Abstract
We consider the ‘two flavour’ Nambu–Jona-Lasinio model in the presence of a vector and an axial external chemical potential and study the phase structure of the model at zero temperature. The Nambu–Jona-Lasinio model is often used as a toy replica of QCD and it is therefore interesting to explore the consequences of adding external vector and axial chemical potentials in this model, mostly motivated by claims that such external drivers could trigger a phase where parity could be broken in QCD. We are also motivated by some lattice analysis that attempt to understand the nature of the so-called Aoki phase using this simplified model. Analogies and differences with the expected behaviour in QCD are discussed and the limitations of the model are pointed out.
Highlights
In spite of the obvious shortcomings of this analogy, Nambu–JonaLasinio model (NJL) is regarded as providing an intuitive picture of the mechanism of chiral symmetry breaking in QCD via a strong effective interaction in the scalar isosinglet channel
It is far from obvious that NJL is a good modellisation of QCD, these tests are still useful to understand in a simpler theory what are the right questions to pose
This is a phase in lattice QCD with Wilson fermions where parity and possibly isospin symmetry is broken
Summary
The possibility that parity breaks in QCD at high temperatures and/or densities has received a lot of attention [1,2,3,4,5,6,7,8]. In the present paper we shall consider the Nambu–JonaLasinio model (NJL) [24,25,26,27,28,29,30], which shares interesting features with QCD such as the appearance of chiral symmetry breaking. NJL is definitely not QCD and the present work does not attempt to draw definite conclusions on the latter theory; just to point out possible phases requiring further analysis. It turns out that the conditions for this phase to be stable and exhibit chiral symmetry breaking too are such that one gets an inverted mass spectrum with mπ > mηq and mσ > ma0 , which is quite different from QCD.
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