Chiral Phase Transition Temperature in 3-flavor QCD
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The nature of the chiral phase transition in QCD with three massless flavors of quarks remains unresolved despite being studied for nearly four decades. This Ph.D. thesis is a study using Lattice QCD to determine the chiral phase transition temperature Tc, at which the spontaneously broken 3- flavor chiral symmetry is expected to restore. Four pion masses - highest being the physical pion mass of about 140 MeV - have been studied. Our analysis takes into account the temperature dependence of various chiral observables, such as 3- flavor chiral condensate and chiral susceptibility. A wide range of temperatures has been explored, starting in the vicinity of the chiral transition temperature to a much higher value. For a fixed quark mass, to take into account the finite size effects, different volumes are also generated and analysed. In the temperature and pion mass range explored, observables show drastic changes, hinting at a crossover. Finally, by employing universal finite size scaling techniques, it is found that the behaviour of chiral observables is consistent with 3-d O(2) universality class. Finite size scaling analysis is used to extract Tc values out of the data using two methods. First, by fi tting pseudocritical temperatures corresponding to different quark masses and volumes to the scaling expectation. Second, by constructing ratio H M=M, where H is the symmetry breaking field constructed using quark mass, M is the order parameter constructed from chiral condensate, and M is the susceptibility of the order parameter constructed from chiral susceptibility, and fi tting this ratio to the scaling expectation. From both the methods, within errors, we nd a temperature of about 100 MeV.