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By means of a relativistic effective potential, we have analyticallyresearched competition between the quark-antiquark condensates $<\bar{q}q>$ andthe diquark condensates $<qq>$ in vacuum in ground state of a two-flavorNambu-Jona-Lasinio (NJL) model and obtained the $G_S-H_S$ phase diagram, where$G_S$ and $H_S$ are the respective four-fermion coupling constants in scalarquark-antiquark channel and scalar color anti-triplet diquark channel. Theresults show that, in the chiral limit, there is only the pure $<\bar{q}q>$phase when $G_S/H_S>2/3$, and as $G_S/H_S$ decreases to $2/3>G_S/H_S\geq 0$ onewill first have a coexistence phase of the condensates $<\bar{q}q>$ and $<qq>$and then a pure $<qq>$ phase. In non-zero bare quark mass case, the criticalvalue of $G_S/H_S$ at which the pure $<\bar{q}q>$ phase will transfer to thecoexistence phase of the condensates $<\bar{q}q>$ and $<qq>$ will be less than2/3. Our theoretical results, combined with present phenomenological fact thatthere is no diquark condensates in the vacuum of QCD, will also impose a realrestriction to any given two-flavor NJL model which is intended to simulateQCD, i.e. in such model the resulting smallest ratio $G_S/H_S$ after the Fierztransformations in the Hartree approximation must be larger than 2/3. A fewphenomenological QCD-like NJL models are checked and analyzed.Comment: 7 pages, revtex4, 1 figure, minor typos correcte

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