We call the simulation with nonzero Γph−ph the anharmonic hot phonon model (AHP model), because it includes anharmonic couling between the G and K phonons. Due to energy and momentum conservation, the two K-phonons can decay into one G-phonon and one Γ phonon in the branch of lower energy, or decay into one G-phonon and one K-phonon in the branch of lower energy (Fig. 5). It agrees much better (Fig. 1(a,b)) with the data. Within this picture, pump of lower power (0.15 mJ/cm2) gives a slower G-phonon buildup (see Fig. 4) consistent with decreased anharmonicity at lower phonon temperature. So the inclusion of ph-ph scattering is essential for explaining the observed time delay.