  The CMS collaboration at the CERN-LHC have searched for the $t$-channel
single top quark production using the spin correlation of the $t$-channel. The
signal extraction and cross section measurement relies on the angular
distribution of the charged lepton in the top quark decays, the angle between
the charged lepton momentum and top spin in the top rest frame. The behavior of
the angular distribution is a distinct slope for the t-channel single top
(signal) while it is flat for the backgrounds. In this letter we investigate
the contributions which this spin correlation may receive from a two-Higgs
doublet model, a top-color assisted technicolor (TC2) and the noncommutative
extension of the Standard Model.
