Charming Darwin: the evolution of QCD parameters across different species

We explore the prospects of measurements of spectral moments of inclusive charm decays with BESIII. The rich and uniquely clean data set of charm mesons and baryons at BESIII offers a unique laboratory to study the evolution of Heavy Quark Expansion (HQE) parameters across different charm hadron species and to shed light on the interplay between heavy quark dynamics and light quark effects. The HQE in terms of inverse powers of the heavy meson mass is well-established in beauty decays, however due to the lighter charm mass its applicability to charm remains an open question. To date no determination of the HQE parameters, the kinetic energy, chromomagnetic moment and Darwin terms, has been attempted. A particularly important role here is given to the Darwin and weak annihilation operators, whose values are important to predict lifetimes of heavy hadrons. Using a fast simulation for the BESIII detector response and predictions for spectral moments, we investigate the sensitivity to HQE parameters with today's and possible future data sets. In addition, we discuss the theory challenges for the HQE in charm and the experimental limitations. We further investigate the sensitivity of determining the CKM matrix element $|V_{cs}|$ with inclusive semileptonic charm decays.