About the rapidity and helicity distributions of the W bosons produced at LHC

$W$ bosons are produced at LHC from a forward-backward symmetric initial state. Their decay to a charged lepton and a neutrino has a strong spin analysing power. The combination of these effects results in characteristic distributions of the pseudorapidity of the leptons decaying from $W^{+}$ and $W^{-}$ of different helicity. This observation may open the possibility to measure precisely the $W^{+}$ and $W^{-}$ rapidity distributions for the two transverse polarisation states of $W$ bosons produced at small transverse momentum.