Moments of semileptonic B decay distributions in the 1/m_b expansion

TL;DR

This work provides OPE-based predictions for lepton-energy and hadronic-mass moments in inclusive $B\to X_c\ell\nu$ decays with a lepton-energy cut, employing a Wilsonian renormalization scheme at $\mu=1$ GeV and avoiding any $1/m_c$ expansion. By using running heavy-quark masses $m_b(\mu)$, $m_c(\mu)$ and the kinetic parameter $\mu_\pi^2(\mu)$, the authors obtain perturbative corrections that are small and well-behaved, and they introduce modified hadronic moments ${\cal N}_X^2$ to improve sensitivity to higher-dimension nonperturbative parameters. The paper provides numerical results based on a baseline parameter set and offers a code-ready framework to study theoretical uncertainties, enabling more precise extractions of heavy-quark parameters and $|V_{cb}|$ once experimental data constrain higher moments. It also discusses uncertainties from perturbative coefficients, nonperturbative matrix elements, and potential intrinsic charm, and recommends measuring higher hadronic moments to tighten bounds on higher-dimension HQ parameters.

Abstract

We report the OPE-based predictions for a number of lepton energy and hadronic mass moments in the inclusive semileptonic B -> X_c \ellνdecays with a lower cut on the charged lepton energy. We rely on the direct OPE approach where no expansion in the charm mass is employed and the theoretical input is a limited set of underlying OPE parameters including m_b and m_c. A Wilsonian treatment with a `hard' cutoff is applied using running low-scale masses m_Q(μ) and kinetic expectation value μ_π^2(μ). This leaves for perturbative corrections only genuinely short-distance effects and makes them numerically small. Predictions are also given for the modified hadronic moments of the kinematic variable \cal N_X^2 which is a combination of M_X^2 and E_X. Measurement of such moments would allow a more reliable extraction of higher-order nonperturbative heavy quark parameters from experiment.

Figures (3)

• Figure 1: Average hadronic invariant mass squared $\langle M_X^2\rangle$ at different lepton energy cuts, for the heavy quark parameters of Eq. (\ref{['120']}).
• Figure 2: Second invariant mass moment $\langle [M_X^2\!-\!\langle M_X^2\rangle]^2\rangle$ (red) and second modified hadronic moment $\langle [{\cal N}_X^2\!-\!\langle {\cal N}_X^2\rangle]^2\rangle$ (blue), in the same setting.
• Figure 3: Different hadronic mass moments $\langle M_X^\nu\rangle^{\frac{1}{\nu}}$ for $\nu\!=\!1$ to $6$ (from lowest to highest), vs. lepton energy cuts; heavy quark parameters as in Eq. (\ref{['120']}).