Test of the $R(D^{(*)})$ anomaly at the LHC

There are discrepancies between the experimental results and the Standard Model predictions, in the lepton flavor universality of the semileptonic $B$ decays: $B\to D^{(*)}\ell \nu$. As the new physics interpretations, new charged vector and charged scalar fields, that dominantly couple to the second and third generations, have been widely discussed. In this paper, we study the signals of the new particles at the LHC, and test the interpretations via the direct search for the new resonances. In particular, we see that the $\tau \nu$ resonance search at the LHC has already covered most of the parameter regions favored by the Belle and BABAR experiments. We find that the bound is already stronger than the one from the $B_c$ decay depending on the mass of the charged scalar.

Figure 1

The upper bound on the cross section times the branching ratio in each model at 95% CL. See the main text for the description.

Figure 2

$R(D)$ vs $R(D^{*})$ with the constraints from the $B_c$ decay (magenta lines) and from the charged heavy resonance search at the LHC. The charged scalar masses are fixed at 400 GeV, 500 GeV, 750 GeV, and 1000 GeV, as denoted on each panel. The gray region is out of our prediction and the region inside of the black lines is realized by taking appropriate $Y_L$ and $Y_{\tau }$. Note that the blue, green, and red ellipses correspond to the $1\sigma$ regions reported by the Belle, BABAR, and the HFLAV collaborations. The SM prediction for $R(D)$ and $R(D^{*})$ is marked with an asterisk. The cyan dashed lines correspond to the predictions by taking $|Y_L|=\pi$. In the light purple region, our model is totally excluded by the $\tau \nu$ resonance search. In the light blue region, our model can be allowed by tuning $Y_L$ and $Y_{\tau }$.

Figure 3

In these figures, the blue (red) lines are for the mass of 1 TeV (400 GeV). The figure on the left (right) above is for the $H_{-}$ ($W_L^{\prime }$) scenario. The last one below is for the $W_R^{\prime }$ scenario. The dotted lines express the combination of couplings that accommodate the $1\sigma$ of $R(D^{(*)})$. The shaded regions are excluded by the collider bound.

Figure 4

$R(D)$ vs $R(D^{*})$ with the constraint from the charged heavy resonance search at the LHC. $R(D)$ and $R(D^{*})$ planes are drawn fixing $W_I^{\prime }$ masses at 400 GeV, 500 GeV, 750 GeV, and 1000 GeV. The prediction of the $W_I^{\prime }$ model is on the black line. The $1\sigma$ regions reported by the Belle, BABAR, and the HFLAV collaborations are depicted by the same colors as in Fig. 2. The SM prediction for $R(D)$ and $R(D^{*})$ is marked with an asterisk. On the magenta thick arrows, the $W_L^{\prime }$ scenario is excluded depending on $g_L$ and $g_{L\tau }$, assuming $|g_L|\le 1$. The points on the magenta dashed arrows are excluded as far as $|g_L|\le 1$ is required but survive allowing for $|g_L|\le \pi$. The green arrows show the corresponding cases for the $W_R^{\prime }$.