  We present results of the location of the closest singularities in the
complex chemical potential plane using a novel method. These results are
obtained with (2+1)-flavor of highly improved staggered quarks (HISQ) on
lattices with temporal extent of Nt=4,6. We show that the scaling is consistent
with the expected scaling of the Lee-Yang edge singularities in the vicinity of
the Roberge-Weiss (RW) transition. We determine various non-universal
parameters using 3D Ising model scaling functions that map QCD in the scaling
region of the RW transition. Furthermore, as a preliminary result we discuss
how the Lee-Yang edge singularity can be used to probe the chiral phase
transition in QCD. The singularity obtained close to the chiral phase
transition temperature Tc seems to be in agreement with the expected scaling of
the Lee-Yang edge singularity. As an outlook, we discuss the scaling of the
Lee-Yang edge singularity in the vicinity of a possible critical end point in
QCD, at even lower temperatures. In the future, such a scaling analysis might
hint on the existence and the location of the critical end point. The work
presented here is a part of an ongoing project of Bielefeld Parma joint
collaboration.
