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

Abstract

We present a model for the vector and axial form factors of the transitions ${\overline{B}}^0\to D^{\ast \ast }$ 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 $D_V^{(\ast )}$ to the broad structures seen in SL decays at low $D^{(\ast )}\pi$ masses - which makes it difficult to isolate the broad resonances denoted as $D_{1/2}$ in the following.

Comments: revised version with modified formatting, references and comments (section II.B.c) added and errors corrected in the formulas of appendix (no impact on the numbers quoted in main text)