Eur. Phys. J. C (2025) 85: 1011
https://doi.org/10.1140/epjc/s10052-025-14691-z

Regular Article - Theoretical Physics

Data determination of HQET parameters in inclusive charm decays

¹ School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
² Frontiers Science Center for Rare Isotopes, and School of Nuclear Science and Technology, Lanzhou University, 730000, Lanzhou, China
³ Physics Department and McDonnell Center for the Space Sciences, Washington University in St. Louis, 63130, St. Louis, MO, USA

^a qqin@hust.edu.cn

Received: 5 March 2025
Accepted: 29 August 2025
Published online: 17 September 2025

Abstract

This work delves into the phenomenology of electronic inclusive decays of D mesons, encompassing $D^0,D^{+},D_s^{+}\to X{e}^{+}\nu$. The theoretical formulas for the decay widths and electron energy moments of these decays are presented as expansions with powers of ${\alpha }_s$ and ${\mathrm{\Lambda }}_{\text{QCD}}/m_c$. Remarkably, the expansion exhibits excellent convergence properties when we choose the 1S mass scheme for charm. The formulas are subsequently fitted to experimental data, and the D meson matrix elements of operators in the heavy quark effective theory are hence determined by data for the first time, including $$\begin{array}{cc}\hfill {\mu }_{\pi }^2(D^{0,+})& =(0.08\pm 0.05){\text{GeV}}^2,\hfill \\ \hfill {\mu }_{\pi }^2(D_s^{+})& =(0.10\pm 0.07){\text{GeV}}^2,\hfill \\ \hfill {\mu }_G^2(D^{0,+})& =(0.33\pm 0.03){\text{GeV}}^2,\hfill \\ \hfill {\mu }_G^2(D_s^{+})& =(0.44\pm 0.06){\text{GeV}}^2,\hfill \\ \hfill {\rho }_D^3(D^{0,+})& =(-0.003\pm 0.002){\text{GeV}}^3,\hfill \\ \hfill {\rho }_D^3(D_s^{+})& =(-0.004\pm 0.002){\text{GeV}}^3,\hfill \\ \hfill {\rho }_{\mathit{LS}}^3(D^{0,+})& =(0.004\pm 0.002){\text{GeV}}^3,\hfill \\ \hfill {\rho }_{\mathit{LS}}^3(D_s^{+})& =(0.005\pm 0.002){\text{GeV}}^3,\hfill \end{array}$$1These determined parameters will play a crucial role as inputs in various physical quantities, including D meson lifetimes.