On Statistical Fluctuations in Collective Flows
Abstract
1. Introduction
2. Eccentricities and Its Fluctuations
3. Variance of the Flow Harmonics
4. Flow Variance Due to Statistical and Initial Geometric Fluctuations
5. Concluding Remarks
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Romatschke, P. New Developments in Relativistic Viscous Hydrodynamics. Int. J. Mod. Phys. 2010, E19, 1. [Google Scholar] [CrossRef]
- Gale, C.; Jeon, S.; Schenke, B. Hydrodynamic Modeling of Heavy-Ion Collisions. Int. J. Mod. Phys. A 2013, 28, 1340011. [Google Scholar] [CrossRef]
- Heinz, U.W.; Snellings, R. Collective flow and viscosity in relativistic heavy-ion collisions. Annu. Rev. Nucl. Part. Sci. 2013, 63, 123. [Google Scholar] [CrossRef]
- Hama, Y.; Kodama, T.; Socolowski, O., Jr. Topics on hydrodynamic model of nucleus-nucleus collisions. Braz. J. Phys. 2015, 35, 24. [Google Scholar] [CrossRef]
- Hama, Y.; Kodama, T.; Qian, W.-L. Two-particle correlations at high-energy nuclear collisions, peripheral-tube model revisited. J. Phys. G 2021, 48, 015104. [Google Scholar] [CrossRef]
- Hirano, T.; Huovinen, P.; Murase, K.; Nara, Y. Integrated Dynamical Approach to Relativistic Heavy Ion Collisions. Prog. Part. Nucl. Phys. 2013, 70, 108. [Google Scholar] [CrossRef]
- Kodama, T.; Stocker, H.; Xu, N. 40 years of collective flow in relativistic heavy ion collisions—The barometer for primordial hot and dense QCD matter. J. Phys. G 2014, 41, 120301. [Google Scholar] [CrossRef]
- de Souza, R.D.; Koide, T.; Kodama, T. Hydrodynamic Approaches in Relativistic Heavy Ion Reactions. Prog. Part. Nucl. Phys. 2016, 86, 35. [Google Scholar] [CrossRef]
- Florkowski, W.; Heller, M.P.; Spalinski, M. New theories of relativistic hydrodynamics in the LHC era. Rept. Prog. Phys. 2018, 81, 046001. [Google Scholar] [CrossRef] [PubMed]
- Danielewicz, P.; Odyniec, G. Transverse Momentum Analysis of Collective Motion in Relativistic Nuclear Collisions. Phys. Lett. B 1985, 157, 146. [Google Scholar] [CrossRef]
- Ollitrault, J.-Y. Anisotropy as a signature of transverse collective flow. Phys. Rev. D 1992, 46, 229. [Google Scholar] [CrossRef] [PubMed]
- Alver, B.; Roland, G. Collision geometry fluctuations and triangular flow in heavy-ion collisions. Phys. Rev. C 2010, 81, 054905. [Google Scholar] [CrossRef]
- Teaney, D.; Yan, L. Triangularity and Dipole Asymmetry in Heavy Ion Collisions. Phys. Rev. C 2011, 83, 064904. [Google Scholar] [CrossRef]
- Qian, W.-L.; Andrade, R.P.G.; Socolowski, O., Jr.; Grassi, F.; Kodama, T.; Hama, Y. p(T) distribution of hyperons in 200-A-GeV Au-Au in smoothed particle hydrodynamics. Braz. J. Phys. 2007, 37, 767. [Google Scholar] [CrossRef]
- Qian, W.-L.; Andrade, R.; Grassi, F.; Socolowski, O., Jr.; Kodama, T.; Hama, Y. Effect of chemical freeze out on identified particle spectra at 200-A-GeV Au-Au Collisions at RHIC using SPheRIO. Int. J. Mod. Phys. E 2007, 16, 1877. [Google Scholar] [CrossRef]
- Hama, Y.; Andrade, R.P.G.; Grassi, F.; Qian, W.L.; Kodama, T. Fluctuation of the Initial Conditions and Its Consequences on Some Observables. Acta Phys. Polon. B 2009, 40, 931. [Google Scholar]
