Hints from Lattice for QCD Critical Point Search Rajiv V. Gavai Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. Abstract The freeze-out curve in the QCD phase diagram embodies a substantial amount of precise experimental data in heavy ion collisions. We present our lattice QCD results along the freeze-out curve. The variance, skew and kurtosis of the event distribution of baryon number are studied at several energies of interest through Pad´ e resummations. A smooth behaviour is predicted for three ratios of these quantities at current RHIC and future LHC energies. Any deviations from these at the RHIC energy scan would signal the presence of a nearby critical point. Our lattice results on the critical point do show such a behaviour. Keywords: QCD Critical Point, Kurtosis & Skew of Baryon number, Lattice QCD, Freeze-out Curve 1. Introduction Critical points in a phase diagram in the temperature-density plane are special for many reasons. Universality of critical indices, diverging correlation length are some of them. For common substances, such as water or carbon dioxide, the existence of critical point has been established experimentally, with its location known rather precisely, since the required conditions were somewhat easy to tune. Nevertheless, even for these getting a theoretical, especially first principles based, computation of their locations is a bit less easy. Strongly interacting matter, which is are naturally described by Quantum Chromo Dynamics (QCD), has inher- ently higher energy scale. Whether the QCD phase diagram has a critical point in its T -μ B plane, where μ B is the baryonic chemical potential, is therefore an even tougher question to address. A variety of models have been success- fully tested for hadronic interactions. These were was also the first set of tools used for getting a glimpse of the QCD phase diagram. For instance, using an effective chiral Nambu-Jana Lasinio type model, a phase diagram was obtained [1], which suggests a critical point to exist in a world with two light quarks and one heavier quark. One usually has to deal with large coupling constants in the world of (low energy) hadronic interactions. Non- perturbative Lattice QCD, defined on a discrete space-time lattice, has proved itself to be the most reliable technique for extracting such information from QCD. The hadron spectrum has been computed successfully and predictions of weak decay constants of heavy mesons have been made. Application of this approach to finite temperature QCD has yielded a slew of thermodynamics determinations, such as the pressure as a function of temperature. It is there- fore natural to ask whether lattice QCD can help us in locating the QCD critical point. Thanks to the impressive developments on the experimental fronts, the Relativistic Heavy Ion Collider (RHIC) at BNL, New York, and the Email address: gavai@tifr.res.in (Rajiv V. Gavai) Nuclear Physics A 862–863 (2011) 104–110 0375-9474/$ – see front matter © 2011 Elsevier B.V. All rights reserved. www.elsevier.com/locate/nuclphysa doi:10.1016/j.nuclphysa.2011.05.027