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Inclusive and exclusive semileptonic decays of heavy mesons on the lattice

We report the recent progress from our group in extracting observables of both inclusive and exclusive semileptonic heavy-meson decays directly from lattice QCD four-point correlators. On the inclusive side, we illustrate how to estimate the systematic uncertainties from omitted higher-order terms and non-zero smearing of the kernel approximation, building on two important features of the Chebyshev expansion. On the exclusive side, we perform BCL parameterizations of the pseudoscalar to pseudoscalar form factors and compare the fitted coefficients with those from earlier results by HPQCD. We also perform a HQET-based parameterization of the P-wave form factors to shed new light on the 1/2-vs-3/2 puzzle. This work constitutes a step toward a unified lattice treatment of inclusive and exclusive semileptonic decays, relevant for the Vcb puzzle. In this study, we use lattice ensembles from the RBC/UKQCD collaboration for numerical investigations. Future developments from our group will focus on the control of other systematic effects for inclusive decays and investigations of other techniques with reduced statistical errors to extract exclusive contributions from lattice four-point correlators.