Impact of vector new physics couplings on $B_s\to (K,K^{*})\tau \nu$ and $B\to \pi \tau \nu$ decays

Experimental measurements of $R_D$, $R_{D^{*}}$ and $R_{J/\mathrm{\Psi }}$ in $B\to (D,D^{*})l\nu$ and $B_c\to J/\mathrm{\Psi }l\nu$ decays mediated via $b\to cl\nu$ charged current interactions deviate from standard model prediction by $2.3\sigma$, $3.0\sigma$ and $1.3\sigma$, respectively. In addition, a deviation of $1.5\sigma$ from the standard model prediction has been witnessed in $\mathcal{B}(B\to \tau \nu )$ mediated via $b\to ul\nu$ charged current interactions as well. Motivated by the anomalies present in $B$ and $B_c$ meson decays, we analyze the corresponding $B_s\to (K,K^{*})\tau \nu$ and $B\to \pi \tau \nu$ semileptonic decays within the standard model and beyond. We use an effective field theory formalism in which $b\to c$ and $b\to u$ semileptonic decays are assumed to exhibit similar new physics patterns. We give the predictions of various observables such as the branching fractions, ratio of branching ratios, lepton side forward backward asymmetry, lepton polarization fraction and convexity parameter for $B_s\to (K,K^{*})\tau \nu$ and $B\to \pi \tau \nu$ decay channels within the standard model and within various new physics scenarios.

Figure 1

$q^2$ dependent observables of $B_s\to Kl\nu$ (first column), $B_s\to K^{*}l\nu$ (second column) and $B\to \pi l\nu$ (third column) decays in the SM for the $\mu$ (violet) and $\tau$ (green) modes.

Figure 2

In the left panel we show the allowed ranges in $V_L$ NP coupling and the corresponding ranges in $R_D$ (violet), $R_{D^{*}}$ (green), $R_{J/\mathrm{\Psi }}$ (blue), and $R_{\pi }^l$ (yellow) once $2\sigma$ experimental constraint is imposed. The corresponding ranges in $\mathcal{B}(B\to \pi \tau \nu )$ and $R_{\pi }$ are shown in the right panel.

Figure 3

Differential ratios $R(q^2)$ and differential branching ratios $\mathrm{DBR}(q^2)$ for $B_s\to K\tau \nu$ (first column), $B_s\to K^{*}\tau \nu$ (second column) and $B\to \pi \tau \nu$ (third column) decays using the $V_L$ NP coupling of Fig. 2 are shown with a violet band, whereas the corresponding SM ranges are shown with a green band. The omitted plots such as $A_{FB}^{\tau }(q^2)$, $P^{\tau }(q^2)$ and $C_F^{\tau }(q^2)$ are not affected by $V_L$ NP coupling.

Figure 4

In the left panel we show the allowed ranges in ${\tilde{V}}_L$ NP coupling and the corresponding ranges in $R_D$ (violet), $R_{D^{*}}$ (green), $R_{J/\mathrm{\Psi }}$ (blue), and $R_{\pi }^l$ (yellow) once $2\sigma$ experimental constraint is imposed. The corresponding ranges in $\mathcal{B}(B\to \pi \tau \nu )$ and $R_{\pi }$ are shown in the right panel.

Figure 5

Differential ratios $R(q^2)$, differential branching ratios $\mathrm{DBR}(q^2)$ and $\tau$ polarization fraction $P^{\tau }(q^2)$ for $B_s\to K\tau \nu$ (first column), $B_s\to K^{*}\tau \nu$ (second column) and $B\to \pi \tau \nu$ (third column) decays using the ${\tilde{V}}_L$ NP coupling of Fig. 4 are shown with a violet band, whereas the corresponding SM ranges are shown with a green band. The omitted plots such as $A_{FB}^{\tau }(q^2)$ and $C_F^{\tau }(q^2)$ are not affected by ${\tilde{V}}_L$ NP coupling.