The Heavy Quark Expansion for Inclusive Semileptonic Charm Decays Revisited

Abstract

The Heavy Quark Expansion (HQE) has become an extremely powerful tool in flavor physics. For charm decays, where the expansion parameters ${\alpha }_s(m_c)$ and ${\Lambda }_{\mathrm{QCD}}/m_c$ are bigger than for bottom decays, it remains to be seen if the HQE can be applied with similar success. Nevertheless, to make optimal use of the plethora of data already available and coming in the near future, a better understanding of HQE for charm decays is crucial. This paper discusses in detail how the HQE for charm decays is set up, what is the role of four-quark (weak annihilation) operators and how this compares to the well understood bottom decays. Subtleties concerning radiative corrections and the charm mass scheme are briefly discussed. An experimental study of the relevant HQE hadronic matrix elements will then show if the HQE expansion for charm converges well enough. Besides serving as an important cross check for inclusive $B$ decays, in the end, this study might open the road for inclusive $|V_{cs}|$ and $|V_{cd}|$ extractions.

arXiv comment27 pages

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Cited by in corpus (12)

• Revisiting Inclusive Decay Widths of Charmed Mesons
• Lifetimes of singly charmed hadrons
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• Measurement of the absolute branching fraction of inclusive semielectronic $D_s^{+}$ decays
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• Inclusive Semileptonic $b\to c\ell \bar{\nu }$ Decays to Order $1/m_b^5$
• Alternative Treatment of the Quark Mass in the Heavy Quark Expansion
• Charming Darwin: the evolution of QCD parameters across different species
• Theory of Inclusive B Decays
• Completing $1/m_b^3$ corrections to non-leptonic bottom-to-up-quark decays
• Measurement of the Ratio of Partial Branching Fractions of Inclusive $\overline{B}\to X_u\ell \overline{\nu }$ to $\overline{B}\to X_c\ell \overline{\nu }$ and the Ratio of their Spectra with Hadronic Tagging
• Standard Model predictions for Lepton Flavour Universality ratios of inclusive semileptonic $B$ decays