Model for nonleptonic and semileptonic decays by ${\overline{B}}^0\to D^{**}$ transitions with $\mathrm{BR}(j=1/2)\ll \mathrm{BR}(j=3/2)$ using the Leibovich-Ligeti-Stewart-Wise scheme

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 semileptonic and class I nonleptonic 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; and (d) the general HQET expansion which constrains the $1/m_Q$ corrections (cf. Leibovich et al. Phys. Rev. Lett. 78, 3995 (1997)., 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.

Figure 1

Expected $q^2$ distributions for ${\overline{B}}^0\to D_2^{*+}$ in semileptonic decays. Hatched areas correspond to uncertainties from the fit; curves with dots indicate the model uncertainty. Other systematic uncertainties, indicated in Table 13, are not displayed.

Figure 2

Expected $q^2$ distributions for ${\overline{B}}^0\to D_1^{+}$ in semileptonic decays. The same conventions are used as in Fig. 1.

Figure 3

Expected $q^2$ distributions for ${\overline{B}}^0\to D_0(2300{)}^{+}$ in semileptonic decays. Hatched areas correspond to uncertainties from the fit; curves with dots indicate the model uncertainty expected from ${\widehat{\tau }}_2$ and ${\widehat{\eta }}_2$ parameters, whereas those with triangles correspond to the uncertainty from ${\widehat{\chi }}_2$ and ${\widehat{\zeta }}_1$. Other systematic uncertainties, given in Table 13, are not displayed.

Figure 4

Expected $q^2$ distributions for ${\overline{B}}^0\to D_1(2430{)}^{+}$ in semileptonic decays. The same conventions are used as in Fig. 3.

Figure 5

Expected $D^{*}\pi$ mass distributions for ${\overline{B}}^0\to D^{*}\pi$ in semileptonic decays. Solid lines correspond to our model, and the dashed line is for LLSWBi. The line with stars gives the $D^{**}$ contribution, and the one with squares is for the $D_V^{(*)}$ component. The red line corresponds to the sum of these two contributions. Only central values of the distributions are displayed.

Figure 6

Expected broad $D^{*}\pi$ mass distributions for ${\overline{B}}^0\to D^{*}\pi$ in semileptonic decays. The same conventions as in Fig. 5 are used. Hatched areas include only the experimental uncertainty given in Eq. (26).

Figure 7

Expected $q^2$ distributions for ${\overline{B}}^0\to D^{*}\pi$, the broad mass component, in semileptonic decays. The same conventions as in Fig. 5 are used.

Figure 8

Expected $D\pi$ mass distributions for ${\overline{B}}^0\to D\pi$ in semileptonic decays. Only central values are displayed.

Figure 9

Expected broad $D\pi$ mass distributions for ${\overline{B}}^0\to D\pi$ in semileptonic decays.

Figure 10

Expected $q^2$ distributions for ${\overline{B}}^0\to D\pi$, the broad mass component, in semileptonic decays.

Figure 11

Expected $D^{*}\pi$ mass distributions from our analysis (solid red curve) and from LLSWBi (dashed blue curve). Left plots correspond to all expected contributing components, whereas the plots on the right are for broad mass components only.

Figure 12

Expected $D\pi$ mass distributions obtained in our model (red solid line) and in LLSWBi (blue dashed line). Left plots correspond to all expected contributing components, whereas plots on the right are for broad mass components only.