Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram |
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Authors: | Aftab Ahmad Ali Murad |
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Institution: | Institute of Physics, Gomal University, 29220, D.I. Khan, Khyber Pakhtunkhaw, Pakistan |
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Abstract: | We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors \begin{document}$ N_f $\end{document}![]() and colors \begin{document}$ N_c $\end{document}![]() using the Nambu-Jona-Lasinio (NJL) model of quarks in the Schwinger-Dyson equation framework, dressed with a color-flavor dependence of effective coupling. For fixed \begin{document}$ N_f = 2 $\end{document}![]() and varying \begin{document}$ N_c $\end{document}![]() , we observe that the dynamical chiral symmetry is broken when \begin{document}$ N_c $\end{document}![]() exceeds its critical value \begin{document}$ N^{c}_{c}\approx2.2 $\end{document}![]() . For a fixed \begin{document}$ N_c = 3 $\end{document}![]() and varying \begin{document}$ N_f $\end{document}![]() , we observe that the dynamical chiral symmetry is restored when \begin{document}$ N_f $\end{document}![]() reaches its critical value \begin{document}$ N^{c}_{f}\approx8 $\end{document}![]() . Strong interplay is observed between \begin{document}$ N_c $\end{document}![]() and \begin{document}$ N_f $\end{document}![]() , i.e., larger values of \begin{document}$ N_c $\end{document}![]() tend to strengthen the dynamical generated quark mass and quark-antiquark condensate, while higher values of \begin{document}$ N_f $\end{document}![]() suppress both parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at a finite temperature T and quark chemical potential μ for various \begin{document}$ N_c $\end{document}![]() and \begin{document}$ N_f $\end{document}![]() . At finite T and μ, we observe that the critical number of colors \begin{document}$ N^{c}_c $\end{document}![]() is enhanced, whereas the critical number of flavors \begin{document}$ N^{c}_f $\end{document}![]() is suppressed as T and μ increase. Consequently, the critical temperature \begin{document}$ T_c $\end{document}![]() , \begin{document}$ \mu_c $\end{document}![]() , and co-ordinates of the critical endpoint \begin{document}$ (T^{E}_c,\mu^{E}_c) $\end{document}![]() in the QCD phase diagram are enhanced as \begin{document}$ N_c $\end{document}![]() increases and suppressed when \begin{document}$ N_f $\end{document}![]() increases. Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions. |
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Keywords: | chiral symmetry breaking Schwinger-Dyson equation finite temperature and density QCD phase diagram |
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