Effects of Superstatistics on the Location of the Effective QCD Critical End Point
DOI:
https://doi.org/10.15407/ujpe64.8.665Keywords:
superstatistics, QCD phase diagram, critical end point, relativistic heavy-ion collisionsAbstract
Effects of the partial thermalization during the chiral symmetry restoration at the finite temperature and quark chemical potential are considered for the position of the critical end point in an effective description of the QCD phase diagram. We find that these effects cause the critical end point to be displaced toward larger values of the temperature and lower values of the quark chemical potential, as compared to the case where the system can be regarded as completely thermalized. These effects may be important for relativistic heavy ion collisions, where the number of subsystems making up the whole interaction volume can be linked to the finite number of participants in the reaction.
References
A. Ayala, C. A. Dominguez, M. Loewe. For a recent review on the QCD sum rules technique at finite temperature. Adv. High Energy Phys. 2017, 9291623 (2017). https://doi.org/10.1155/2017/9291623
P. Costa, M.C. Ruivo, C.A. de Sousa. Thermodynamics and critical behavior in the Nambu-Jona-Lasinio model of QCD. Phys. Rev. D 77, 096001 (2008). https://doi.org/10.1103/PhysRevD.77.096001
G.A. Contrera, D. Gomez-Dumm, N.N. Scoccola. Nonlocal SU(3) chiral quark models at finite temperature: The role of the Polyakov loop. Phys. Lett. B 661, 113 (2008). https://doi.org/10.1016/j.physletb.2008.01.069
A. Ayala, A. Bashir, C. A. Dominguez, E. Gutierrez, M. Loewe, A. Raya. QCD phase diagram from finite energy sum rules. Phys. Rev. D 84, 056004 (2011). https://doi.org/10.1103/PhysRevD.84.056004
X.-Y. Xin, S.-X. Qin, Y.-X. Liu. Quark number fluctuations at finite temperature and finite chemical potential via the Dyson-Schwinger equation approach. Phys. Rev. D 90, 076006 (2014). https://doi.org/10.1103/PhysRevD.90.076006
C.S. Fischer, J. Luecker, C.A. Welzbacher. Phase structure of three and four flavor QCD. Phys. Rev. D 90, 034022 (2014). https://doi.org/10.1103/PhysRevD.90.034022
Y. Lu, Y.-L. Du, Z.-F. Cui, H.-S. Zong. Critical behaviors near the (tri-) critical end point of QCD within the NJL model. Eur. Phys. J. C 75, 495 (2015). https://doi.org/10.1140/epjc/s10052-015-3720-2
A. Ayala, M. Loewe, R. Zamora. Inverse magnetic catalysis in the linear sigma model with quarks. Phys. Rev. D 91, 016002 (2015). https://doi.org/10.1103/PhysRevD.91.016002
A. Ayala, M. Loewe, A.J. Mizher, R. Zamora. Inverse magnetic catalysis for the chiral transition induced by thermomagnetic effects on the coupling constant. Phys. Rev. D 90, 036001 (2014). https://doi.org/10.1103/PhysRevD.90.036001
A. Ayala, C.A. Dominguez, L.A. Hern?andez, M. Loewe, R. Zamora. Magnetized effective QCD phase diagram. Phys. Rev. D 92, 096011 (2015). https://doi.org/10.1103/PhysRevD.92.096011
C. Shi, Y.-L. Du, S.-S. Xu, X.-J. Liu, H.-S. Zong. Continuum study of the QCD phase diagram through an OPE-modified gluon propagator. Phys. Rev. D 93, 036006 (2016). https://doi.org/10.1103/PhysRevD.93.036006
G.A. Contrera, A.G. Grunfeld, D. Blaschke. Supporting the search for the CEP location with nonlocal PNJL models constrained by lattice QCD. Eur. Phys. J. A 52, 231 (2016). https://doi.org/10.1140/epja/i2016-16231-x
A. Ayala, C.A. Dominguez, L.A. Hern?andez, M. Loewe, A. Raya, J.C. Rojas, C. Villavicencio. Thermomagnetic properties of the strong coupling in the local Nambu-Jona-Lasinio model. Phys. Rev. D 94, 054019 (2016). https://doi.org/10.1103/PhysRevD.94.054019
Z.-F. Cui, J.-L. Zhang, H.-S. Zong. Proper time regularization and the QCD chiral phase transition. Sci. Rep. 7, 45937 (2017). https://doi.org/10.1038/srep45937
S. Datta, R.V. Gavai, S. Gupta. Quark number susceptibilities and equation of state at finite chemical potential in staggered QCD with Nt = 8. Phys. Rev. D 95, 054512 (2017). https://doi.org/10.1103/PhysRevD.95.054512
