  We discuss results of the CMS collaboration on the sensitivity of the LHC to
$W$ boson polarisation in the process $pp\to W^\pm + jet \to e^\pm
jet+\not\!\!P_T$ using the $L_P$ variable directly connected to $\theta^*$
angle of the outgoing lepton in the rest frame of the decaying $W$. We have
shown that for a given $L_P$, interference between different polarizations of
the $W$-boson is not negligible, and needs to be taken into account when
considering the differential cross-section with respect to $L_P$. The $L_P$
variable suggested by CMS collaboration is highly suitable variable to study
LHC sensitivity to $g_V,g_A$ couplings of $W$-boson to fermions. We note that
the experimental sensitivity to W-boson polarization which is much higher than
that to ($g_V,g_A$) parameter space can be turned around and used to identify
deviations from the Standard Model as a signal for new physics at the LHC.
