Measuring Fluctuations in RHIC Collisions
by Jeffrey Mitchell
A new form of nuclear matter that appears to have the properties of a perfect liquid is currently being studied at RHIC. This new form of matter is created in collisions of pairs of ions that initially contain ordinary nuclear matter. During the collisions, the nuclear matter is heated and compressed to a very high degree. At some point during the collision, the matter goes through a phase transition to the new state, much like ice undergoes a phase transition to water when heated. The measurement of fluctuations is a powerful tool in the search for direct evidence of the phase transition.
The motivation for fluctuation measurements in RHIC collisions comes from what is known about continuous phase transitions in ordinary materials. When a material approaches a critical point, several thermodynamic properties of the material will diverge as the system approaches its critical temperature, TC. The divergences of these quantities behave as power laws in the quantity (T-TC) and can be characterized by the exponents of the power laws, which are called critical exponents. Nature tends to group different systems into classes, where all systems in the same universality class will share the same critical exponents.
In RHIC collisions, a variety of fluctuation observables are measured that can be directly related to thermodynamic properties of the systems being studied. An example is the measurement of the fluctuations of the number of charged particles produced in each event, which can be related to the isothermal compressibility of the system. The compressibility diverges at the critical point with a critical exponent called gamma. Another example is that of the fluctuations of the mean transverse momentum of produced charged particles in an event, which can be related to the heat capacity of the system. The heat capacity diverges with a critical exponent called alpha. The goal of the measurements is to look for power law behavior in the fluctuation quantities as the system temperature is varied, which is typically done by changing the collision energy of the ions in the collider. In addition, measuring identical critical exponents in different systems like Au+Au and Cu+Cu collisions would produce strong evidence of the critical behavior signaling a phase transition.
The measurement of fluctuations in relativistic heavy ion collisions is extremely difficult because there are many contributions to the dynamical fluctuations of interest from non-dynamical sources such as fluctuations in the geometry of the collisions, contributions from known physical processes such as jets and flow, and the dependence of the measurements on the size of the active area of the detector. Most of these non-dynamical contributions can be estimated and subtracted with careful measurements and simulations. However, to date, none of the fluctuation observables measured by the RHIC experiments have unveiled unambiguous signs of power law behavior at different collision energies and significant collision energy dependence is not yet seen. This is surprising since measurements of the freeze-out temperature (the temperature at which the hadrons are formed) indicates that RHIC may be in the phase transition region of the heating curve. It is possible that the small number of energies scanned thus far do not bring the system sufficiently close to the critical point predicted by Quantum Chromo-Dynamics (QCD) to be reflected in the fluctuations. Hence, interest has been growing to perform a systematic energy scan with the RHIC collider in order to hopefully reveal unambiguous signatures of critical behavior and the location of the critical point. Recently, a pair of workshops, one at BNL in March 2006 focused on RHIC, and one at the Galileo Galilei Institute in Florence, Italy in July 2006 have discussed the details of a search for the QCD critical point. Information about the location of the critical point would help further our understanding of QCD and the new state of matter currently under study at RHIC.