J.P. Carlomagno, M. Loewe. Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters. Phys. Rev. D 95, 036003 (2017). https://doi.org/10.1103/PhysRevD.95.036003
J. Knaute, R. Yaresko, B. K?ampfer. Holographic QCD phase diagram with critical point from Einstein-Maxwell dilaton dynamics. Phys. Lett. B 778, 419 (2018). https://doi.org/10.1016/j.physletb.2018.01.053
N.G. Antoniou, F.K. Diakonos, X.N. Maintas. C.E. Tsagkarakis. Locating the QCD critical endpoint through finite-size scaling. Phys. Rev. D 97, 034015 (2018). https://doi.org/10.1103/PhysRevD.97.034015
R. Rougemont, R. Critelli, J. Noronha-Hostler, J. Noronha, C. Ratti. Dynamical versus equilibrium properties of the QCD phase transition: A holographic perspective. Phys. Rev. D 96, 014032 (2017). https://doi.org/10.1103/PhysRevD.96.014032
A. Ayala, S. Hern?andez-Ortiz, L.A. Hern?andez. QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the linear sigma model with quarks. Rev. Mex. Fis. 64, 302 (2018). https://doi.org/10.31349/RevMexFis.64.302
L. Adamczyk et al., [STAR Collaboration]. Energy dependence of moments of net-proton multiplicity distributions at RHIC. Phys. Rev. Lett. 112, 032302 (2014)
Beam energy dependence of moments of the net-charge multiplicity distributions in Au+Au collisions at RHIC. Phys. Rev. Lett. 113, 092301 (2014).
C. Yang, [for the STAR Collaboration]. The STAR beam energy scan phase II physics and upgrades. Nucl. Phys. A 967, 800 (2017). https://doi.org/10.1016/j.nuclphysa.2017.05.042
P. Senger. The heavy-ion program of the future FAIR facility. J. Phys. Conf. Ser. 798, 012062 (2017). https://doi.org/10.1088/1742-6596/798/1/012062
V. Kekelidze, A. Kovalenko, R. Lednicky, V. Matveev, I. Meshkov, A. Sorin, G. Trubnikov. Feasibility study of heavy-ion collision physics at NICA JINR. Nucl. Phys. A 967, 884 (2017). https://doi.org/10.1016/j.nuclphysa.2017.06.031
G. Wilk, Z. Wlodarczyk. Multiplicity fluctuations due to the temperature fluctuations in high-energy nuclear collisions. Phys. Rev. C 79, 054903 (2009). https://doi.org/10.1103/PhysRevC.79.054903
G. Wilk, Z. Wlodarczyk. Power laws in elementary and heavy-ion collisions. Eur. Phys. J. A 40, 299 (2009). https://doi.org/10.1140/epja/i2009-10803-9
G. Wilk, Z. Wlodarczyk. The imprints of superstatistics in multiparticle production processes. Cent. Eur. J. Phys. 10, 568 (2012). https://doi.org/10.2478/s11534-011-0111-7
M. Rybczynski, Z. Wlodarczyk. Tsallis statistics approach to the transverse momentum distributions in p-p collisions. Eur. Phys. J. C 74, 2785 (2014). https://doi.org/10.1140/epjc/s10052-014-2785-7
C.Y. Wong, G. Wilk, L.J.L. Cirto, C. Tsallis. From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy pp and pp collisions. Phys. Rev. D 91, 114027 (2015). https://doi.org/10.1103/PhysRevD.91.114027
G. Wilk, Z. Wlodarczyk. Superstatistical cluster decay. Phys. Lett. A 379, 2941 (2015). https://doi.org/10.1016/j.physleta.2015.08.038
A. Bialas. Tsallis p? distribution from statistical clusters. Phys. Lett. B 747, 190 (2015). https://doi.org/10.1016/j.physletb.2015.05.076
T. Bhattacharyya, J. Cleymans, A. Khuntia, P. Pareek, R. Sahoo. Radial flow in non-extensive thermodynamics and study of particle spectra at LHC in the limit of small (q ? 1). Eur. Phys. J. A 52, 30 (2016). https://doi.org/10.1140/epja/i2016-16030-5
A. Bialas, A. Bzdak. Short-range two-particle correlations from statistical clusters. Phys. Rev. D 93, 094015 (2016). https://doi.org/10.1103/PhysRevD.93.094015
J. Rozynek, G.Wilk. An example of the interplay of nonextensivity and dynamics in the description of QCD matter. Eur. Phys. J. A 52, 294 (2016). https://doi.org/10.1140/epja/i2016-16294-7
S. Tripathy, T. Bhattacharyya, P. Garg, P. Kumar, R. Sahoo, J. Cleymans. Nuclear modification factor using Tsallis non-extensive statistics. Eur. Phys. J. A 52, 289 (2016). https://doi.org/10.1140/epja/i2016-16289-4
S. Grigoryan. Using the Tsallis distribution for hadron spectra in pp collisions: Pions and quarkonia at vs = 5-13000 GeV. Phys. Rev. D 95, 056021 (2017). https://doi.org/10.1103/PhysRevD.95.056021
