Searching for the QCD Critical Point with Net-Proton Number Fluctuations
Keywords:net-proton number fluctuations, QCD critical point, heavy-ion collisions
Net-proton number fluctuations can be measured experimentally and, hence, provide a source of important information about the matter created during relativistic heavy ion collisions. Particularly, they may give us clues about the conjectured QCD critical point. In this work, the beam-energy dependence of ratios of the first four cumulants of the net-proton number is discussed. These quantities are calculated using a phenomenologically motivated model in which critical mode fluctuations couple to protons and antiprotons. Our model qualitatively captures both the monotonic behavior of the lowest-order ratio, as well as the non-monotonic behavior of higher-order ratios, as seen in the experimental data from the STAR Collaboration. We also discuss the dependence of our results on the coupling strength and the location of the critical point.
M.A. Stephanov, K. Rajagopal, E.V. Shuryak. Signatures of the tricritical point in QCD. Phys. Rev. Lett. 81, 4816 (1998). https://doi.org/10.1103/PhysRevLett.81.4816
M.A. Stephanov, K. Rajagopal, E.V. Shuryak. Event-by-event fluctuations in heavy ion collisions and the QCD critical point. Phys. Rev. D 60, 114028 (1999). https://doi.org/10.1103/PhysRevD.60.114028
X. Luo, [STAR Collaboration]. Energy dependence of moments of net-proton and net-charge multiplicity distributions at STAR. PoS CPOD 2014, 019 (2015). https://doi.org/10.22323/1.217.0019
X. Luo. Exploring the QCD phase structure with beam energy scan in heavy-ion collisions. Nucl. Phys. A 956, 75 (2016). https://doi.org/10.1016/j.nuclphysa.2016.03.025
J. Th?ader [STAR Collaboration]. Higher moments of net-particle multiplicity distributions. Nucl. Phys. A 956, 320 (2016). https://doi.org/10.1016/j.nuclphysa.2016.02.047
G.A. Almasi, B. Friman, K. Redlich. Baryon number fluctuations in chiral effective models and their phenomeno-logical implications. Phys. Rev. D 96, 014027 (2017). https://doi.org/10.1103/PhysRevD.96.014027
F. Karsch. Lattice QCD results on cumulant ratios at freeze-out. J. Phys. Conf. Ser. 779, 012015 (2017). https://doi.org/10.1088/1742-6596/779/1/012015
A.Bzdak,V.Koch.Net-baryonmultiplicity distribution consistentwith latticeQCD.Phys.Rev.C99, 024913 (2019). https://doi.org/10.1103/PhysRevC.99.024913
V. Koch, A. Bzdak. Fluctuations and the QCD phase diagram. Acta Phys. Polon. B 47, 1867 (2016). https://doi.org/10.5506/APhysPolB.47.1867
M. Bluhm, M. Nahrgang, S.A. Bass, T. Sch?afer. Impact of resonance decays on critical point signals in net-proton fluctuations. Eur. Phys. J. C 77, 210 (2017). https://doi.org/10.1140/epjc/s10052-017-4771-3
M. Szyma?nski, M. Bluhm, K. Redlich, C. Sasaki. Netproton number fluctuations in the presence of the QCD critical point. arXiv:1905.00667 [nucl-th].
C. Sasaki, B. Friman, K. Redlich. Quark number fluctuations in a chiral model at finite baryon chemical potential. Phys. Rev. D 75, 054026 (2007). https://doi.org/10.1103/PhysRevD.75.054026
C. Sasaki, B. Friman, K. Redlich. Chiral phase transition in the presence of spinodal decomposition. Phys. Rev. D 77, 034024 (2008). https://doi.org/10.1103/PhysRevD.77.034024
J. Zinn-Justin. Quantum Field Theory and Critical Phenomena (Clarendon Press, 2002). https://doi.org/10.1093/acprof:oso/9780198509233.001.0001
A. Andronic, P. Braun-Munzinger, K. Redlich, J. Stachel. Decoding the phase structure of QCD via particle production at high energy. Nature 561, 321 (2018). https://doi.org/10.1038/s41586-018-0491-6
F. Wilczek. Application of the renormalization group to a second-order QCD phase transition. Int. J. Mod. Phys. A 07, 3911 (1992). https://doi.org/10.1142/S0217751X92001757
A.M. Halasz, A.D. Jackson, R.E. Shrock, M.A. Stephanov, J.J.M. Verbaarschot. Phase diagram of QCD. Phys. Rev. D 58, 096007 (1998). https://doi.org/10.1103/PhysRevD.58.096007
H.-T. Ding, F. Karsch, S. Mukherjee. Thermodynamics of strong-interaction matter from Lattice QCD. Int. J. Mod. Phys. E 24, 1530007 (2015). https://doi.org/10.1142/S0218301315300076
Y. Hatta, T. Ikeda. Universality, the QCD critical/tricritical point and the quark number susceptibility. Phys. Rev. D 67, 014028 (2003). https://doi.org/10.1103/PhysRevD.67.014028
S. Mukherjee, R. Venugopalan, Y. Yin. Real time evolution of non-Gaussian cumulants in the QCD critical regime. Phys. Rev. C 92, 034912 (2015). https://doi.org/10.1103/PhysRevC.92.034912
C. Nonaka, M. Asakawa. Hydrodynamical evolution near the QCD critical end point.Phys.Rev.C71, 044904 (2005). https://doi.org/10.1103/PhysRevC.71.044904
R. Guida, J. Zinn-Justin. 3-D Ising model: The scaling equation of state. Nucl. Phys. B 489, 626 (1997). https://doi.org/10.1016/S0550-3213(96)00704-3
B. Abelev et al., [ALICE Collaboration]. Centrality dependence of п, K, p production in Pb-Pb collisions at vSNN = 2.76 TeV. Phys. Rev. C 88, 044910 (2013).
B.B. Abelev et al., [ALICE Collaboration]. K0S and ? production in Pb-Pb collisions at vSNN = 2.76 TeV. Phys. Rev. Lett. 111, 222301 (2013).
B.B. Abelev et al., [ALICE Collaboration]. Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at vSNN = 2.76 TeV. Phys. Lett. B 728, 216 (2014), Erratum: [Phys. Lett. B 734, 409 (2014)]. https://doi.org/10.1016/j.physletb.2014.05.052
B.B. Abelev et al., [ALICE Collaboration]. K*(892)0 and ffl(1020) production in Pb-Pb collisions at vSNN = 2.76 TeV. Phys. Rev. C 91, 024609 (2015).
J. Adam et al., [ALICE Collaboration]. 3?H and 3?H production in Pb-Pb collisions at vSNN = 2.76 TeV. Phys. Lett. B 754, 360 (2016).
J. Adam et al., [ALICE Collaboration]. Production of light nuclei and anti-nuclei in pp and Pb-Pb collisions at energies available at the CERN large hadron collider. Phys. Rev. C 93, 024917 (2016). https://doi.org/10.1103/PhysRevC.93.044907
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.