What are the physical origin of those two timescales ~8ps and 0.2ps ? (when I am using Double Debye relaxation model to fit the data)
The Double Debey model is just a fit model. Two terms are being used since the simple Debye model with one term does not provide a good fit. Nobody knows the meaning of the two new constants in the model. People are just guessing. A Triple-Debye model wold give an even better fit. And so on. But nobody can tell you for sure if the new fit parameters have any meaning.
Here's a good paper on THz dielectric relaxation in polar liquids. http://www.sciencedirect.com/science/article/pii/S0009261407003843 And here is one on just H20 and D20 in range of your interests. http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.82.2888 The authors identify a slow and fast relaxation times, but I'm not sure how well this is understood microscopically. I would guess these are rotational and librational relaxations. In any case these two times are equivalent to the two Debye relaxation constants.
I assume you mean liquid water. Water vapor is much more complicated.
Although not measured in the THz range you can have a look at these two papers
J. Chem. Phys. 126, 034511 2007
J. Chem. Phys. 121, 7908 (2004)
They contain data that confirm what John Scales said.
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