Semileptonic decays of ${\mathrm{\Lambda }}_b$ baryons in the relativistic quark model

Semileptonic ${\mathrm{\Lambda }}_b$ decays are investigated in the framework of the relativistic quark model based on the quasipotential approach and the quark-diquark picture of baryons. The decay form factors are expressed through the overlap integrals of the initial and final baryon wave functions. All calculations are done without employing nonrelativistic and heavy quark expansions. The momentum transfer dependence of the decay form factors is explicitly determined in the whole accessible kinematical range without any extrapolations or model assumptions. Both the heavy-to-heavy ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\ell {\nu }_{\ell }$ and heavy-to-light ${\mathrm{\Lambda }}_b\to p\ell {\nu }_{\ell }$ decay branching fractions are calculated. The results agree within error bars with the experimental value of the branching fraction of the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c^{+}{l}^{-}{\overline{\nu }}_l$ decay. From the recent LHCb data on the ratio of the branching fractions of the heavy-to-light and heavy-to-heavy semileptonic ${\mathrm{\Lambda }}_b$ decays the ratio of the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{ub}|/|V_{cb}|$ is obtained. It is consistent with the corresponding ratio determined from the inclusive $B$ meson decays.

Figure 1

Lowest-order vertex function ${\mathrm{\Gamma }}^{(1)}$ contributing to the current matrix element (8).

Figure 2

Vertex function ${\mathrm{\Gamma }}^{(2)}$ taking the quark interaction into account. Dashed lines correspond to the effective potential ${\mathcal{V}}_{Qd}$ in Eq. (3). Bold lines denote the negative-energy part of the quark propagator.

Figure 3

Form factors of the weak ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c$ transition.

Figure 4

Form factors of the weak ${\mathrm{\Lambda }}_b\to p$ transition.

Figure 5

Predictions for the differential decay rates of the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\ell {\nu }_{\ell }$ (left) and ${\mathrm{\Lambda }}_b\to p\ell {\nu }_{\ell }$ (right) semileptonic decays.

Figure 6

Predictions for the forward-backward asymmetries $A_{FB}(q^2)$ in the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{\ell }^{-}{\nu }_{\ell }$ (left) and ${\mathrm{\Lambda }}_b\to p{\ell }^{-}{\nu }_{\ell }$ (right) semileptonic decays.

Figure 7

Predictions for the convexity parameter $C_F(q^2)$ in the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\ell {\nu }_{\ell }$ (left) and ${\mathrm{\Lambda }}_b\to p\ell {\nu }_{\ell }$ (right) semileptonic decays.

Figure 8

Predictions for the longitudinal polarization $P_L(q^2)$ of the final baryon in the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\ell {\nu }_{\ell }$ (left) and ${\mathrm{\Lambda }}_b\to p\ell {\nu }_{\ell }$ (right) semileptonic decays.