  Differential measurements of single top quark $t$-channel cross sections as a
function of the transverse momentum and the absolute value of the rapidity of
the top quark are presented. The data collected by the CMS experiment at the
LHC at a center-of-mass energy of 8 TeV corresponds to an integrated luminosity
of 19.7 fb$^{-1}$. Leptonic decay channels of the top quark, with either a muon
or an electron in the final state, are considered. Neural networks are used to
separate signal from background contributions. After correcting for selection
efficiencies and detector resolution with an unfolding technique, the resulting
distributions are found to agree with predictions from different Monte Carlo
generators within the estimated uncertainties.
