What Does the CMS Measurement of W-polarization Tell Us about the Underlying Theory of the Coupling of W-Bosons to Matter?

We discuss results of the CMS collaboration on the sensitivity of the LHC to $W$ boson polarisation in the process $pp\to W^\pm + jet \to e^\pm jet$ 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 the interference between $W$-boson polarisations for $L_P$ is not negligible which makes $L_P$ to be actually not a quite proper variable to study $W$-boson polarisation. On the other hand the $L_P$ variable suggested by CMS collaboration is a quite proper 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 pin down new physics at the LHC.