Dispersion laws for in-medium fermions and gluons in the CFL phase of QCD

We evaluate several quantities appearing in the effective Lagrangian for the color–flavor locked phase of high density QCD using a formalism which exploits the approximate decoupling of fermions with energy negative with respect to the Fermi energy. The effective theory is essentially two-dimensional and exhibits a Fermi velocity superselection rule, similar to the one found in the Heavy Quark Effective Theory. Within the formalism we reproduce, using gradient expansion, the results for the effective parameters of the Nambu–Goldstone bosons. We also determine the dispersion laws for the gluons. By coupling the theory to fermions and integrating over the two-dimensional degrees of freedom we obtain the effective description of in-medium fermions.