Interplay between quark-antiquark and diquark condensates in vacuum in a two-flavor Nambu-Jona-Lasinio model
arXiv:hep-th/0703059 · doi:10.1088/0253-6102/47/1/019
Abstract
By means of a relativistic effective potential, we have analytically researched competition between the quark-antiquark condensates and the diquark condensates in vacuum in ground state of a two-flavor Nambu-Jona-Lasinio (NJL) model and obtained the phase diagram, where and 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 phase when , and as decreases to one will first have a coexistence phase of the condensates and and then a pure phase. In non-zero bare quark mass case, the critical value of at which the pure phase will transfer to the coexistence phase of the condensates and 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 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.
7 pages, revtex4, 1 figure, minor typos corrected