A model for NL and SL decays by $\overline{B}^0 \to D^{**}$ transitions with $BR(j=1/2) \ll BR(j=3/2)$ using the $LLSW$ scheme

TL;DR

This paper develops a comprehensive model for $ar{B}^0 o D^{**}$ decays, integrating lattice QCD, quark models, and heavy quark effective theory to explain decay rates and form factors, emphasizing the suppression of $j=1/2$ states.

Contribution

It introduces a combined theoretical framework for $ar{B}^0 o D^{**}$ transitions that aligns with current data and clarifies the suppression of $j=1/2$ states compared to $j=3/2$ states.

Findings

The model agrees with lattice QCD and experimental data.

$ au_{1/2}(w)$ is much smaller than $ au_{3/2}(w)$, consistent with theoretical expectations.

Virtual $D^{(*)}_V$ contributions complicate the identification of broad $D_{1/2}$ resonances.

Abstract

We present a model for the vector and axial form factors of the transitions $\overline{B}^0 \to D^{**}$ in good agreement with the presently available data and based on the present theoretical knowledge, combining a) the safe lattice QCD predictions at $m_Q=\infty$ and $w=1$ ; b) the predictions at general $w$ of a relativistic, covariant quark model at $m_Q=\infty$, including the well tested Godfrey and Isgur spectroscopic model and which agrees with lattice QCD at $w=1$ ; c) the constraint of Bjorken and Neubert relating Semi-leptonic (SL) and Class I Non-leptonic (NL) decays, which shows that $\overline{B}^0 \to D_0(2300)^{+} \pi^-$ strongly constrains $\tau_{1/2}(w)$ to be much smaller than $\tau_{3/2}(w)$, in agreement with the theoretical expectation; d) the general HQET expansion which constrains the $1/m_Q$ corrections (cf \cite{LLSW}, denoted hereafter as $LLSW$). An important element in the understanding of data is the large contribution of virtual $D^{(*)}_V$ to the broad structures seen in SL decays at low $D^{(*)} \pi$ masses - which makes it difficult to isolate the broad resonances denoted as $D_{1/2}$ in the following.