A unified scheme for calculating the exclusive semi-leptonic decays of hadrons

TL;DR

This work tackles inconsistencies in exclusive semi-leptonic decays by replacing the traditional hadronic transition-matrix-element approach with a hadron-tensor framework. Using cutting rules and a Taylor expansion in q^2, it derives a unified description where the width and its moments depend on a minimal set of coefficients Y_0, Y_1, reducing reliance on conventional LCSR form factors. The framework yields consistent results for baryons and provides a revised meson parameterization, with measurable differences in double differential widths that offer a direct experimental test. If validated, this approach could simplify the interpretation of heavy-flavor decays and address long-standing tensions in CKM determinations and heavy-quark lifetimes.

Abstract

Exclusive semi-leptonic decay stands as a pivotal channel in the exploration of heavy flavor physics, primarily due to its straightforward experimental measurability. In this work, we delve into the hadron matrix element and hadron tensor within the context of exclusive semi-leptonic decays. We challenge the conventional exclusive decay theory by introducing a fresh perspective, revealing that while the baryon sector is consistent, the meson sector warrants revision. Employing a novel form factor derived from the Taylor series expansion in our differential width calculations, we demonstrate that fitting experimental data necessitates a more streamlined and minimal parameter set compared to the standard Light Cone Sun Rul(LCSR) form factors. Furthermore, we propose that our hypothesis can be empirically validated or refuted through the precise measurement of the double differential decay width, offering a tangible path forward for experimental validation.

Figures (4)

• Figure 1: Comparison of the differential decay rates of $\Lambda_c \to \Lambda+e^{+}+v_{e}$BESIII:2022ysawith different parameters. The blue line has two parameters with total uncertainty, the red line has one parameter, and the yellow dots are data point.
• Figure 2: Comparison of the differential decay rates of $\Lambda_c \to \Lambda+e^{+}+v_{e}$BESIII:2022ysawith different parameters. The blue line has two parameters, the red line has two parameters, the green line has four parameters , and the yellow dots are data point.
• Figure 3: Comparison of the differential decay rates of $\bar{B}^0\to D^{*+} +e^{-}+v_{e}$Belle-II:2023okj with different parameters. The blue line has two parameters with total uncertainty, and the red line has one parameter, and the black dots are data with total uncertainty.
• Figure 4: The distribution of electron energy, neutrino energy, and lepton energy at low($\frac{\hat{q^2}|_{\text{max}}}{50}$) , middle($\frac{\hat{q^2}|_{\text{max}}}{2}$) , high($\frac{49\hat{q^2}|_{\text{max}}}{50}$) $\hat{q^2}$.