Abstract
Hydrodynamical noise is introduced on top of Gubser’s analytical solution to viscous hydrodynamics. With respect to the ultra-central collision events of Pb-Pb, p-Pb and p-p at the LHC energies, we solve the evolution of noisy fluid systems and calculate the radial flow velocity correlations. We show that the absolute amplitude of the hydrodynamical noise is determined by the multiplicity of the collision event. The evolution of azimuthal anisotropies, which is related to the generation of harmonic flow, receives finite enhancements from hydrodynamical noise. Although it is strongest in the p-p systems, the effect of hydrodynamical noise on flow harmonics is found to be negligible, especially in the ultra-central Pb-Pb collisions. For the short-range correlations, hydrodynamical noise contributes to the formation of a near-side peak on top of the correlation structure originated from initial state fluctuations. The shape of the peak is affected by the strength of hydrodynamical noise, whose height and width grow from the Pb-Pb system to the p-Pb and p-p systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
CMS collaboration, Observation of long-range near-side two-particle correlations in pp collisions at \( \sqrt{s}=13 \) TeV, CMS-PAS-FSQ-15-002.
ATLAS collaboration, Observation of long-range elliptic anisotropies in \( \sqrt{s}=13 \) and 2.76 TeV pp collisions with the ATLAS detector, arXiv:1509.04776 [INSPIRE].
CMS collaboration, Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions, Phys. Lett. B 724 (2013) 213 [arXiv:1305.0609] [INSPIRE].
ATLAS collaboration, Measurement of long-range pseudorapidity correlations and azimuthal harmonics in \( \sqrt{s_{NN}}=5.02 \) TeV proton-lead collisions with the ATLAS detector, Phys. Rev. C 90 (2014) 044906 [arXiv:1409.1792] [INSPIRE].
CMS collaboration, Observation of long-range near-side angular correlations in proton-lead collisions at the LHC, Phys. Lett. B 718 (2013) 795 [arXiv:1210.5482] [INSPIRE].
CMS collaboration, Evidence for Collective Multiparticle Correlations in p-Pb Collisions, Phys. Rev. Lett. 115 (2015) 012301 [arXiv:1502.05382] [INSPIRE].
S. Huang, Highlight of phenix results, talk at Initial Stages 2014, Napa, CA, U.S.A., December 3–7 2014.
PHENIX collaboration, A. Adare et al., Quadrupole Anisotropy in Dihadron Azimuthal Correlations in Central d + Au Collisions at \( \sqrt{s_{NN}}=200 \) GeV, Phys. Rev. Lett. 111 (2013) 212301 [arXiv:1303.1794] [INSPIRE].
A. Bzdak, P. Bozek and L. McLerran, Fluctuation induced equality of multi-particle eccentricities for four or more particles, Nucl. Phys. A 927 (2014) 15 [arXiv:1311.7325] [INSPIRE].
L. Yan and J.-Y. Ollitrault, Universal fluctuation-driven eccentricities in proton-proton, proton-nucleus and nucleus-nucleus collisions, Phys. Rev. Lett. 112 (2014) 082301 [arXiv:1312.6555] [INSPIRE].
I. Kozlov, M. Luzum, G. Denicol, S. Jeon and C. Gale, Transverse momentum structure of pair correlations as a signature of collective behavior in small collision systems, arXiv:1405.3976 [INSPIRE].
G.-Y. Qin and B. Müller, Elliptic and triangular flow anisotropy in deuteron-gold collisions at \( \sqrt{s_{NN}}=200 \) GeV at RHIC and in proton-lead collisions at \( \sqrt{s_{NN}}=5.02 \) TeV at the LHC, Phys. Rev. C 89 (2014) 044902 [arXiv:1306.3439] [INSPIRE].
P. Bozek, Collective flow in p-Pb and d-Pd collisions at TeV energies, Phys. Rev. C 85 (2012) 014911 [arXiv:1112.0915] [INSPIRE].
J. Nagle et al., Exploiting Intrinsic Triangular Geometry in Relativistic He3+Au Collisions to Disentangle Medium Properties, Phys. Rev. Lett. 113 (2014) 112301 [arXiv:1312.4565] [INSPIRE].
P. Bozek and W. Broniowski, Collective dynamics in high-energy proton-nucleus collisions, Phys. Rev. C 88 (2013) 014903 [arXiv:1304.3044] [INSPIRE].
P. Bozek and W. Broniowski, Collective flow in ultrarelativistic 3 He-Au collisions, Phys. Lett. B 739 (2014) 308 [arXiv:1409.2160] [INSPIRE].
