[Paper Review] Correlation Probes of a QCD Critical Point

T. Csörgő|arXiv (Cornell University)|Mar 4, 2009

High-Energy Particle Collisions Research2 references3 citations

TL;DR

This paper proposes using jet-induced opacity and Bose-Einstein correlation functions as experimental probes to identify the QCD critical point in heavy-ion collisions. By measuring the Lévy index of stability in HBT correlations and the multiplicity distribution's negative binomial fit, the critical exponents of correlation length and correlation function are extracted, enabling determination of the universality class of the second-order phase transition at the critical point.

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 Lévy 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 $γ$ + jet correlation functions.

Motivation & Objective

• To identify the QCD critical point in heavy-ion collisions using experimentally accessible observables.
• To characterize the second-order phase transition at the critical point through measurable critical exponents.
• To determine the universality class of the QCD phase transition using event-by-event fluctuation measurements.
• To validate the critical point signature via cross-checking multiple critical exponents, including heat capacity and correlation length.

Proposed method

• Measure the opacity of the medium via the combination of HBT radii and nuclear modification factors, with maximum opacity indicating proximity to the critical point.
• Use the Lévy index of stability in Bose-Einstein correlation functions to extract the critical exponent of the correlation function.
• Fit multiplicity distributions in pseudorapidity intervals with the negative binomial distribution to determine the correlation length and its critical exponent.
• Perform event-by-event analysis of chemical freeze-out temperature to study power-law behavior near the critical point.
• Cross-validate results by measuring the critical exponent of the specific heat capacity from event-by-event fluctuations in chemical freeze-out temperature.
• Apply theoretical relations between critical exponents to reconstruct the full set of six critical exponents from two measured ones.

Experimental results

Research questions

• RQ1 Can the QCD critical point be experimentally located by identifying the maximum in medium opacity or minimum in attenuation length?
• RQ2 Does the Lévy index of stability in HBT correlations exhibit a non-Gaussian shape near the critical point, indicating critical behavior?
• RQ3 Is the correlation length's dependence on temperature consistent with a power-law scaling near the critical point?
• RQ4 Can the universality class of the QCD phase transition be determined from measured critical exponents?
• RQ5 Do event-by-event fluctuations in chemical freeze-out temperature yield a measurable critical exponent for the specific heat capacity?

Key findings

• The opacity of the medium, derived from HBT radii and nuclear modification factors, is predicted to peak at the QCD critical point, serving as a smoking gun signature.
• The critical exponent of the correlation function can be extracted from the Lévy index of stability in Bose-Einstein correlations, with the exponent directly measurable from momentum-space correlation functions.
• The correlation length's critical exponent is determined from fits to the negative binomial distribution of multiplicity in pseudorapidity intervals, showing power-law dependence on temperature.
• The critical exponents of the correlation function and correlation length are sufficient to reconstruct all six critical exponents via theoretical relations, enabling universality class determination.
• The critical exponent of the specific heat capacity can be measured via event-by-event fluctuations in chemical freeze-out temperature, providing a cross-check on the critical behavior.
• The method is applicable to RHIC, SPS, and FAIR experiments, offering a systematic strategy to locate and characterize the QCD critical point.