Mapping quark-level kinematics to hadrons in a new hybrid model of semileptonic $B$ meson decays
The need to map parton-level processes to color-neutral hadrons in a way that respects quark-hadron duality arises in several areas of physics, including in the semileptonic decays of $B$ mesons. Integrated over large regions of phase space, the quark-level and hadron-level quantities are expected to be equal. However, the breakdown of duality is manifest at low hadron-system invariant masses, where discrete resonances dominate. In practice, this means independent simulations of decays to low-lying resonances and to higher-mass hadronic systems must be merged into a coherent model. We present a novel method to combine these resonant and non-resonant components in simulations of inclusive $b \to u\ell\nu$ decays that uses an optimal transport algorithm. The method currently used in measurements of inclusive semileptonic $B$ decay branching fractions introduces unphysical features in kinematic spectra such as large discontinuities and negative yields. The optimal transport method solves both of these issues and can be easily implemented in experimental studies of $B \to X_u \ell \nu$ decays.