  We determine experimentally the spinor interaction constants of
lower-polaritons $\alpha_1$ and $\alpha_2$ using resonant pump-probe
spectroscopy with a spectrally narrow pump pulse. Our experimental findings are
analyzed with the Bogoliubov-like theory and mean-field two channel model based
on the lower-polariton and biexciton basis. We find an enhancement of the
attractive interaction and dissipative nonlinearity of lower-polaritons with
anti-parallel spins in the vicinity of the biexciton resonance when the energy
of two lower-polaritons approaches energetically that of the biexciton. These
observations are consistent with the existence of a scattering resonance
between lower-polaritons and biexcitons (polaritonic Feshbach resonance).
