Establish a controlled critical-response framework for transverse-momentum correlations

Establish a controlled quantitative framework that relates the measured two-particle transverse-momentum correlation observable C_{p_T} to the underlying equilibrium critical response and demonstrates its expected critical scaling.

Background

The paper emphasizes that C_{p_T} receives contributions from temperature fluctuations as well as rapid expansion, collective flow, finite size and lifetime, hadronic rescattering, baryon transport, resonance decays, diffusion, and changing particle composition. Consequently, a non-monotonic beam-energy dependence cannot be interpreted quantitatively as evidence for a QCD critical end point without a framework that separates or controls these effects.

The authors contrast C_{p_T} with higher-order conserved-charge cumulants and other observables for which finite-size scaling has been used to establish critical behavior. They explicitly state that no comparable framework currently demonstrates either the connection of C_{p_T} to the critical response or its critical scaling.

References

No well-established framework presently demonstrates such a connection or critical scaling for $C_{p_T}$.

— Comment on "Non-Monotonicity of Transverse-Momentum Correlations in Au+Au Collisions at RHIC"  (2609.17279 - Lacey, 15 Sep 2026) in Section discussing the thermodynamic interpretation of C_{p_T}

Moreover, no controlled finite-size scaling or other quantitative framework has established how the location of the observed $C_{p_T}$ extremum should map onto the underlying thermodynamic CEP.

— Comment on "Non-Monotonicity of Transverse-Momentum Correlations in Au+Au Collisions at RHIC"  (2609.17279 - Lacey, 15 Sep 2026) in Section discussing the discrepancy between the C_{p_T} extremum and susceptibility-based CEP constraints