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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 ⟨q̄q⟩ 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 ⟨q̄q⟩ 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 ⟨q̄q⟩ 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 ⟨q̄q⟩ phase will transfer to the coexistence phase of the condensates ⟨q̄q⟩ 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.