  In the regime of strong nonlinearity, the validity of conventional
perturbation based phonon transport theories is questionable. In particular,
the renormalized phonons instead of phonons are responsible for heat transport
in nonlinear lattices. In this work, we directly study the temperature and
frequency dependent Mean Free Path (MFP) of renormalized phonons with the newly
developed numerical tuning fork method. The typical 1D nonlinear lattices such
as Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice and $\phi^4$ lattice are
investigated in details. It is found that the MFPs are inversely proportional
to the frequencies of renormalized phonons rather than the square of phonon
frequencies predicted by existing phonon scattering theory.
