  We revisit the constraints on semileptonic operators derived from the
mono-$\tau$ high-$p_T$ events in $pp$ collisions at LHC. Like in previous
studies, we obtain limits on the New Physics couplings from the CMS data much
stronger than from the ATLAS data, despite a nearly equal integrated
luminosity. We find that a neglected systematics on the $\tau$ lepton
reconstruction efficiency can partly explain that difference. We then provide
new limits on the New Physics couplings relevant to decays based on $b\to
c\tau\bar{\nu}$ by using the recent ATLAS data with 139 ${\rm fb}^{-1}$. We
also show that the inclusion of propagation of the New Physics particle can
significantly worsen the bounds obtained by relying on Effective Field
Theoretical treatment of New Physics.
