Revisiting Inclusive Decay Widths of Charmed Mesons

Abstract

Determining for the first time the Darwin operator contribution for the non-leptonic charm-quark decays and using new non-perturbative results for the matrix elements of $\Delta C=0$ four-quark operators, including eye-contractions, we present a comprehensive study of the lifetimes of charmed mesons and inclusive semileptonic decay rates as well as the ratios, within the framework of the Heavy Quark Expansion (HQE). We find good agreement with experiment for the ratio $\tau (D^{+})/\tau (D^0)$, for the total $D_s^{+}$-meson decay rate, for the semileptonic rates of all three mesons $D^0$, $D^{+}$ and $D_s^{+}$, and for the semileptonic ratio ${\Gamma }_{sl}^{D^{+}}/{\Gamma }_{sl}^{D^0}$. The total decay rates of the $D^0$ and $D^{+}$ mesons are underestimated in our HQE approach and we suspect that this is due to missing higher-order QCD corrections to the free charm quark decay and the Pauli interference contribution. For the $SU(3{)}_F$ breaking ratios $\tau (D_s^{+})/\tau (D^0)$ and ${\Gamma }_{sl}^{D_s^{+}}/{\Gamma }_{sl}^{D^0}$ our predictions lie closer to one than experiment. This might originate from the poor knowledge of the non-perturbative parameters ${\mu }_G^2$, ${\mu }_{\pi }^2$ and ${\rho }_D^3$ in the $D^0$ and $D_s^{+}$ systems. These parameters could be determined by experimental studies of the moments of inclusive semileptonic $D$ meson decays.

50 pages, 18 Tables, 7 Figures

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• Dispersive constraints on fermion masses
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• Recent advances in charm mixing and $CP$ violation at LHCb
• Alternative Treatment of the Quark Mass in the Heavy Quark Expansion
• Revisiting quark-hadron duality for heavy meson non-leptonic decays in two-dimensional QCD
• Determination of Strong Coupling Constant from Inclusive Semileptonic Decays of Charmed Mesons
• Theory Motivation: What measurements are needed?
• Standard Model predictions for Lepton Flavour Universality ratios of inclusive semileptonic $B$ decays
• The strangest lifetime: A bizarre story of $\tau ({\Omega }_c^0)$