Lee-Yang edge singularities in a nonlocal Nambu–Jona-Lasinio model

We investigate the QCD phase diagram and the associated Lee–Yang edge singularities using the two-flavor nonlocal Nambu–Jona-Lasinio model extended to complex chemical potential. We show explicitly there exists a strong correlation between the chiral phase transition and the patterns in the effective potential in the complex plane of order parameter, serving as a criterion to differentiate crossover from first-order transitions. Typically, the Lee–Yang edge singularities can be understood as a generalization of the critical end point (CEP) separating the crossover and the first-order transition, where the positive Nambu phase and the Wigner phase coalesce. We further analyze the scaling behavior near the CEP by extracting the critical exponent associated with the Lee–Yang singularities. Additionally, we confirm that the extrapolation of the Lee–Yang edge singularity trajectories provides an efficient method of determining the CEP location, even at a small real chemical potential. This provides a viable method for exploring regions of the QCD phase diagram that remain inaccessible to lattice QCD.