ states with the $1+J\to2$ finite-volume formalism to access the relevant matrix elements. The computation is carried out on an RBC/UKQCD domain-wall fermion ensemble with $a^{-1} \approx 2.7\,\mathrm{GeV}$ and employs a dual heavy-quark strategy, using both a relativistic heavy-quark action tuned to the physical $b$ mass and domain-wall heavy masses extrapolating from charm. All correlation functions are computed using (stochastic) distillation, providing a versatile setup that supports a broad range of heavy-to-light transitions into resonant final states. We show first two-point results for the $K^*\leftrightarrow K\pi$ system and discuss the accessible kinematic region, which allows for a controlled study at high $q^2$. The outlook for extending the calculation to lower $q^2$ and for incorporating effects from charmonium resonances is outlined.

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Felix Erben, Matthew Black, Peter Boyle, Matteo Di Carlo, Vera Gülpers, Maxwell T. Hansen, Nelson Pitanga Lachini, Rajnandini Mukherjee, Antonin Portelli, J. Tobias Tsang. 2026-03-18. $K \pi$ scattering as a step towards $B \to K^* \ell^+ \ell^-$ from Lattice QCD. https://arxiv.org/abs/2603.17900

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