Comparative analysis of the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\ell }^{+}{\ell }^{-}$ decay in the SM, SUSY, and RS model with custodial protection

We comparatively analyze the rare ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\ell }^{+}{\ell }^{-}$ channel in the standard model, supersymmetry, and Randall-Sundrum model with custodial protection (${\mathrm{RS}}_c$). Using the parametrization of the matrix elements entering the low-energy effective Hamiltonian in terms of form factors, we calculate the corresponding differential decay width and lepton forward-backward asymmetry in these models. We compare the results obtained with the most recent data from LHCb as well as lattice QCD results on the considered quantities. It is obtained that the standard model, with the form factors calculated in light-cone QCD sum rules, cannot reproduce some experimental data on the physical quantities under consideration, but the supersymmetry model can do it. The ${\mathrm{RS}}_c$ model predictions are roughly the same as the standard model, and there are no considerable differences between the predictions of these two models. In the case of differential decay rate, the data in the range $4{\mathrm{GeV}}^2/{\mathrm{c}}^4\le q^2\le 6{\mathrm{GeV}}^2/{\mathrm{c}}^4$ cannot be described by any of the considered models.

Figure 1

The dependence of the differential branching ratio on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ transition in the SMLCSR and ${\mathrm{RS}}_c$ models. The lattice QCD [18] and recent experimental data by the LHCb [11] Collaboration are also included.

Figure 2

The dependence of the differential branching ratio on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ transition in the SMLCSR and ${\mathrm{RS}}_c$ models.

Figure 3

The dependence of the differential branching ratio on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ transition in the SMLCSR and SUSY I and II models. The lattice QCD [18] and recent experimental data by the LHCb [11] Collaboration are also included.

Figure 4

The dependence of the differential branching ratio on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ transition in the SMLCSR and SUSY III and SO(10) models. The lattice QCD [18] and recent experimental data by the LHCb [11] Collaboration are also included.

Figure 5

The dependence of the differential branching ratio on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ transition in the SMLCSR and SUSY I and II models.

Figure 6

The dependence of the differential branching ratio on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ transition in the SMLCSR and SUSY III and SO(10) models.

Figure 7

The dependence of ${\mathcal{A}}_{FB}$ on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ transition in the SMLCSR, lattice QCD [18], and ${\mathrm{RS}}_c$ models together with recent experimental data by LHCb [11].

Figure 8

The dependence of ${\mathcal{A}}_{FB}$ on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ transition in the SMLCSR and ${\mathrm{RS}}_c$ models.

Figure 9

The dependence of ${\mathcal{A}}_{FB}$ on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ transition in the SMLCSR, lattice QCD [18], and SUSY I and II models together with recent experimental data by LHCb [11].

Figure 10

The dependence of ${\mathcal{A}}_{FB}$ on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ transition in the SMLCSR, lattice QCD [18], and SUSY III and SO(10) models together with recent experimental data by LHCb [11].

Figure 11

The dependence of ${\mathcal{A}}_{FB}$ on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ transition in the SMLCSR and SUSY I and II scenarios.

Figure 12

The dependence of ${\mathcal{A}}_{FB}$ on $q^2$ for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ transition in the SMLCSR and SUSY III and SO(10) scenarios.