The production of correlated Stokes (S) and anti-Stokes (aS) photons (SaS process) mediated by real or virtual phonon exchange has been reported in many transparent materials. In this work, we investigate the polarization and time correlations of SaS photon pairs produced in a diamond sample. We demonstrate that both S and aS photons have mainly the same polarization of the excitation laser. We also perform a pump-and-probe experiment to measure the decay rate of the SaS pair production, evidencing the fundamental diference between the real and virtual (phonon exchange) processes. In real processes, the rate of SaS pair production is governed by the phonon lifetime of $(2.8 pm 0.3)$ ps, while virtual processes only take place within the time width of the pump laser pulses of approximately 0.2 ps. We explain the diference between real and virtual SaS processes by a phenomenological model, based on probabilities of phonon creation and decay.
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