Semileptonic decays ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\ell }^{+}{\nu }_{\ell }(\ell =e,\mu )$ in the covariant quark model and comparison with the new absolute branching fraction measurements of Belle and BESIII

We present precise theoretical predictions for the absolute branching fractions of ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\ell }^{+}{\nu }_{\ell }(\ell =e,\mu )$ decays in the covariant confined quark model. This study is motivated by two recent and accurate measurements of the absolute branching fractions of ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$ and ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{e}^{+}{\nu }_e$ by the Belle Collaboration at the KEKB and by the BESIII Collaboration at the BEPCII. Our predictions for the branching fractions are consistent with both experimental results. We also provide detailed numerical results for differential decay distributions and polarization observables.

Figure 1

Definition of the polar and the azimuthal angles.

Figure 2

Form factor $F_1^V(q^2)$: solid line (exact result), dashed line (HQL).

Figure 3

Form factor $F_2^V(q^2)$: solid line (exact result), dashed line (HQL).

Figure 4

The $q^2$ dependence of the partial rates $d{\mathrm{\Gamma }}_U/d{q}^2$ (dashed), $d{\mathrm{\Gamma }}_L/d{q}^2$ (dot-dashed) and their sum $d{\mathrm{\Gamma }}_{U+L}/d{q}^2$ (solid) for the $e^{+}$ mode (in units of $10^{-15}{\mathrm{GeV}}^{-1}$).

Figure 5

The $q^2$ dependence of the partial rates $d{\mathrm{\Gamma }}_U/d{q}^2$ (dashed), $d{\mathrm{\Gamma }}_L/d{q}^2$ (dot-dashed) and their sum $d{\mathrm{\Gamma }}_{U+L}/d{q}^2$ (solid) for the ${\mu }^{+}$ mode (in units of $10^{-15}{\mathrm{GeV}}^{-1}$).

Figure 6

$A_{FB}^{\ell }(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 7

$C_F(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 8

$P_z^h(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 9

$P_x^h(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 10

$|{\overrightarrow{P}}^h|(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 11

$P_z^{\ell }(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 12

$P_x^{\ell }(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).

Figure 13

$|{\overrightarrow{P}}^{\ell }|(q^2)$ plot: $e^{+}$ (solid) and ${\mu }^{+}$ (dashed).