NJL model derived from QCD

Abstract

We apply Bogolubov approach to QCD with two light quarks to demonstrate a spontaneous generation of an effective interaction, leading to the Nambu -- Jona-Lasinio model. The resulting theory contains two parameters: average low-energy value of $\alpha_s$ and current light quark mass $m_0$. All other low-energy parameters: the pion decay constant, mass of the $\pi$-meson, mass of the $\sigma$-meson and its width, the constituent quark mass, the quark condensate are expressed in terms of the two input parameters in satisfactory correspondence to experimental data and chiral phenomenology. {\it E.g.} in the approximation being used we have for $\alpha_s = 0.67$ and $m_0 = 20 MeV$: $f_\pi = 93 MeV, m_\pi = 135 MeV, m_\sigma = 492 MeV, \Gamma_\sigma = 574 MeV, m_q = 295 MeV, <\bar q q> = -(222 MeV)^3$.