Next to leading order calculation with dimensional regularization in Nambu--Jona-Lasinio Model

The Nambu–Jona-Lasinio model is investigated in the $1\mathrm{/}{N}_c$ expansion with the dimensional regularization. At the four-dimensional limit the meson propagators have simple forms in the leading order of the $1\mathrm{/}{N}_c$ expansion. Thus the next to leading order calculation reduces to an ordinary one loop calculation. Here we obtain an explicit form of the $1\mathrm{/}{N}_c$ correction and numerically evaluate the $N_c$ dependence for the gap equation.