Isgur-Wise function within a modified heavy-light chiral quark model

We consider the Isgur-Wise function $\xi (\omega )$ within a new modified version of a heavy-light chiral quark model. While early versions of such models gave an absolute value of the slope that was too small, namely ${\xi }^{\prime }(1)\simeq -0.4$ to $-0.3$, we show how extended version(s) may lead to values around $-1$, in better agreement with recent measurements. This is obtained by introducing a new mass parameter in the heavy-quark propagator. We also shortly comment on the consequences for the decay modes $B\to D\overline{D}$.

Figure 1

Feynman rule for the light quark–soft gluon vertex.

Figure 2

Coupling to vector and axial vector current.

Figure 3

The decay constant $f_B$ in dependence on $m$ and $\Delta$. The condensates are taken to be $⟨\overline{q}q⟩=(-0.27\mathrm{GeV}{)}^3$ and $⟨\frac{{\alpha }_s}{\pi }{G}^2⟩=(0.32\mathrm{GeV}{)}^4$.

Figure 4

Diagrams for bosonization of the left-handed quark current to leading order, determining ${\alpha }_H$.

Figure 5

Bosonization corresponding to the Isgur-Wise function.

Figure 6

The slope of Isgur-Wise function ${\xi }^{\prime }(1)$ in dependence on the gluon condensate for various choices of the light-quark constituent mass $m$ (a), and the decay constant $f_B$ in dependence on the quark condensate (b), for $\Delta =0.1\mathrm{GeV}$. Complementary plots are not so interesting because the dependence of ${\xi }^{\prime }(1)$ on the quark condensate and the dependence of $f_B$ on the gluon condensate are rather small.

Figure 7

The slope of Isgur-Wise function ${\xi }^{\prime }(1)$ at no-recoil point as a function of $\Delta$ for three values of $m$ (a), and as a function of $m$ for three values of $\Delta$ (b). The condensates are taken to be $⟨\overline{q}q⟩=(-0.27\mathrm{GeV}{)}^3$ and $⟨\frac{{\alpha }_s}{\pi }{G}^2⟩=(0.32\mathrm{GeV}{)}^4$.