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Exploring the QCD phase transition is one of the most important goals in relativistic heavy-ion collisions. The Beam Energy Scan Program at RHIC has revealed a preliminary non-monotonic behavior of net-proton multiplicity fluctuations with increasing collision energy [1], which is consistent with theoretical predictions [2].
However, the quark-gluon plasma created in relativistic heavy-ion collisions is a complex system, where multiple physical effects may distort theoretical predictions of net-proton multiplicity fluctuations. In particular, realistic dynamical modeling incorporating experimental conditions near the QCD phase transition is indispensable for ultimately identifying the QCD phase transition in heavy-ion collision experiments. As a most relevant degree of freedom in the vicinity of the QCD critical point, the dynamical behavior of conserved baryon density has attracted extensive attention [3-5]. Nevertheless, a fully realistic framework capable of describing the dynamical evolution of non-Gaussian fluctuations over the entire QCD phase diagram remains far from complete.
Using the deterministic equations that govern the non-Gaussian fluctuation dynamics of baryon density [6], we systematically explore the time evolution of baryon density fluctuations [7] across the QCD phase diagram that constructed via the functional renormalization group approach [8]. Our results reveal that critical slowing down induces a more suppression of the non-monotonic behavior of kurtosis with varying collision energies. Furthermore, we also investigate the extended diffusion framework within Maxwell-Cattaneo theory that incorporates finite relaxation time corrections [9]. This mechanism is found to exert substantial impacts, most notably shifting the peak position of non-monotonic kurtosis toward higher baryon chemical potential.
[1] STAR Collaboration, Phys.Rev.Lett. 135, 142301(2025)
[2] M.Stephanov, arXiv:2410.02861
[3] M.Sakaida, M.Asakawa, H.Fujii, M.Kitazawa, Phys.Rev.C 95, 064905 (2017)
[4] G. Pihan, M.Bluhm, M.Kitazawa, T. Sami, M.Nahrgang, Phys.Rev.C 107,014908 (2023)
[5] S.Wu, Phys.Rev.C 111 (2025) 014915
[6] X. An, G. Ba¸sar, M. Stephanov, and H.-U. Yee, Phys. Rev. Lett. 127, 072301 (2021)
[7] S.Wu, S.Yin and W.-j. Fu, in preparation.
[8] W.-j., X. Luo, J.M. Pawlowski, F. Rennecke, S. Yin, Phys. Rev, D 111, L031502 (2025)
[9] N. Abbasi, X. An and S.Wu, to appear
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