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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>3</a:mn> <a:mi>π</a:mi> <a:mi>T</a:mi> </a:math> . We elaborate that this cutoff behavior is caused by the RW symmetry that is symmetric to the imaginary chemical potential <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>Im</c:mi> <c:mi>μ</c:mi> <c:mo>=</c:mo> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:mn>3</c:mn> <c:mi>π</c:mi> <c:mi>T</c:mi> </c:math> .