Comment on "Non-Monotonicity of Transverse-Momentum Correlations in Au+Au Collisions at RHIC"

Abstract: Recent measurements of two-particle transverse-momentum correlations, $C_{p_T}$, in Au+Au collisions have revealed a statistically significant non-monotonic beam-energy dependence over the range $\sqrt{s_{NN}}=3.0$--$7.7$~GeV that has been interpreted as potentially indicative of critical phenomena associated with a critical end point (CEP) in the QCD phase diagram. This interpretation is assessed in light of the absence of a controlled framework establishing $C_{p_T}$ as a quantitative proxy for the underlying critical response. The implications of this limitation are examined by considering the expected finite-size and finite-time modification of critical fluctuations, substantial non-critical dynamical contributions, the lack of demonstrated critical scaling, and the sizeable discrepancy between the CEP region inferred from the observed $C_{p_T}$ non-monotonicity and that constrained by susceptibility-based measurements and finite-size scaling analyses. Taken together, these considerations indicate that the observed $C_{p_T}$ non-monotonicity does not, by itself, establish a critical origin nor provide reliable quantitative constraints on the existence or location of a possible CEP.