- Andrade, R.; Grassi, F.; Hama, Y.; Qian, W.-L. A Closer look at the influence of tubular initial conditions on two-particle correlations. J. Phys. G 2010, 37, 094043. [Google Scholar] [CrossRef]
- Andrade, R.P.G.; Grassi, F.; Hama, Y.; Qian, W.-L. Temporal evolution of tubular initial conditions and their influence on two-particle correlations in relativistic nuclear collisions. Phys. Lett. B 2012, 712, 226. [Google Scholar] [CrossRef]
- Andrade, R.; Grassi, F.; Hama, Y.; Qian, W.-L. Hydrodynamics: Fluctuating Initial Conditions and Two-particle Correlations. Nucl. Phys. A 2011, 854, 81. [Google Scholar] [CrossRef]
- Castilho, W.M.; Qian, W.-L.; Gardim, F.G.; Hama, Y.; Kodama, T. Hydrodynamic approach to the centrality dependence of di-hadron correlations. Phys. Rev. C 2017, 95, 064908. [Google Scholar] [CrossRef]
- Castilho, W.M.; Qian, W.-L.; Hama, Y.; Kodama, T. Event-plane dependent di-hadron correlations with harmonic vn subtraction in a hydrodynamic model. Phys. Lett. B 2018, 777, 369. [Google Scholar] [CrossRef]
- Wen, D.; Lin, K.; Qian, W.L.; Wang, B.; Hama, Y.; Kodama, T. On nonlinearity in hydrodynamic response to the initial geometry in relativistic heavy-ion collisions. Eur. Phys. J. A 2020, 56, 222. [Google Scholar] [CrossRef]
- Voloshin, S.; Zhang, Y. Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions. Z. Phys. C 1996, 70, 665. [Google Scholar] [CrossRef]
- Niemi, H.; Denicol, G.; Holopainen, H.; Huovinen, P. Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions. Phys. Rev. C 2012, 87, 054901. [Google Scholar] [CrossRef]
- Yan, L.; Ollitrault, J.-Y. Universal fluctuation-driven eccentricities in proton-proton, proton-nucleus and nucleus-nucleus collisions. Phys. Rev. Lett. 2014, 112, 082301. [Google Scholar] [CrossRef]
- Qian, W.-L.; Andrade, R.; Gardim, F.; Grassi, F.; Hama, Y. On the origin of trigger-angle dependence of di-hadron correlations. Phys. Rev. C 2013, 87, 014904. [Google Scholar] [CrossRef]
- Qian, W.-L.; Mota, P.; Andrade, R.; Gardim, F.; Grassi, F.; Hama, Y.; Kodama, T. Decomposition of fluctuating initial conditions and flow harmonics. J. Phys. G 2014, 41, 015103. [Google Scholar] [CrossRef]
- Yan, L.; Ollitrault, J.-Y. ν4,ν5,ν6,ν7: Nonlinear hydrodynamic response versus LHC data. Phys. Lett. B 2015, 744, 82. [Google Scholar] [CrossRef]
- Yan, L.; Pal, S.; Ollitrault, J.-Y. Nonlinear hydrodynamic response confronts LHC data. Nucl. Phys. A 2016, 956, 340. [Google Scholar] [CrossRef]
- Bhalerao, R.S.; Ollitrault, J.-Y.; Pal, S. Characterizing flow fluctuations with moments. Phys. Lett. B 2015, 742, 94. [Google Scholar] [CrossRef]
- Grönqvist, H.; Blaizot, J.-P.; Ollitrault, J.-Y. Non-Gaussian eccentricity fluctuations. Phys. Rev. C 2016, 94, 034905. [Google Scholar] [CrossRef]
- Poskanzer, A.M.; Voloshin, S.A. Methods for analyzing anisotropic flow in relativistic nuclear collisions. Phys. Rev. C 1998, 58, 1671. [Google Scholar] [CrossRef]
- Voloshin, S.A.; Poskanzer, A.M.; Snellings, R. Collective phenomena in non-central nuclear collisions. arXiv 2008, arXiv:0809.2949. [Google Scholar]
- Borghini, N.; Dinh, P.M.; Ollitrault, J.-Y. A New method for measuring azimuthal distributions in nucleus-nucleus collisions. Phys. Rev. C 2001, 63, 054906. [Google Scholar] [CrossRef]
