Truncation orders, external constraints, and the determination of $|V_{cb}|$

TL;DR

This paper introduces an AIC-based model selection framework for extracting the CKM matrix element |V_{cb}| from B meson decays, improving reliability over previous methods by addressing truncation and constraints.

Contribution

It applies the Akaike Information Criterion to select optimal truncation orders in the BGL parameterization and explores model averaging with gAIC for unbiased |V_{cb}| estimates.

Findings

AIC-based approach yields unbiased |V_{cb}| estimates

Model averaging with gAIC improves coverage properties

Comparison shows AIC outperforms NHT in bias and reliability

Abstract

We present a model selection framework for the extraction of the CKM matrix element $|V_{cb}|$ from exclusive $B \to D^* l \nu$ decays. By framing the truncation of the Boyd-Grinstein-Lebed (BGL) parameterization as a model selection task, we apply the Akaike Information Criterion (AIC) to choose the optimal truncation order. We demonstrate the performance of our approach through a comprehensive toy study, comparing it to the Nested Hypothesis Test (NHT) method used in previous analyses. Our results show that the AIC-based approach produces unbiased estimates of $|V_{cb}|$, albeit with some issues of undercoverage. We further investigate the impact of unitarity constraints and explore model averaging using the Global AIC (gAIC) approach, which produced unbiased results with correct coverage properties. Our findings suggest that model selection techniques based on information criteria and model averaging offer a promising path towards more reliable $|V_{cb}|$ determinations.