Interplay Between Quark-Antiquark and DiquarkCondensates in Vacuum in a Two-Flavor Nambu–Jona–LasinioModel

Abstract

By means of a relativistic effective potential, weanalytically research competition between the quark-antiquarkcondensates ⟨q̄q⟩ and the diquark condensates⟨qq⟩ in vacuum in ground state of a two-flavorNambu–Jona–Lasinio (NJL) model and obtain the GS-HS phasediagram, where GS and HS are the respective four-fermioncoupling constants in scalar quark-antiquark channel and scalarcolor anti-triplet diquark channel. The results show that, in thechiral limit, there is only the pure ⟨q̄q⟩phase when GS/HS>2/3, and as GS/HS decreases to2/3>GS/HS⩾0 one will first have a coexistence phase of thecondensates ⟨q̄q⟩ and ⟨qq⟩ andthen a pure ⟨qq⟩ phase. In non-zero bare quarkmass case, the critical value of GS/HS at which the pure⟨q̄q⟩ phase will transfer to the coexistencephase of the condensates ⟨q̄q⟩ and ⟨qq⟩ will be less than 2/3. Our theoretical results,combined with present phenomenological fact that there is nodiquark condensates in the vacuum of QCD, will also impose a realrestriction to any given two-flavor NJL model which is intended tosimulate QCD, i.e. in such model the resulting smallest ratioGS/HS after the Fierz transformations in the Hartreeapproximation must be larger than 2/3. A few phenomenologicalQCD-like NJL models are checked and analyzed.