Energy dependence of fluctuation and correlation observables of transverse momentum in heavy-ion collisions

In collisions of heavy ions of sufficient energy, cold nuclear matter can be forced into a strongly interacting state of quark-gloun plasma (QGP). To study the properties of QGP and the phase transition to hadronic matter, Au+Au collisions were performed at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and studied using the Solendoidal Tracker at RHIC (STAR) detector. These Au+Au collision were taken during 2010 and 2011 as part of the RHIC Beam Energy Scan (BES) at energies NsN = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. The primary goal of the BES was to search for the critical point of the phase transition between the QGP phase and the hadronic matter phase of nuclear matter.;In this dissertation two analyses on these data are presented which focus on fluctuations of the average transverse momentum (⟨p t⟩) of the particles produced in heavy-ion collisions. ⟨ pt⟩ is related to the temperature of the systems produced in the collisions [35], and fluctuations of ⟨p t⟩ should be sensitive to fluctuations of the temperature [40]. The moments of the ⟨pt⟩ distributions has also been proposed to be sensitive to the correlation length of the QGP medium [41, 42], which will diverge at the critical point.;Fluctuations of ⟨pt⟩ will depend upon both dynamic fluctuations of the produced systems, and statistical fluctuations due to limited statistics. The first analysis presented in this dissertation is of the two particle relative momentum correlator ⟨Delta pt,i, Deltapt,j⟩ which is a direct measure of the dynamic fluctuations of the variance of the ⟨ pt⟩ distribution, s2&angl0;pt&angr0; ,dynamic . The second analysis presented in this dissertation is of the higher moments of the ⟨pt⟩ distribution. The dynamic higher moments are inferred by comparison of the measured data with mixed events and statically sampled events which reproduce the statistical fluctuations while having no dynamic fluctuations.;No consistent non-monotonic behavior, which would be a conclusive indication of the QGP critical point, is observed. Some anomalous behavior of the higher moments is noted which will require further analysis. Dynamic fluctuations of the ⟨pt⟩ distribution, as measured by the two particle correlator Dpt,i, Dpt,j and the higher moments of the ⟨pt⟩ distribution, are observed to increase with energy. There is a strong energy dependence below NsN =19.6GeV , and the dynamic fluctuations of ⟨pt⟩ are consistent with zero at 7.7 GeV.