Different scenarios of dynamical chiral symmetry breaking in the interacting instanton liquid model via flavor symmetry breaking

We investigate a type of dynamical chiral symmetry breaking (D⁢𝜒⁢SB) for various current quark masses using the interacting instanton liquid model. The type of D⁢𝜒⁢SB is classified based on the sign of the second derivative of the free energy density with respect to the quark condensate at the origin. We perform numerical simulations of the interacting instanton liquid model with the flavor SU(2) symmetric and (2+1)-flavor quarks. We find that the curvature is negative in the SU(2) case. This means the ordinary type of D⁢𝜒⁢SB. In contrast, in the (2+1)-flavor case, a positive curvature is observed when the strange quark mass is as small as those of the up and down quarks. This suggests that the anomaly-driven type of D⁢𝜒⁢SB can occur under the approximate flavor SU(3) symmetry. As the strange quark mass increases, the curvature gradually decreases and becomes negative when the strange quark mass is approximately three times larger than those of the light quarks. This difference can be understood in terms of the ’t Hooft vertex which induces a six-quark interaction in the 𝑁𝑓 =3 case and does a four-quark interaction in the 𝑁𝑓 =2 case. Our results might indicate that the ratio between the strange and light quark masses plays a crucial role in understanding the microscopic relationship between and the anomaly effect.