Correlation Probes of a QCD Critical Point

TL;DR

This paper proposes new experimental measures to identify the QCD critical point in heavy ion collisions by analyzing opacity, correlation functions, and fluctuations, aiming to determine critical exponents and universality class of the phase transition.

Contribution

It introduces novel methods to measure opacity, correlation length exponents, and specific heat critical exponents in heavy ion collisions, linking them to the QCD critical point.

Findings

Opacity peaks at the critical point.

Correlation exponents can be extracted from Bose-Einstein correlations.

Fluctuation measurements can determine specific heat critical exponent.

Abstract

Critical opalescence is a characteristic experimental signature of a second order phase transition in solid state physics. A new, experimentally accessible measure of opacity and of attenuation length in heavy ion reactions is suggested, as a combination of HBT radii and nuclear modification factors. This opacity is maximal when $\sqrt{s_{NN}}$, the system size and centrality correspond to the critical point of QCD. To characterize the phase transition at this critical point, the critical exponent of the correlation function can be determined by measuring the L\'evy index of stability of the Bose-Einstein or HBT correlations. The exponent of the correlation length can be determined from fits to the multiplicity distribution in various pseudorapidity intervals, also as a function of colliding energy, system size, centrality and (chemical) freeze-out temperature. These two critical exponents determine the remaining four critical exponents and the universality class of this second order phase transition. As a control experiment, the determination of the critical exponent of the specific heat capacity is proposed, from event-by-event fluctuation measurements. To measure opacity precisely, well calibrated high transverse momentum probes are needed, such as given by the excitation function of $\gamma$ + jet correlation functions.