  $W$ 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.
