arXiv subjects

An Sun

Publications and source records attributed to An Sun.

2 recordsLinked to original sources

arXiv2018

A new algorithm towards quasi-Wigner solution of the gap equation beyond the chiral limit

We propose a new algorithm to solve the quasi-Wigner solution of the gap equation beyond chiral limit. Employing a Gaussian gluon model and rainbow truncation, we find that the quasi-Wigner solution exists in a limited region of current quark mass, $m<43.1$ MeV, at zero temperature $T$ and zero chemical potential $\mu$. The difference between Cornwall-Jackiw-Tomboulis (CJT) effective actions of quasi-Wigner and Nambu-Goldstone solutions shows that the Nambu-Goldstone solution is chosen by physics. Moreover, the quasi-Wigner solution is studied at finite temperature and chemical potential, the far infrared mass function of quasi-Wigner solution is negative and decrease along with $T$ at $\mu=0$. Its susceptibility is divergent at certain temperature with small $m$, and this temperature decreases along with $m$. Taking $T=80$ MeV as an example, the quasi-Wigner solution is shown at finite chemical potential upto $\mu=350$ MeV as well as Nambu solution, the coexistence of these two solutions indicates that the QCD system suffers the first order phase transition. The first order chiral phase transition line is determined by the difference of CJT effective actions.

hep-ph↗

arXiv2018

Wigner solution of the quark gap equation

Solutions and their evolutions of the quark gap equation are studied within the Nambu-Jona--Lasinio model, which is a basic issue for studying the QCD phase structure and locating the possible critical end point. It is shown that in the chiral limit case of the vacuum, chiral symmetry will hold if the coupling strength $G$ is small, then the system only has the Wigner solution at $M=0$. If increasing $G$, two symmetric minima will appear as the positive and `negative' Nambu solutions, however, the solution $M=0$ now corresponds to a maximum instead of a minimum of the thermodynamical potential, so is not a physically stable state anymore (we call it `pseudo-Wigner solution'). Besides, it is shown that as the current quark mass $m$ increases, the pseudo-Wigner solution will become negative, and disappear together with the negative Nambu solution if $m$ is large enough. Similar things happen if we increase the temperature or quark chemical potential $\mu$. Some interesting phenomenon is, from some $\mu$ a second local minimum will show up. As $\mu$ increases gradually, it will be stabler than the Nambu solution, survives even the Nambu solution disappears, and approaches $m$, which are just the features of the Wigner solution we expect.

hep-ph↗