The Heavy Quark Expansion for Inclusive Semileptonic Charm Decays Revisited

TL;DR

This paper revisits the application of the Heavy Quark Expansion to charm decays, analyzing its setup, challenges, and potential for extracting CKM matrix elements, with implications for flavor physics.

Contribution

It provides a detailed discussion of the HQE framework for charm decays, compares it to bottom decays, and explores its convergence and potential for CKM element extraction.

Findings

Analysis of HQE setup for charm decays

Comparison of four-quark operator roles in charm and bottom decays

Discussion on radiative corrections and mass schemes

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 $\Lambda_{\rm QCD}/m_c$ 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.