Rare semileptonic $B\to K(\pi )l_i^{-}{l}_j^{+}$ decay in a vector leptoquark model

We investigate the consequence of vector leptoquarks on the rare semileptonic lepton flavor violating decays of the $B$ meson which are more promising and effective channels to probe the new physics signal. We constrain the resulting new leptoquark parameter space by using the branching ratios of $B_{s,d}\to l^{+}{l}^{-}$, $K_L\to l^{+}{l}^{-}$ and ${\tau }^{-}\to l^{-}\gamma$ processes. We estimate the branching ratios of rare lepton flavor violating $B\to K(\pi )l_i^{-}{l}_j^{+}$ processes using the constrained leptoquark couplings. We also compute the forward-backward asymmetries and the lepton nonuniversality parameters of the LFV decays in the vector leptoquark model. Furthermore, we study the effect of vector leptoquark on the $(g-2{)}_{\mu }$ anomaly.

Figure 1

Constraint on the combination of scalar Wilson coefficient from $B_s\to {\mu }^{+}{\mu }^{-}$ process. The left panel is for real $C_S^{\mathrm{LQ}}\pm C_S^{\prime \mathrm{LQ}}$ Wilson coefficients and right panel is for complex Wilson coefficients.

Figure 2

Constraint on $C_S^{\mathrm{LQ}}\pm C_S^{\prime \mathrm{LQ}}$ Wilson coefficients from $B_d\to {\mu }^{+}{\mu }^{-}$ process. The left panel is for real Wilson coefficients and right panel is for complex Wilson coefficients.

Figure 3

The allowed region of $C_S^{\mathrm{LQ}}-C_S^{\prime \mathrm{LQ}}$ and $C_S^{\mathrm{LQ}}+C_S^{\prime \mathrm{LQ}}$ Wilson coefficients from $B_s\to e^{+}{e}^{-}$ (left panel) and $B_d\to e^{+}{e}^{-}$ (right panel) processes.

Figure 4

The allowed region of $C_S^{\mathrm{LQ}}-C_S^{\prime \mathrm{LQ}}$ and $C_S^{\mathrm{LQ}}+C_S^{\prime \mathrm{LQ}}$ Wilson coefficients from $B_s\to {\tau }^{+}{\tau }^{-}$ (left panel) and $B_d\to {\tau }^{+}{\tau }^{-}$ (right panel) processes.

Figure 5

The allowed region of $C_S^{\mathrm{LQ}}\pm C_S^{\prime \mathrm{LQ}}$ Wilson coefficients from $K_L\to e^{+}{e}^{-}$ (left panel) and $K_L\to {\mu }^{+}{\mu }^{-}$ (right panel) processes.

Figure 6

The constraint on $(g_L{)}_{b{l}_i}(g_L{)}_{b{l}_j}^{*}$ and $(g_R{)}_{b{l}_i}(g_R{)}_{b{l}_j}^{*}$ leptoquark couplings from ${\tau }^{-}\to e^{-}\gamma$ (left panel) and ${\tau }^{-}\to {\mu }^{-}\gamma$ (right panel) processes.

Figure 7

The constraint on $(g_L{)}_{b{l}_i}(g_R{)}_{b{l}_j}^{*}$ and $(g_R{)}_{b{l}_i}(g_L{)}_{b{l}_j}^{*}$ leptoquark couplings from ${\tau }^{-}\to e^{-}\gamma$ (left panel) and ${\tau }^{-}\to {\mu }^{-}\gamma$ (right panel) processes.

Figure 8

The variation of branching ratios of $B^{+}\to K^{+}{\mu }^{-}{e}^{+}$ (top left panel), $B^{+}\to K^{+}{\tau }^{-}{e}^{+}$ (top right panel) and $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$ (bottom panel) processes (in units of ${\mathrm{GeV}}^{-2}$) in the $V^{1,3}$ vector leptoquark model. Here purple bands represent the contribution from $V^1$ leptoquark model and green solid lines are for $V^3$ leptoquark.

Figure 9

The variation of forward-backward asymmetries of $B^{+}\to K^{+}{\mu }^{-}{e}^{+}$ (top left panel), $B^{+}\to K^{+}{\tau }^{-}{e}^{+}$ (top right panel) and $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$ (bottom panel) processes in the leptoquark model.

Figure 10

The plots for lepton nonuniversality parameters, $R_{Ke}^{\mu e}$ (top right panel), $R_{Ke}^{\tau e}$ (bottom left panel) and $R_{Ke}^{\tau \mu }$ (bottom right panel) in high $q^2$ region. Here the top left panel shows the nonuniversality $R_{Ke}^{\mu e}$ in low $q^2\in [1,6]$ region.

Figure 11

The plots for lepton nonuniversality parameters, $R_{K\mu }^{\mu e}$ (top right panel), $R_{K\mu }^{\tau e}$ (bottom left panel) and $R_{K\mu }^{\tau \mu }$ (bottom right panel) in high $q^2$ region. Here the top left panel shows the nonuniversality $R_{K\mu }^{\mu e}$ in low $q^2\in [1,6]$ region.

Figure 12

The variation of lepton nonuniversality parameter $R_K^{\mu \mu }$ for low $q^2\in [1,6]$ (left panel) and high $q^2$ (right panel) regimes.

Figure 13

The $q^2$ variation of branching ratios of $B^{+}\to {\pi }^{+}{\mu }^{-}{e}^{+}$ (top left panel), $B^{+}\to {\pi }^{+}{\tau }^{-}{e}^{+}$ (top right panel) and $B^{+}\to {\pi }^{+}{\tau }^{-}{\mu }^{+}$ (bottom panel) processes in the $V^{1,3}$ vector leptoquark model.

Figure 14

The variations of forward-backward asymmetries of $B^{+}\to {\pi }^{+}{\mu }^{-}{e}^{+}$ (left panel), $B^{+}\to {\pi }^{+}{\tau }^{-}{e}^{+}$ (middle panel) and $B^{+}\to {\pi }^{+}{\tau }^{-}{\mu }^{+}$ (right panel) processes in leptoquark model.

Figure 15

The $q^2$ variations of $R_{\pi \mu }^{\mu e}$ (top right panel), $R_{\pi \mu }^{\tau e}$ (bottom left panel) and $R_{\pi \mu }^{\tau \mu }$ (bottom right panel) parameters in high $q^2$ region in the leptoquark model. Here $R_{\pi \mu }^{\mu e}$ (top left panel) shows the lepton nonuniversality for low $q^2\in [1,6]$ region.