One-Loop QCD Corrections to $\bar{B}\to X_c \ell \barν_\ell$ in and Beyond the Standard Model

TL;DR

This paper addresses precise predictions for inclusive $\bar{B} \to X_c \ell \bar{\nu}_\ell$ decays in the presence of new physics, by computing one-loop QCD corrections to the full set of dimension-six WET operators at leading power in the HQE. The authors derive analytic $\mathcal{O}(\alpha_s)$ expressions for the first three moments of the lepton-energy, hadronic invariant mass, and dilepton invariant mass distributions, including NP contributions, and present a complete framework for constructing normalized moments with various kinematic cuts. They implement a thorough calculation using dimensional regularization, BMHV treatment of $\gamma^5$, and IBP reduction to master integrals, delivering structure functions $w_i$ from which observables are built. A detailed numerical analysis demonstrates the impact of the corrections on central moments, provides a parametric NP decomposition, and corroborates tensions in the CLEO $q^2$ data, highlighting the importance of updated measurements and global NP fits. The work supplies analytic expressions and numerical tables (in the kinetic scheme) to facilitate precise phenomenology and global constraints on beyond-Standard-Model physics in inclusive $b \to c \ell \bar{\nu}$ transitions.

Abstract

We compute one-loop QCD corrections to the triple differential width of the inclusive decay $\bar{B} \to X_c \ell \barν_\ell$ including contributions from all relevant dimension-six operators in the Weak Effective Theory (WET), at leading power in heavy quark expansion. Furthermore we derive for the first time up to order $\mathcal{O}(α_s)$ analytic expressions for the first three moments of the distribution in the lepton energy, hadronic invariant mass and dilepton invariant mass, in the presence of beyond the Standard Model contributions from the WET.

Figures (6)

• Figure 1: Tree level contribution to $T_{\Gamma\Gamma'}$ where the square dot denotes an insertion of $\Gamma M_\Gamma$ and the round dot denotes an insertion of $\gamma^0 M_{\Gamma'}^\dagger \Gamma^{\prime\dagger} \gamma^0$.
• Figure 2: One-loop diagrams in QCD for $T_{\Gamma\Gamma'}$ where the square dot denotes an insertion of $\Gamma M_\Gamma$ and the round dot denotes an insertion of $\gamma^0 M_{\Gamma'}^\dagger \Gamma^{\prime\dagger} \gamma^0$. The dashed lines represent the injected momentum.
• Figure 3: $q^2$ spectrum at LO (dashed) and NLO (solid). The contributions are labelled according to a decomposition analogous to \ref{['eq:xidec']}. The coefficient of the tensor term has been divided by 10 for presentation purposes, while the function $\xi_{RR}$ is not shown as it is identical to $\xi_{\rm SM}$.
• Figure 4: Plots for the several $\xi_i$ contributions to the lepton energy moments (upper panels) and hadronic invariant mass moments (lower panels). Different colours stand for different $\xi_i$, defined in \ref{['eq:xidec']}. Dashed lines stand for LO while solid lines for NLO.
• Figure 5: Plots for the several $\xi_i$ contributions to the $q^2$ moments with a lower cut on the lepton energy (upper panels) or on $q^2$ (lower panels). Different colours stand for different $\xi_i$, defined in \ref{['eq:xidec']}. Dashed lines stand for LO while solid lines for NLO.