  We study the electronic relaxation in a quantum dot within the polaron
approach, by focusing on the {\it reversible} anharmonic decay of longitudinal
optical (LO) phonons forming the polaron into longitudinal acoustic (LA)
phonons. The coherent coupling between the LO and LA phonons is treated within
a mean-field approach. We derive a temperature-dependent inter-level coupling
parameter, related to the Gr\"uneisen parameter and the thermal expansion
coefficient, that characterizes an effective decay channel for the electronic
(or excitonic) states. Within this theory, we obtain a characteristic
anharmonic decay time of 1ns, 2-3 orders of magnitude longer than previous
predictions based on the Fermi's Golden Rule. We suggest that coherent
relaxation due to carrier-carrier interaction is an efficient alternative to
the (too slow) polaron decay.
