Revisiting Inclusive Decay Widths of Charmed Mesons

TL;DR

This paper uses the Heavy Quark Expansion to analyze charmed meson decay widths, incorporating new non-perturbative results and the Darwin operator, achieving good experimental agreement for some ratios but underestimating total decay rates.

Contribution

First comprehensive calculation of Darwin operator effects in non-leptonic charm decays using updated non-perturbative matrix elements within HQE framework.

Findings

Good agreement with experiment for lifetime ratios and semileptonic decay rates.

Underestimation of total decay rates for D0 and D+ mesons.

Predictions for SU(3)_F breaking ratios are closer to one than experimental values.

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.