Lee Yang edge singularities of QCD in association with the Roberge-Weiss and chiral phase transitions

We study the quantum chromodynamics (QCD) phase transitions in the complex chemical potential plane via the Dyson-Schwinger equation approach, incorporating a constant gluonic background field that represents the confining dynamics. We solve the quark gap equation and the background field equation self-consistently, which allows us to directly explore the confinement phase transition and furthermore, evaluate the impact of the back-coupling of confinement on chiral symmetry breaking. Moreover, within such a coupled framework toward the complex chemical potential region, we demonstrate the emergence of Roberge-Weiss (RW) symmetry and investigate the trajectory of Lee-Yang edge singularities (LYESs). Our analysis reveals that the LYESs scaling behavior is similar to our previous findings without the background field condensate. However, a significant difference from our earlier work is that the trajectory of LYESs terminates when the imaginary part of the singularity becomes 1=3πT. We elaborate that this cutoff behavior is caused by the RW symmetry that is symmetric to the imaginary chemical potential Im μ ¼ 1=3πT.