Energy scale dependence of coupling constants

I am trying to understand the meaning of the renormalization group equation and what i have understood is that, since observable (or physical?) quantities must not depend on arbitrary energy scales, the RG equation must hold. But why do then the coupling constants, for example depend on the energy scale? Are they not observable quantities?

• Sorry, I can't think of a book on this particular topic. The definition of observables depends on the theory that you consider and is usually clear. In quantum physics, they are computed by bracketing operators in the system state, $\langle \psi | O | \psi \rangle$. In statistical physics they are averages over microscopic fluctuations, $\int P(\{\mu \}) \, O(\{\mu \} )$. The $\{\mu \}$'s are the micro-states of the system and $P(\{\mu \})$ is the corresponding probability. – Steven Mathey Jan 30 '16 at 14:49