Semileptonic and nonleptonic weak decays of ${\mathrm{\Lambda }}_b^0$

The recent experimental developments require a more precise theoretical study of weak decays of heavy baryon ${\mathrm{\Lambda }}_b^0$. In this work, we provide an updated and systematic analysis of both the semi-leptonic and nonleptonic decays of ${\mathrm{\Lambda }}_b^0$ into baryons ${\mathrm{\Lambda }}_c^{+}$, $\mathrm{\Lambda }$, $p$, and $n$. The diquark approximation is adopted so that the methods developed in the $B$ meson system can be extended into the baryon system. The baryon-to-baryon transition form factors are calculated in the framework of a covariant light-front quark model. The form factors $f_3$, $g_3$ can be extracted and are found to be non-negligible. The semileptonic processes of ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}(p)l^{-}{\overline{\nu }}_l$ are calculated and the results are consistent with the experiment. We study the nonleptonic processes within the QCD factorization approach. The decay amplitudes are calculated at the next-to-leading order in strong coupling constant ${\alpha }_s$. We calculate the nonleptonic decays of ${\mathrm{\Lambda }}_b^0$ into a baryon and a s-wave meson (pseudoscalar or vector) including 44 processes in total. The branching ratios and direct $CP$ asymmetries are predicted. The numerical results are compared to the experimental data and those in the other theoretical approaches. Our results show validity of the diquark approximation and application of QCD factorization approach into the heavy baryon system.

Figure 1

Feynman diagram for the baryon to baryon transition amplitudes. The “$\times$” denotes the corresponding $V-A$ current vertex.

Figure 2

Feynman diagrams in the QCD factorization approach.

Figure 3

The $q^2$-dependence of the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ transition form factors. The horizontal $q^2$ variable is given in units of ${\mathrm{GeV}}^2$.

Figure 4

The $q^2$-dependence of the ${\mathrm{\Lambda }}_b\to p$ transition form factors. The horizontal $q^2$ variable is given in units of ${\mathrm{GeV}}^2$.

Figure 5

The $q^2$-dependence of the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }$ transition form factors. The horizontal $q^2$ variable is given in units of ${\mathrm{GeV}}^2$.

Figure 6

The $q^2$-dependence of the ${\mathrm{\Lambda }}_b\to n$ transition form factors. The horizontal $q^2$ variable is given in units of ${\mathrm{GeV}}^2$.

Figure 7

The $q^2$-dependence of the ${\mathrm{\Lambda }}_b\to p$ transition form factors. The horizontal $q^2$ variable is given in units of ${\mathrm{GeV}}^2$. In each diagram, the solid line represents the central values; the dashed lines represent the values with errors in the $\beta$ parameters only; the dot dashed lines represent the values with errors in both the $\beta$ parameters and the diquark mass.