- Borghini, N.; Dinh, P.M.; Ollitrault, J.-Y. Flow analysis from multiparticle azimuthal correlations. Phys. Rev. C 2001, 64, 054901. [Google Scholar] [CrossRef]
- Bilandzic, A.; Snellings, R.; Voloshin, S. Flow analysis with cumulants: Direct calculations. Phys. Rev. C 2011, 83, 044913. [Google Scholar] [CrossRef]
- Bhalerao, R.S.; Luzum, M.; Ollitrault, J.-Y. Determining initial-state fluctuations from flow measurements in heavy-ion collisions. Phys. Rev. C 2011, 84, 034910. [Google Scholar] [CrossRef]
- Bhalerao, R.S.; Borghini, N.; Ollitrault, J.Y. Analysis of anisotropic flow with Lee-Yang zeroes. Nucl. Phys. A 2003, 727, 373. [Google Scholar] [CrossRef]
- Bastid, N.; Andronic, A.; Barret, V.; Basrak, Z.; Benabderrahmane, M.L.; Čaplar, R.; Cordier, E.; Crochet, P.; Dupieux, P.; Dželalija, M.; et al. First analysis of anisotropic flow with Lee-Yang zeroes. Phys. Rev. C 2005, 72, 011901. [Google Scholar] [CrossRef]
- Bilandzic, A.; van Kolk, N.; Ollitrault, J.-Y.; Snellings, R. Event-plane flow analysis without non-flow effects. Phys. Rev. C 2011, 83, 014909. [Google Scholar] [CrossRef]
- Bilandzic, A.; Christensen, C.H.; Gulbrandsen, K.; Hansen, A.; Zhou, Y. Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations. Phys. Rev. C 2014, 89, 064904. [Google Scholar] [CrossRef]
- Bhalerao, R.S.; Ollitrault, J.-Y.; Pal, S. Event-plane correlators. Phys. Rev. C 2013, 88, 024909. [Google Scholar] [CrossRef]
- Di Francesco, P.; Guilbaud, M.; Luzum, M.; Ollitrault, J.-Y. Systematic procedure for analyzing cumulants at any order. Phys. Rev. C 2017, 95, 044911. [Google Scholar] [CrossRef]
- Miller, M.L.; Reygers, K.; Sanders, S.J.; Steinberg, P. Glauber modeling in high energy nuclear collisions. Ann. Rev. Nucl. Part. Sci. 2007, 57, 205. [Google Scholar] [CrossRef]
- Kharzeev, D.; Nardi, M. Hadron production in nuclear collisions at RHIC and high density QCD. Phys. Lett. B 2001, 507, 121. [Google Scholar] [CrossRef]
- Kharzeev, D.; Levin, E. Manifestations of high density QCD in the first RHIC data. Phys. Lett. B 2001, 523, 79. [Google Scholar] [CrossRef]
- Drescher, H.J.; Nara, Y. Effects of fluctuations on the initial eccentricity from the Color Glass Condensate in heavy ion collisions. Phys. Rev. C 2007, 75, 034905. [Google Scholar] [CrossRef]
- Drescher, H.-J.; Nara, Y. Eccentricity fluctuations from the color glass condensate at RHIC and LHC. Phys. Rev. C 2007, 76, 041903. [Google Scholar] [CrossRef]
- Drescher, H.; Ostapchenko, S.; Pierog, T.; Werner, K. Initial condition for QGP evolution from NEXUS. Phys. Rev. C 2002, 65, 054902. [Google Scholar] [CrossRef]
- Drescher, H.; Hladik, M.; Ostapchenko, S.; Pierog, T.; Werner, K. Parton based Gribov-Regge theory. Phys. Rep. 2001, 350, 93. [Google Scholar] [CrossRef]
- Werner, K.; Liu, F.-M.; Pierog, T. Parton ladder splitting and the rapidity dependence of transverse momentum spectra in deuteron-gold collisions at RHIC. Phys. Rev. C 2006, 74, 044902. [Google Scholar] [CrossRef]
- Werner, K.; Karpenko, I.; Pierog, T. The ’Ridge’ in Proton-Proton Scattering at 7 TeV. Phys. Rev. Lett. 2011, 106, 122004. [Google Scholar] [CrossRef]
