Shear and Bulk Viscosities of a Hadron Gas Within Relaxation Time Approximation and its Test
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.
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]].
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]].
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]].
A. Tawfik and M. Wahba, Annalen Phys. 522, 849 (2010) [arXiv:1005.3946 [hep-ph]].
Y.M. Sinyukov, S.V. Akkelin, and Y. Hama, Phys. Rev. Lett. 89, 052301 (2002) [nucl-th/0201015].
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]].
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).
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).
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).
S. Borsanyi et al. [Wuppertal-Budapest Collaboration], JHEP 1009, 073 (2010).
M. Bleicher and J. Aichelin, Phys. Lett. B 530, 81 (2002).