Melting the diquark condensate in two-color QCD: A renormalization group analysis

We use a Landau theory and the $\epsilon$ expansion to study the superfluid phase transition of two-color QCD at a nonzero temperature T and baryonic chemical potential $\mu .$ At low T, and for $N_f$ flavors of massless quarks, the global $\mathrm{SU}\left({\mathrm{N}}_f\right)\times \mathrm{SU}\left({\mathrm{N}}_f\right)\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ symmetry is spontaneously broken by a diquark condensate down to $\mathrm{Sp}\left({\mathrm{N}}_f\right)\times \mathrm{Sp}\left({\mathrm{N}}_f\right)$ for any $\mu >0.\mathrm{}$ As the temperature increases, the diquark condensate melts, and at sufficiently large T the symmetry is restored. Using renormalization group arguments, we find that in the presence of the chiral anomaly term there can be a second order phase transition when $N_f=2\mathrm{}$ or $N_f>~6,$ while the transition is first order for $N_f=4.\mathrm{}$ We discuss the relevance of these results for the emergence of a tricritical point recently observed in lattice simulations.