$R_{D^{(*)}}$ motivated ${\mathcal{S}}_1$ leptoquark scenarios: Impact of interference on the exclusion limits from LHC data

Motivated by the persistent anomalies in the semileptonic $B$-meson decays, we investigate the competency of LHC data to constrain the $R_{D^{(*)}}$-favored parameter space in a charge $-1/3$ scalar leptoquark (${\mathcal{S}}_1$) model. We consider some scenarios with one large free coupling to accommodate the $R_{D^{(*)}}$ anomalies. As a result, some of them dominantly yield nonresonant $\tau \tau$ and $\tau \nu$ events at the LHC through the $t$-channel ${\mathcal{S}}_1$ exchange. So far, no experiment has searched for leptoquarks using these signatures and the relevant resonant leptoquark searches are yet to put any strong exclusion limit on the parameter space. We recast the latest $\tau \tau$ and $\tau \nu$ resonance search data to obtain new exclusion limits. The nonresonant processes strongly interfere (destructively in our case) with the Standard Model background and play the determining role in setting the exclusion limits. To obtain precise limits, we include non-negligible effects coming from the subdominant (resonant) pair and inclusive single leptoquark productions systematically in our analysis. To deal with large destructive interference, we make use of the transverse mass distributions from the experiments in our statistical analysis. In addition, we also recast the relevant direct search results to obtain the most stringent collider bounds on these scenarios to date. These are independent bounds and are competitive to other known bounds. Finally, we indicate how one can adopt these bounds to a wide class of models with ${\mathcal{S}}_1$ that are proposed to accommodate the $R_{D^{(*)}}$ anomalies.

Figure 1

Leading order processes responsible for $B\to D^{(*)}\tau \nu$ decay. In the SM (a) and in the ${\mathcal{S}}_1$ leptoquark model (b).

Figure 2

The parton-level cross sections of different production channels of ${\mathcal{S}}_1$ at the 13 TeV LHC as functions of $M_{{\mathcal{S}}_1}$ in Scenario I. These cross sections are computed for a benchmark coupling ${\lambda }_{23}^L=1$. Here, the $j$ in the ${\mathcal{S}}_1\tau j$ and ${\mathcal{S}}_1\nu j$ processes includes all the light jets as well as $b$ jets. Their cross sections are generated with a cut on the transverse momentum of the jet, $p_{\mathrm{T}}^j>20\mathrm{GeV}$.

Figure 3

The $1\sigma$ and $2\sigma$ CL exclusion limits on $\lambda ={\lambda }_{23}^L$ in Scenario I as functions of $M_{{\mathcal{S}}_1}$ using the ATLAS (a) $\tau \tau$ [62] and (b) $\tau \nu$ [63] resonance search data. The colored regions are excluded. We keep $\lambda \le 3.5$ to ensure ${\lambda }^2/4\pi <1$.

Figure 4

The 95% CL ($2\sigma$) exclusion limits from the LHC in the $M_{{\mathcal{S}}_1}\text{−}\lambda$ plane for the three scenarios in the minimal model with ${\mathcal{S}}_1$ [Eq. (3)] and the preferred regions by the $R_{D^{(*)}}$ anomalies with (a) $\lambda ={\lambda }_{23}^L$, ${\lambda }_{33}^L=0$ (Scenario I), (b) ${\lambda }_{23}^L=0$, $\lambda ={\lambda }_{33}^L$ (Scenario II), (c) $\lambda ={\lambda }_{23}^L$, ${\lambda }_{33}^L=0.5$ (Scenario III) and (d) $\lambda ={\lambda }_{23}^L$, ${\lambda }_{33}^L=1$ (Scenario III). The blue and red dashed lines show the $2\sigma$ exclusion limits obtained by recasting the ATLAS $\tau \tau$ [62] and $\tau \nu$ [63] resonance search data, respectively. The grey shaded region is the union of the regions excluded in these two channels. The excluded mass ranges from the direct (pair production) searches are shown with shades of purple—in Scenario I the limit [635 GeV, deep purple in (a)] comes from the CMS search for $jj+{\cancel{E}}_{\mathrm{T}}$ [42], in Scenario II, from the CMS $tt\tau \tau$ [41] [565 GeV, shown with deep purple in (b)] and $bb+{\cancel{E}}_{\mathrm{T}}$ searches [42] [800 GeV, shown with light purple in (b)]. We recast the pair production limit on Scenario II from the CMS $bb+{\cancel{E}}_{\mathrm{T}}$ search [42] data (i.e., the stronger one) in the Scenario III plots [shown with light purple in (c) and (d)]. However, since with varying ${\lambda }_{23}^L$, $\mathrm{Br}({\mathcal{S}}_1\to b\nu )$ varies, the limit changes with ${\lambda }_{23}^L$—it decreases as ${\lambda }_{23}^L$ increases. Similarly, the pair production limit from the CMS search for $jj+{\cancel{E}}_{\mathrm{T}}$ [42] on Scenario I is recast for Scenario III [shown with deep purple in (c) and (d)]. The green and yellow bands show the regions favored by the $R_{D^{(*)}}$ anomalies within $1\sigma$ and $2\sigma$, respectively. We have used Eqs. (5)–(10) to obtain these.

Figure 5

The $1\sigma$ and $2\sigma$ CL exclusion limits on ${\lambda }_{23}^R$ as functions of $M_{{\mathcal{S}}_1}$ using the ATLAS $\tau \tau$ [62] resonance search data. The colored regions are excluded. To obtain this plot we have assumed ${\lambda }_{23}^L,{\lambda }_{3\alpha }^L=0$. We keep ${\lambda }_{23}^R\le 3.5$ to ensure ${({\lambda }_{23}^R)}^2/4\pi <1$.