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 $m_0=20MeV$: $f_{\pi }=93MeV,m_{\pi }=135MeV,m_{\sigma }=492MeV,{\Gamma }_{\sigma }=574MeV,m_q=295MeV,<\bar{q}q>=-(222MeV{)}^3$.

19 pages, 2 figures

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