Non-resonant new physics search at the LHC for the $b \to c \tau \nu$ anomalies

Motivated by the $b \to c \tau \overline{\nu}$ anomalies, we study non-resonant searches for new physics at the large hadron collider (LHC) by considering final states with an energetic and hadronically decaying $\tau$ lepton, a $b$-jet and large missing transverse momentum ($pp \to \tau_h \overline{b} + E_{\rm T}^{\rm miss}$). Such searches can be useful to probe new physics contributions to $b \to c \tau \overline{\nu}$. They are analyzed not only within the dimension-six effective field theory (EFT) but also in explicit leptoquark (LQ) models with the LQ non-decoupled. The former is realized by taking a limit of large LQ mass in the latter. It is clarified that the LHC sensitivity is sensitive to the LQ mass for $O(1)$ TeV even in the search of $pp \to \tau_h \overline{b} + E_{\rm T}^{\rm miss}$. Although the LQ models provide a weaker sensitivity than the EFT limit, it is found that the non-resonant search of $pp \to \tau_h \overline{b} + E_{\rm T}^{\rm miss}$ can improve the sensitivity by $\approx 40\%$ versus a conventional mono-$\tau$ search ($pp \to \tau_h + E_{\rm T}^{\rm miss}$) in the whole LQ mass region. Consequently, it is expected that most of the parameter regions suggested by the $b \to c \tau \overline{\nu}$ anomalies can be probed at the HL-LHC. Also, it is shown that $\text{R}_2$ LQ scenario is accessible entirely once the LHC Run 2 data are analyzed. In addition, we discuss a charge selection of $\tau_h$ to further suppress the standard-model background, and investigate the angular correlations among $b,\, \tau$ and the missing transverse momentum to discriminate the LQ scenarios.