Explaining the $R_K$ and $R_{D^{\mathbf{(}*\mathbf{)}}}$ anomalies with vector leptoquarks

Recently, the $B$ factories BABAR and Belle as well as the LHCb experiment have reported several anomalies in the semileptonic $B$ meson decays, such as the $R_K$ and $R_{D^{(*)}}$ etc. We investigate these deviations by considering the vector leptoquarks relevant for both $b\to s{l}^{+}{l}^{-}$ and $b\to cl{\overline{\nu }}_l$ transitions. The leptoquark parameter space is constrained by using the experimentally measured branching ratios of $B_s\to l^{+}{l}^{-}$, $\overline{B}\to X_s{l}^{+}{l}^{-}(\nu \overline{\nu })$, and $B_u^{+}\to l^{+}{\nu }_l$ processes. Using the constrained leptoquark couplings, we compute the branching ratios, forward-backward asymmetries, $\tau$, and $D^{*}$ polarization parameters in the $\overline{B}\to D^{(*)}l{\overline{\nu }}_l$ processes. We find that the vector leptoquarks can explain both the $R_{D^{(*)}}$ and $R_K$ anomalies, simultaneously. Furthermore, we study the rare leptonic $B_{u,c}^{*}\to l\overline{\nu }$ decay processes in this model.

Figure 1

Constraints on the real and imaginary parts of the leptoquark couplings from $B_s\to e^{+}{e}^{-}$ (top left panel), $B_s\to {\mu }^{+}{\mu }^{-}$ (top right panel), and $B_s\to {\tau }^{+}{\tau }^{-}$ (bottom panel) processes in the $U(3,3,2/3)$ leptoquark model.

Figure 2

Constraints on the real and imaginary parts of the leptoquark couplings from $B_s\to e^{+}{e}^{-}$ (top left panel), $B_s\to {\mu }^{+}{\mu }^{-}$ (top right panel), and $B_s\to {\tau }^{+}{\tau }^{-}$ (bottom panel) processes in the $U(3,1,2/3)$ leptoquark model.

Figure 3

Constraints on the real and imaginary parts of the leptoquark couplings from the $\overline{B}\to X_s{e}^{+}{e}^{-}$ process in low $q^2$ (left panel) and high $q^2$ region (right panel) in the $U(3,3,2/3)$ leptoquark model.

Figure 4

Constraints on the real and imaginary parts of the leptoquark couplings from the $\overline{B}\to X_s{\mu }^{+}{\mu }^{-}$ process in low $q^2$ (left panel) and high $q^2$ region (right panel) in the $U(3,3,2/3)$ leptoquark model.

Figure 5

Constraints on the real and imaginary parts of the leptoquark couplings from the $\overline{B}\to X_s{\tau }^{+}{\tau }^{-}$ process in the $U(3,3,2/3)$ leptoquark model.

Figure 6

Constraints on the real and imaginary parts of the leptoquark couplings from the $\overline{B}\to X_s\nu \overline{\nu }$ process in the $U(3,3,2/3)$ leptoquark model.

Figure 7

Constraints on the real and imaginary parts of the leptoquark couplings from $B_u^{+}\to e^{+}{\nu }_e$ (left panel), $B_u^{+}\to {\mu }^{+}{\nu }_{\mu }$ (right panel), and $B_u^{+}\to {\tau }^{+}{\nu }_{\tau }$ (bottom panel) processes in the $U(3,3,2/3)$ leptoquark model.

Figure 8

Constraints on the real and imaginary parts of the leptoquark couplings from $B_u^{+}\to e^{+}{\nu }_e$ (left panel), $B_u^{+}\to {\mu }^{+}{\nu }_{\mu }$ (right panel), and $B_u^{+}\to {\tau }^{+}{\nu }_{\tau }$ (bottom panel) processes in the $U(3,1,2/3)$ leptoquark model.

Figure 9

The variation of branching ratios of $B\to De\overline{\nu }$ (left panel), $B\to D\mu \overline{\nu }$ (right panel), and $B\to D\tau \overline{\nu }$ (bottom panel) processes with respect to $q^2$ in the leptoquark model. Here, darker blue dashed lines are for the SM and orange bands represent the leptoquark model. The lighter blue bands stand for the theoretical uncertainties that arise due to the input parameters in the SM.

Figure 10

The variation of branching ratios of $B\to D^{*}e\overline{\nu }$ (left panel), $B\to D^{*}\mu \overline{\nu }$ (right panel), and $B\to D^{*}\tau \overline{\nu }$ (bottom panel) processes with respect to $q^2$ in the leptoquark model.

Figure 11

The plot for $R_L^{D^{*}}$ (left panel) and $R_T^{D^{*}}$ (right panel) in the leptoquark model.

Figure 12

The $q^2$ variation of lepton nonuniversality $R_D(q^2)$ (left panel) and $R_{D^{*}}(q^2)$ (right panel) in the leptoquark model.

Figure 13

The plot for $R_K(q^2)$ in low $q^2$ (left panel) and high $q^2$ (right panel) in the leptoquark model.

Figure 14

The plot for $R_{K^{*}}(q^2)$ in low $q^2$ (left panel) and high $q^2$ (right panel) in the leptoquark model.