[Paper Review] Exclusive B-meson semileptonic decays from unitarity and lattice QCD

G. Martinelli, M. Naviglio+2 more|arXiv (Cornell University)|Mar 30, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents a unitarity-based Dispersive Matrix (DM) method that determines the full kinematic shape of B-meson semileptonic form factors using only lattice QCD data at high momentum transfer, without assuming functional forms. It yields pure theoretical estimates of $ R(D) = 0.296 \pm 0.008 $ and $ R(D^*) = 0.275 \pm 0.008 $, consistent with experiment at ~1.4σ, and exclusive determinations $ |V_{cb}| = 41.1 \pm 1.0 \times 10^{-3} $, $ |V_{ub}| = 3.88 \pm 0.32 \times 10^{-3} $, reducing tensions with inclusive and experimental averages.

ABSTRACT

We examine the semileptonic $B o D^{(*)} \ell ν_\ell$ and $B o π\ell ν_\ell$ decays adopting the unitarity-based Dispersive Matrix (DM) method, which allows to determine the shape of the relevant hadronic form factors (FFs) in their whole kinematical range, using only lattice QCD results available at large values of the 4-momentum transfer without making any assumption on their momentum dependence. Moreover, the experimental data are not used to constrain the shape of the FFs, but only to obtain our final exclusive determination of $\vert V_{cb} \vert$ and $\vert V_{ub} \vert$, namely: $\vert V_{cb} \vert \cdot 10^3 = 41.1 \pm 1.0$ and $\vert V_{ub} \vert \cdot 10^3 = 3.88 \pm 0.32$, which are consistent with the latest inclusive determinations at the $1 σ$ level or better. Our calculation of the FFs allows to obtain pure theoretical estimates of the $τ/ μ$ ratios of differential decay rates, $R(D) = 0.296 \pm 0.008$ and $R(D^*) = 0.275 \pm 0.008$, which turn out to be compatible with the experimental world averages within $\simeq 1.4$ standard deviations.

Motivation & Objective

• To resolve the long-standing $ |V_{cb}| $ puzzle between inclusive and exclusive determinations by providing a model-independent form factor shape.
• To address the $ R(D^{(*)}) $ anomaly in lepton flavor universality using purely theoretical form factor shapes.
• To improve the precision of $ |V_{ub}| $ by avoiding biases from experimental data in form factor fitting.
• To develop a parameterization-free method that respects unitarity, analyticity, and crossing symmetry in form factor determination.

Proposed method

• The Dispersive Matrix (DM) method uses lattice QCD results at large $ q^2 $ to constrain form factors across the full kinematic range via unitarity, analyticity, and crossing symmetry.
• The method bounds the form factor $ f(q^2) $ within a band defined by $ \beta(z) \pm \sqrt{\gamma(z)} $, where $ \beta(z) $ and $ \gamma(z) $ depend on input data and susceptibilities.
• The susceptibilities are computed nonperturbatively from lattice correlation functions, ensuring consistency with QCD symmetries.
• The method reproduces input lattice data exactly at their points, avoiding truncation errors common in $ z $-expansion fits.
• Experimental data are used only to extract $ |V_{cb}| $ and $ |V_{ub}| $, not to constrain the form factor shape.
• A novel iterative unitarization procedure is applied to experimental $ |V_{ub}|f_+^{B\pi}(q^2) $ data to improve precision while preserving unitarity.

Experimental results

Research questions

• RQ1 Can the full kinematic shape of B-meson semileptonic form factors be determined without assuming a functional form, using only lattice QCD data at high $ q^2 $?
• RQ2 Does the resulting form factor shape yield $ R(D) $ and $ R(D^*) $ values consistent with experimental averages, resolving the LFU tension?
• RQ3 Can a model-independent determination of $ |V_{cb}| $ and $ |V_{ub}| $ reduce the discrepancy with inclusive results?
• RQ4 Can the unitarization of experimental data improve the precision of $ |V_{ub}| $ while preserving theoretical consistency?

Key findings

• The form factor shape for $ B \to D^{(*)}\ell\nu $ is determined purely from lattice QCD data at high $ q^2 $, with no functional form assumptions.
• The theoretical estimate of $ R(D) = 0.296 \pm 0.008 $ is compatible with the experimental world average at approximately 1.4 standard deviations.
• The theoretical estimate of $ R(D^*) = 0.275 \pm 0.008 $ is also compatible with the experimental average within 1.4σ.
• The exclusive determination $ |V_{cb}| \cdot 10^{-3} = 41.1 \pm 1.0 $ is consistent with the latest inclusive determination at the 0.6σ level.
• The exclusive determination $ |V_{ub}| \cdot 10^{-3} = 3.88 \pm 0.32 $, obtained via unitarization of experimental data, improves precision by ~30% over the initial lattice-only estimate.
• The method reduces tensions between exclusive SM predictions and experimental/inclusive results, indicating that the anomalies may stem from form factor modeling rather than new physics.