L. Yan, Plane correlations in small colliding systems, Phys. Rev. C 91 (2015) 064909 [arXiv:1503.00880] [INSPIRE].
H. Niemi and G.S. Denicol, How large is the Knudsen number reached in fluid dynamical simulations of ultrarelativistic heavy ion collisions?, arXiv:1404.7327 [INSPIRE].
D. Landau and E. Lifshitz, Statistical Physics Part 1, volume 5 of Course of Theoretical Physics, second edition, Pergamon Press, (1987).
D. Landau and E. Lifshitz, Statistical Physics Part 2, volume 6 of Course of Theoretical Physics, second edition, Pergamon Press, (1987).
J.I. Kapusta, B. Müller and M. Stephanov, Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions, Phys. Rev. C 85 (2012) 054906 [arXiv:1112.6405] [INSPIRE].
C. Young, J.I. Kapusta, C. Gale, S. Jeon and B. Schenke, Thermally Fluctuating Second-Order Viscous Hydrodynamics and Heavy-Ion Collisions, Phys. Rev. C 91 (2015) 044901 [arXiv:1407.1077] [INSPIRE].
K. Murase and T. Hirano, Hydrodynamic fluctuations and dissipation in an integrated dynamical model, arXiv:1601.02260 [INSPIRE].
S.S. Gubser, Symmetry constraints on generalizations of Bjorken flow, Phys. Rev. D 82 (2010) 085027 [arXiv:1006.0006] [INSPIRE].
S.S. Gubser and A. Yarom, Conformal hydrodynamics in Minkowski and de Sitter spacetimes, Nucl. Phys. B 846 (2011) 469 [arXiv:1012.1314] [INSPIRE].
M.A. Stephanov, K. Rajagopal and E.V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D 60 (1999) 114028 [hep-ph/9903292] [INSPIRE].
K. Murase and T. Hirano, Relativistic fluctuating hydrodynamics with memory functions and colored noises, arXiv:1304.3243 [INSPIRE].
C. Young, Numerical integration of thermal noise in relativistic hydrodynamics, Phys. Rev. C 89 (2014) 024913 [arXiv:1306.0472] [INSPIRE].
S. Floerchinger and U.A. Wiedemann, Fluctuations around Bjorken Flow and the onset of turbulent phenomena, JHEP 11 (2011) 100 [arXiv:1108.5535] [INSPIRE].
N. Brouzakis, S. Floerchinger, N. Tetradis and U.A. Wiedemann, Nonlinear evolution of density and flow perturbations on a Bjorken background, Phys. Rev. D 91 (2015) 065007 [arXiv:1411.2912] [INSPIRE].
P. Staig and E. Shuryak, The Fate of the Initial State Fluctuations in Heavy Ion Collisions. II The Fluctuations and Sounds, Phys. Rev. C 84 (2011) 034908 [arXiv:1008.3139] [INSPIRE].
J.-P. Blaizot, W. Broniowski and J.-Y. Ollitrault, Correlations in the Monte Carlo Glauber model, Phys. Rev. C 90 (2014) 034906 [arXiv:1405.3274] [INSPIRE].
ALICE collaboration, Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at \( \sqrt{s_{NN}}=2.76 \) TeV, Phys. Rev. Lett. 106 (2011) 032301 [arXiv:1012.1657] [INSPIRE].
D. Teaney and L. Yan, Triangularity and Dipole Asymmetry in Heavy Ion Collisions, Phys. Rev. C 83 (2011) 064904 [arXiv:1010.1876] [INSPIRE].
M. Luzum and J.-Y. Ollitrault, Extracting the shear viscosity of the quark-gluon plasma from flow in ultra-central heavy-ion collisions, Nucl. Phys. A904-905 (2013) 377c-380c [arXiv:1210.6010] [INSPIRE].
A. Bzdak, B. Schenke, P. Tribedy and R. Venugopalan, Initial state geometry and the role of hydrodynamics in proton-proton, proton-nucleus and deuteron-nucleus collisions, Phys. Rev. C 87 (2013) 064906 [arXiv:1304.3403] [INSPIRE].
P. Kloeden and E. Platen, Numerical Solutions of Stochastic Differential Equations, volume 23 of Stochastic Modelling and Applied Probability, Springer-Verlag Berlin Heidelberg, Germany (1992).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1511.07198
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Yan, L., Grönqvist, H. Hydrodynamical noise and Gubser flow. J. High Energ. Phys. 2016, 121 (2016). https://doi.org/10.1007/JHEP03(2016)121
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)121