Fundamental constants in effective theory

There is a discussion between L. B. Okun, G. Veneziano and M. J. Duff, concerning the number of fundamental dimensionful constants in physics. They advocated correspondingly 3, 2 and 0 fundamental constants. Here we consider this problem on example of the effective relativistic quantum field theory, which emerges in the low energy corner of quantum liquids and which reproduces many features of our physics including Lorentz invariance, chiral fermions, gauge fields and dynamical gravity.