Decay $D\to K^{(*)}{\ell }^{+}{\nu }_{\ell }$ in covariant quark model

We study the leptonic and semileptonic $D$-meson decays ($D\to {\mathit{\ell }}^{+}{\nu }_{\mathit{\ell }}$ and $D\to K^{(*)}{\mathit{\ell }}^{+}{\nu }_{\mathit{\ell }}$) in the framework of covariant quark model with built-in infrared confinement. We compute the required form factors in the entire kinematical momentum transfer region. The calculated form factors are used to evaluate the branching fractions of these transitions. We determine the following ratios of the partial widths: $\mathrm{\Gamma }(D^0\to K^{-}{e}^{+}{\nu }_e)/\mathrm{\Gamma }(D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e)=1.02$, $\mathrm{\Gamma }(D^0\to K^{-}{\mu }^{+}{\nu }_{\mu })/\mathrm{\Gamma }(D^{+}\to {\overline{K}}^0{\mu }^{+}{\nu }_{\mu })=0.99$ and $\mathrm{\Gamma }(D^{+}\to {\overline{K}}^0{\mu }^{+}{\nu }_{\mu })/\mathrm{\Gamma }(D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e)=0.97$ which are in close resemblance with the isospin invariance and experimental results.

Figure 1

Diagram describing meson mass operator.

Figure 2

Quark model diagrams for the $D$-meson leptonic decay.

Figure 3

Quark model diagrams for the $D$-meson semileptonic decay.

Figure 4

The results for the form factors appearing in Eq. (10) for semileptonic $D\to \pi$ and $D\to K$ transitions. We compare our plot with the results from LCSR Ref. [18], LFQM Ref. [21], LQCD Ref. [10] as well with the BESIII data Ref. [4].

Figure 5

The form factors appearing in Eq. (11) for semileptonic $D\to K^{*}$ transitions. We compare our results with LFQM Ref. [21], chiral quark model ($\chi \mathrm{QM}$) Ref. [22] and heavy meson chiral theory ($\mathrm{HM}\chi \mathrm{T}$) [24].

Figure 6

Differential branching fractions of the decays $D\to K^{(*)}{\mathit{\ell }}^{+}{\nu }_{\ell }$.

Figure 7

Forward-backward asymmetries of the decays $D\to K^{(*)}{\ell }^{+}{\nu }_{\ell }$.