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\Large
%\title{
\large Rapidity Dependence  of Proton Higher-Order Cumulants in $\sqrt{s_{NN}}$ = 3.2, 3.5 and 3.9 GeV Au+Au Collisions


%\author{
\normalsize Zhaohui Wang$^{(1)}$, Yongcong Xu$^{(1,2)}$, Xin Zhang$^{(3,2)}$ \\ $^{(1)}$ Central China Normal University \\ $^{(2)}$  GSI, Helmholtz Center for Heavy Ion Research \\ $^{(3)}$  Institute of Modern Physics, Chinese Academy of Sciences
%}



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Fluctuations of conserved quantities are proposed as a useful observable to study the QCD phase structure including the search for the first-order phase boundary and critical point~\cite{STAR:2024}. Lattice QCD calculations have shown that  there is no critical point for $\mu_B \le$ 450 MeV and few phenomenology models calculations have shown that the critical point could be at temperature of $T \sim$ 100 MeV and baryonic chemical potential of $\mu_B \sim$ 600 - 650 MeV~\cite{Hippert:2023bel,Fu:2019hdw,PhysRevD.104.054022,Basar:2023nkp,Clarke:2024ugt}.  

Rapidity dependence of the higher order cumulant ratios have been argued to be sensitive to the QCD critical point~\cite{Ling:2015yau}. In this talk, we will report rapidity dependence of both higher order cumulants and factorial cumulants of proton multiplicity distribution, up to $6^{TH}$ order from Au+Au collisions, at $\sqrt{s_{NN}}$ = 3.2, 3.5 and 3.9 GeV (699 $\ge \mu_B \ge$ 633 MeV) from the STAR experiment at RHIC. Collision centrality dependence of these rapidity distributions and relevant ratios will be discussed. In addition, the results will be compared with the calculations from transport model UrQMD.




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\textbf{\Large{References}}

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Reference.bib:


% Acceptance dependence of fluctuation measures near the QCD critical point
%arXiv, 1512.09125, nucl-th
@article{Ling:2015yau,
    author = "Ling, Bo and others",
    title = "",
    doi = "10.1103/PhysRevC.93.034915",
    journal = "Phys. Rev. C",
    volume = "93",
    number = "3",
    pages = "034915",
    year = "2016"
}

@article{STAR:2024,
    author = "",
    title = "{STAR Note}",
    eprint = "",
    archivePrefix = "",
    primaryClass = "",
    doi = "",
    journal = "",
    volume = "",
    number = "",
    pages = "",
    year = "",
    note = "\url{https://drupal.star.bnl.gov/STAR/starnotes/public/sn0598}",
}


% QCD critical point, Lee-Yang edge singularities, and Pad\'e resummations (3)
%arXiv, 2312.06952, hep-th
@article{Basar:2023nkp,
    author = "Basar, Gokce",
    title = "",
    doi = "10.1103/PhysRevC.110.015203",
    journal = "Phys. Rev. C",
    volume = "110",
    number = "1",
    pages = "015203",
    year = "2024"
}

% Bayesian location of the QCD critical point from a holographic perspective (1)
@article{Hippert:2023bel,
    author = "Hippert, Mauricio and others",
    title = "",
    eprint = "2309.00579",
    archivePrefix = "arXiv",
    primaryClass = "nucl-th",
    month = "9",
    year = "2023"
}

% Searching for the QCD critical endpoint using multi-point Pad\'e approximations (4)
@article{Clarke:2024ugt,
    author = "Clarke, David A. and others",
    title = "",
    eprint = "2405.10196",
    archivePrefix = "arXiv",
    primaryClass = "hep-lat",
    month = "5",
    year = "2024"
}

% QCD phase structure at finite temperature and density (2-1)
% arXiv, 1909.02991, hep-ph
@article{Fu:2019hdw,
    author = "Fu, Wei-jie and others",
    title = "",
    doi = "10.1103/PhysRevD.101.054032",
    journal = "Phys. Rev. D",
    volume = "101",
    number = "5",
    pages = "054032",
    year = "2020"
}

% Locating the critical endpoint of QCD: Mesonic backcoupling effects (2-2)
@article{PhysRevD.104.054022,
  title = {},
  author = {Gunkel, Pascal J. and others},
  journal = {Phys. Rev. D},
  volume = {104},
  issue = {5},
  pages = {054022},
  numpages = {8},
  year = {2021},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.104.054022},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.104.054022}
}

@article{STAR:2022etb,
    author = "Abdallah, Mohamed and others",
    collaboration = "STAR",
    title = "",
    eprint = "2209.11940",
    archivePrefix = "arXiv",
    primaryClass = "nucl-ex",
    number = "2"
}