Shear and Bulk Viscosities of a Hadron Gas Within Relaxation Time Approximation and its Test
DOI:
https://doi.org/10.15407/ujpe58.12.1127Keywords:
relaxation time approximation, bulk viscosity, shear viscosity, hadron gasAbstract
We concentrate on the calculation of the shear and bulk viscosities of a hadron gas. They define its dissipative dynamics and influence its experimentally measurable elliptic flow. Due to the difficulty of this calculation, the relaxation time approximation (RTA) was used in previous works. As those results have approached the realistic ones, there is a need to find out how accurate RTA is. For this sake, we calculate the viscosities in RTA, by using the cross sections extracted from the ultrarelativistic quantum molecular dynamics (UrQMD) model and compare them with the same ones calculated without RTA. This allows us to find the estimates of errors due to the application of RTA in the calculations of viscosities, which are valid also for other similar models. For instance, in the temperature region 100 MeV < T < 160 MeV at zero chemical potentials, the shear viscosity becomes smaller up to 1.57 times or up to 1.45 times if the averaged relaxation time is used. This has important consequences for the interpretation of the previously made calculations of viscosities and some other related calculations. Within RTA, we also find estimation of the enhancement of the bulk viscosity of a hadron gas because of the nonconservation of particle numbers.
References
J.I. Kapusta, [arXiv:0809.3746 [nucl-th]].
A.S. Khvorostukhin, V.D. Toneev, and D.N. Voskresensky, Nucl. Phys. A 845, 106 (2010) [arXiv:1003.3531 [nucl-th]].
https://doi.org/10.1016/j.nuclphysa.2010.05.058
F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), Chap. 13.
S. Plumari, A. Puglisi, F. Scardina, and V. Greco, Phys. Rev. C 86, 054902 (2012) [arXiv:1208.0481 [nucl-th]].
https://doi.org/10.1103/PhysRevC.86.054902
A. Wiranata, M. Prakash, and P. Chakraborty, Central Eur. J. Phys. 10, 1349 (2012) [arXiv:1201.3104 [nucl-th]].
A. Wiranata and M. Prakash, Phys. Rev. C 85, 054908 (2012) [arXiv:1203.0281 [nucl-th]].
https://doi.org/10.1103/PhysRevC.85.054908
A. Tawfik and M. Wahba, Annalen Phys. 522, 849 (2010) [arXiv:1005.3946 [hep-ph]].
https://doi.org/10.1002/andp.201000056
Y.M. Sinyukov, S.V. Akkelin, and Y. Hama, Phys. Rev. Lett. 89, 052301 (2002) [nucl-th/0201015].
https://doi.org/10.1103/PhysRevLett.89.052301
O.N. Moroz, arXiv:1301.6670 [hep-ph].
P. Chakraborty and J.I. Kapusta, Phys. Rev. C 83, 014906 (2011) [arXiv:1006.0257 [nucl-th]].
https://doi.org/10.1103/PhysRevC.83.014906
S.R. de Groot, W.A. van Leeuwen, and Ch.G. van Weert, Relativistic Kinetic Theory (North-Holland, Amsterdam, 1980), Chap. I, Sec. 2.
E.M. Lifschitz and L.P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, 1981), Sec. 11.
S.A. Bass, M. Belkacem, M. Bleicher, M. Brandstetter, . Bravina, C. Ernst, L. Gerland, M. Hofmann et al., Prog. Part. Nucl. Phys. 41, 225 (1998).
https://doi.org/10.1016/S0146-6410(98)00058-1
M. Bleicher, E. Zabrodin, C. Spieles, S. A. Bass, C. Ernst, S. Soff, L. Bravina, M. Belkacem et al., J. Phys. G 25, 1859 (1999).
https://doi.org/10.1088/0954-3899/25/9/308
O.N. Moroz, arXiv:1112.0277 [hep-ph].
A.S. Khvorostukhin, V.D. Toneev, and D.N. Voskresensky, NPA 915, 159 (2013) [arXiv:1204.5855 [nucl-th]].
U.W. Heinz and G. Kestin, Eur. Phys. J. ST 155, 75 (2008).
https://doi.org/10.1140/epjst/e2008-00591-4
S. Borsanyi et al. [Wuppertal-Budapest Collaboration], JHEP 1009, 073 (2010).
M. Bleicher and J. Aichelin, Phys. Lett. B 530, 81 (2002).
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.
.png){kind=small}
