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
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.