Supplement No 2 CONSERVED CHARGE FLUCTUATIONS IN THE CHIRAL LIMIT ∗

Understanding of the phase diagram of QCD in the plane of temperature and various chemical potentials is one of the primary goals of lattice QCD calculations and the heavy-ion collision experiments at RHIC and the LHC. The temperature variation at zero chemical potential is being explored at the LHC and studied extensively using lattice techniques due to the absence of the infamous sign problem. At physical quark masses, there exists a chiral crossover at a temperature Tpc around 157 MeV [1, 2]. A schematic phase diagram of QCD with an additional axis for degenerate light (up and down) quark masses is shown in Fig. 1 [3]. In the figure, the dotted lines along the horizontal and vertical axes correspond to the plane of physical quark masses and the dashed line is the chiral crossover line which ends at a critical end point Tcep, which is being actively pursued in experiments. The chiral limit, however, is not accessible to experiments and can only be studied via theoretical techniques. The spontaneous symmetry breaking of the exact SU(2) × SU(2) symmetry in the chiral limit of two light quarks is expected to be a phase transition belonging to the universality class of 3d O(4) spin model [4]. There exists an alternative scenario where the chiral