  We study the effective field theory sensitivity of an LHC analysis for the
$\tau \nu$ final state with an associated b-jet. To illustrate the improvement
due to the b-tagging, we first recast the recent CMS analysis in the $\tau\nu$
channel, using an integrated luminosity of 35.9 fb$^{-1}$ at $\sqrt{s}=13$ TeV,
and provide limits on all the dimension-six effective operators which
contribute to the process. The expected limits from the b-tagged analysis are
then derived and compared. We find an improvement of approximately $\sim 30\%$
in the bounds for operators with a b quark. We also discuss in detail possible
angular observables to be used as a discriminator between dimension-six
operators with different Lorentz structure. Finally, we study the impact of
these limits on some simplified scenarios aimed at addressing the observed
deviations from the Standard Model in lepton flavor universality ratios of
semileptonic B-meson decays. In particular, we compare the collider limits on
those scenarios set by our analysis either with or without the b-tagging,
assuming an integrated luminosity of 300 fb$^{-1}$, with relevant low-energy
flavor measurements.
