Interplay Between Quark-Antiquark and Diquark Condensates in Vacuum in a Two-Flavor Nambu-Jona-Lasinio Model

By means of a relativistic effective potential, we analytically research competition between the quark-antiquark condensates (q-bar q) and the diquark condensates (qq) in vacuum in ground state of a two-flavor Nambu-Jona-Lasinio (NJL) model and obtain the GS-HS phase diagram, where GS and HS are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure (q-bar q) phase when GS/HS>2/3, and as GS/HS decreases to 2/3>GS/HS≥0 one will first have a coexistence phase of the condensates (q-bar q) and (qq) and then a pure (qq) phase. In non-zero bare quark mass case, the critical value of GS/HS at which the pure (q-bar q) phase will transfer to the coexistence phase of the condensates (q-bar q) and (qq) will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting smallest ratio GS/HS after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.