- Werner, K.; Bleicher, M.; Guiot, B.; Karpenko, I.; Pierog, T. Evidence for Flow from Hydrodynamic Simulations of p-Pb Collisions at 5.02 TeV from ν2 Mass Splitting. Phys. Rev. Lett. 2014, 112, 232301. [Google Scholar] [CrossRef] [PubMed]
- Schenke, B.; Tribedy, P.; Venugopalan, R. Fluctuating Glasma initial conditions and flow in heavy ion collisions. Phys. Rev. Lett. 2012, 108, 252301. [Google Scholar] [CrossRef] [PubMed]
- Nahrgang, M.; Aichelin, J.; Gossiaux, P.B.; Werner, K. D mesons in non-central heavy-ion collisions: Fluctuating vs. averaged initial conditions. Nucl. Phys. A 2014, 932, 555. [Google Scholar] [CrossRef]
- Danielewicz, P.; Gyulassy, M. JACOBIAN FREE GLOBAL EVENT ANALYSIS. Phys. Lett. B 1983, 129, 283. [Google Scholar] [CrossRef]
- Bhalerao, R.S.; Ollitrault, J.-Y. Eccentricity fluctuations and elliptic flow at RHIC. Phys. Lett. B 2006, 641, 260. [Google Scholar] [CrossRef]
- Alver, B.; Back, B.B.; Baker, M.; Ballintijn, M.; Barton, D.S.; Betts, R.R.; Bindel, R.; Busza, W.; Chetluru, V.; Garcia, E.; et al. Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions. Phys. Rev. C 2008, 77, 014906. [Google Scholar] [CrossRef]
- Bhalerao, R.S.; Luzum, M.; Ollitrault, J.-Y. Understanding anisotropy generated by fluctuations in heavy-ion collisions. Phys. Rev. C 2011, 84, 054901. [Google Scholar] [CrossRef]
- Rice, J.A. Mathematical Statistics and Data Analysis, 3rd ed.; Duxbury Resource Center: Duxbury, MA, USA, 2006. [Google Scholar]
M | IC | E | Var | E | Var |
---|---|---|---|---|---|
10 | smooth | 0.375 | 0.393 | ||
fluctuating | 0.397 | 0.409 | |||
20 | smooth | 0.316 | 0.338 | ||
fluctuating | 0.341 | 0.359 | |||
50 | smooth | 0.283 | 0.321 | ||
fluctuating | 0.307 | 0.335 | |||
100 | smooth | 0.287 | 0.328 | ||
fluctuating | 0.292 | 0.324 | |||
500 | smooth | 0.295 | 0.331 | ||
fluctuating | 0.282 | 0.319 | |||
1000 | smooth | 0.297 | 0.333 | ||
fluctuating | 0.289 | 0.317 |
M | IC | E | Var | E | Var |
---|---|---|---|---|---|
10 | smooth | 0.312 | 0.342 | ||
fluctuating | 0.348 | 0.347 | |||
20 | smooth | 0.249 | 0.275 | ||
fluctuating | 0.251 | 0.287 | |||
50 | smooth | 0.193 | 0.216 | ||
fluctuating | 0.215 | 0.242 | |||
100 | smooth | 0.173 | 0.207 | ||
fluctuating | 0.186 | 0.221 | |||
500 | smooth | 0.167 | 0.217 | ||
fluctuating | 0.169 | 0.215 | |||
1000 | smooth | 0.174 | 0.213 | ||
fluctuating | 0.170 | 0.209 |
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Qian, W.-L.; Lin, K.; Ye, C.; Li, J.; Pan, Y.; Yue, R.-H. On Statistical Fluctuations in Collective Flows. Universe 2023, 9, 67. https://doi.org/10.3390/universe9020067
Qian W-L, Lin K, Ye C, Li J, Pan Y, Yue R-H. On Statistical Fluctuations in Collective Flows. Universe. 2023; 9(2):67. https://doi.org/10.3390/universe9020067
Chicago/Turabian StyleQian, Wei-Liang, Kai Lin, Chong Ye, Jin Li, Yu Pan, and Rui-Hong Yue. 2023. "On Statistical Fluctuations in Collective Flows" Universe 9, no. 2: 67. https://doi.org/10.3390/universe9020067
APA StyleQian, W.-L., Lin, K., Ye, C., Li, J., Pan, Y., & Yue, R.-H. (2023). On Statistical Fluctuations in Collective Flows. Universe, 9(2), 67. https://doi.org/10.3390/universe9020067