A. Khuntia, S. Tripathy, R. Sahoo, J. Cleymans. Multiplicity dependence of non-extensive parameters for strange and multi-strange particles in proton-proton collisions at vs = 7 TeV at the LHC. Eur. Phys. J. A 53, 103 (2017). https://doi.org/10.1140/epja/i2017-12291-8
T. Bhattacharyya, J. Cleymans, L. Marques, S. Mogliacci, M.W. Paradza. On the precise determination of the Tsallis parameters in proton-proton collisions at LHC energies. J. Phys. G 45, 055001 (2018). https://doi.org/10.1088/1361-6471/aaaea0
S. Tripathy, S.K. Tiwari, M. Younus, R. Sahoo. Elliptic flow in Pb+Pb collisions at vSNN = 2.76 TeV at the LHC using Boltzmann transport equation with non-extensive statistics. Eur. Phys. J. A 54, 38 (2018). https://doi.org/10.1140/epja/i2018-12461-2
M. Ishihara. Phase transition for the system of finite volume in the ф4 theory in the Tsallis nonextensive statistics. Int. J. Mod. Phys. A 33, 1850067 (2018). https://doi.org/10.1142/S0217751X18500677
G. Wilk, Z. Wlodarczyk. Some intriguing aspects of multiparticle production processes. Int. J. Mod. Phys. A 33, 1830008 (2018). https://doi.org/10.1142/S0217751X18300089
C. Tsallis. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479 (1988). https://doi.org/10.1007/BF01016429
A. Simon, G. Wolschin. Examining nonextensive statistics in relativistic heavy-ion collisions. Phys. Rev. C 97, 044913 (2018). https://doi.org/10.1103/PhysRevC.97.044913
O. Obreg?on, A. Gil-Villegas. Generalized information entropies depending only on the probability distribution. Phys. Rev. E 88, 062146 (2013). https://doi.org/10.1103/PhysRevE.88.062146
A. Mart? inez-Merino, O. Obreg?on, M.P. Ryan, jr. Modified entropies, their corresponding Newtonian forces, potentials, and temperatures. Phys. Rev. D 95, 124031 (2017). https://doi.org/10.1103/PhysRevD.95.124031
O. Obreg?on. Superstatistics and gravitation. Entropy 2010 12, 2067 (2010). https://doi.org/10.3390/e12092067
O. Obreg?on. Superstatistics and gravitation. Entropy 2010 12, 2067 (2010). https://doi.org/10.3390/e12092067
C. Beck, E.G.D. Cohen. Superstatistics. Phys. A 322, 267 (2003). https://doi.org/10.1016/S0378-4371(03)00019-0
C. Beck. Superstatistics: theory and applications. Continuum Mech. Thermodyn. 16, 293 (2004) https://doi.org/10.1007/s00161-003-0145-1
C. Beck. Recent developments in superstatistics. Braz. J. Phys. 39, 2A, 357 (2009). https://doi.org/10.1590/S0103-97332009000400003
Al. Ayala, M. Hentschinski, L.A. Hernandez, M. Loewe, R. Zamora. Superstatistics and the effective QCD phase diagram. Phys. Rev. D 98, 114002 (2018). https://doi.org/10.1103/PhysRevD.98.114002
A. Ayala, A. Sanchez, G. Piccinelli, S. Sahu. Effective potential at finite temperature in a constant magnetic field. I. Ring diagrams in a scalar theory. Phys. Rev. D 71, 023004 (2005). https://doi.org/10.1103/PhysRevD.71.023004
M.E. Carrington. The effective potential at finite temperature in the Standard Model. Phys. Rev. D 45, 2933 (1992). https://doi.org/10.1103/PhysRevD.45.2933
J. Rozynek, G.Wilk. An example of the interplay of nonextensivity and dynamics in the description of QCD matter. Eur. Phys. J. A 52, 294 (2016). https://doi.org/10.1140/epja/i2016-16294-7
G. Wilk, Z. Wlodarczyk. Multiplicity fluctuations due to the temperature fluctuations in high-energy nuclear collisions. Phys. Rev. C 79, 054903 (2009). https://doi.org/10.1103/PhysRevC.79.054903
L.D. Landau, E.M. Lifshitz. Statistical Physics (Elsevier, 2013), ISBN 9780080570464.
S. Basu, S. Chatterjee, R. Chatterjee, T.K. Nayak, B.K. Nandi. Specific heat of matter formed in relativistic nuclear collisions. Phys. Rev. C 94, 044901 (2016). https://doi.org/10.1103/PhysRevC.94.044901
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
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. Duration.
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. Loyalty.
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.