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

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