Improved Determination of |V_{ub}| from Inclusive Semileptonic B-Meson Decays

TL;DR

This paper improves the theoretical determination of $|V_{ub}|$ from inclusive semileptonic $B$ decays by applying a two-step hybrid expansion to $B\to X_u\,l\,\nu$ with a dilepton invariant-mass cut $q^2>(M_B-M_D)^2$. It combines RG-improved perturbation theory with an operator-product expansion in a low-energy HQET framework, calculating the rate to subleading order in $\mu_c/m_b$ and next-to-leading order in $\alpha_s$, including resummation of leading power corrections. The authors show stability across different heavy-quark mass definitions (PS and Upsilon schemes) and report a central result $\text{Br}(B\to X_u l\nu) = (20.9 \pm 4.0)\,|V_{ub}|^2$, implying a $|V_{ub}|$ precision at the ~10% level. They provide a detailed error budget with the $b$-quark mass being the dominant source of uncertainty, highlighting the method's potential for robust CKM parameter extraction when the experimental cut is optimized.

Abstract

We reduce the perturbative uncertainty in the determination of |V_{ub}| from inclusive semileptonic B decays by calculating the rate of B -> X_u l nu events with dilepton invariant mass q^2>(M_B-M_D)^2 at subleading order in the hybrid expansion, and to next-to-leading order in renormalization-group improved perturbation theory. We also resum logarithmic corrections to the leading power-suppressed contributions. Studying the effect of different b-quark mass definitions we find that the branching ratio after the cut is Br(B -> X_u l nu)=(20.9+-4.0)|V_{ub}|^2, where the dominant error is due to the uncertainty in the b-quark mass. This implies that |V_{ub}| can be determined with a precision of about 10%.

Figures (2)

• Figure 1: One-loop graphs contributing to the hadronic tensor. The crossed circles represent insertions of the operators $O_i$ or $Q_j$. The solid squares in the last eight diagrams denote insertions of $O_{\rm kin}$ or $O_{\rm mag}$.
• Figure 2: Scale dependence of the $B\to X_u\,l\,\nu$ branching ratio in units of $|V_{ub}|^2$ for $q_0^2=(M_B-M_D)^2$, and for different mass definitions. The two bands refer to the PS mass subtracted at $\mu_f=\mu_c$ (dark), and to the Upsilon mass (light). The dashed lines refer to extreme choices of the subtraction scale for the PS mass. The gray rectangle shows our estimate of the perturbative uncertainty (see text for further explanation).