Fluctuating initial conditions and fluctuations in elliptic and triangular flow
Introduction
It is expected that collisions between two nuclei at ultra-relativistic energies will lead to a phase transition from hadrons to the fundamental constituents, quarks and gluons, usually referred to as Quark–Gluon Plasma (QGP). One of the experimental observables of QGP is the azimuthal distribution of produced particles. In non-zero impact parameter collision between two identical nuclei, the collision zone is asymmetric. Multiple collisions transform the initial asymmetry into momentum anisotropy. Momentum anisotropy is best studied by decomposing it in a Fourier series, ϕ is the azimuthal angle of the detected particle and is the plane of the symmetry of initial collision zone. For smooth initial matter distribution, plane of symmetry of the collision zone coincides with the reaction plane (the plane containing the impact parameter and the beam axis), . The odd Fourier coefficients are zero by symmetry. However, fluctuations in the positions of the participating nucleons can lead to non-smooth density distribution, which will fluctuate on event-by-event basis. The participating nucleons then determine the symmetry plane (), which fluctuate around the reaction plane [1]. As a result odd harmonics, which were exactly zero for smoothed initial distribution, can be developed. It has been conjectured that third harmonic , which is response of the initial triangularity of the medium, is responsible for the observed structures in two particle correlation in Au + Au collisions [2], [3], [4], [5], [6], [7]. The ridge structure in pp collisions also has a natural explanation if odd harmonic flow develops. Recently, ALICE Collaboration has observed odd harmonic flows in Pb + Pb collisions [8]. In most central collisions, the elliptic flow () and triangular flow () are of similar magnitude. In peripheral collisions however, elliptic flow dominates.
The second harmonic or the elliptic flow () has been studied extensively in Au + Au collisions at RHIC [9], [10]. Recently, ALICE Collaboration measured elliptic flow in Pb + Pb collisions at LHC [8], [11]. Large elliptic flow has provided compelling evidence that at RHIC and LHC, nearly perfect fluid is produced. Deviation from the ideal fluid behavior is controlled by shear viscosity to entropy ratio (). Effect of shear viscosity is to dampen the flow coefficients. Elliptic flow has sensitive dependence on . In smooth hydrodynamics, sensitivity of elliptic flow has been utilized to obtain phenomenological estimates of [12], [13], [14], [15], [16], [17], [18], [19]. Triangular flow is supposed to be more sensitive to viscosity than the elliptic flow [6], [7] and one expects that triangular flow measurements will constrain more accurately.
Event-by-event fluctuations in initial conditions generate the triangular flow. It is then natural that the triangular flow itself will also fluctuate, event-by-event. Unless the fluctuations are within some reasonable limit, sensitivity of the flow to will reduce greatly. In the present Letter, in a hydrodynamic model, we have studied the fluctuations in elliptic and triangular flow due to fluctuating initial conditions. Its sensitivity to the is also studied. It appear that with fluctuating initial conditions, the sensitivity of elliptic and triangular flow to is greatly reduced. Triangular flow fluctuates more strongly than the elliptic flow and become even less sensitive to than the elliptic flow. Large fluctuations belie the possibility of constraining viscosity to entropy ratio from triangular flow measurements.
Section snippets
Hydrodynamic equations, equation of state and initial conditions
We assume that in , Pb + Pb collisions at LHC, a baryon free fluid is formed. Only dissipative effect we consider is the shear viscosity. Heat conduction and bulk viscosity is neglected. The space–time evolution of the fluid is obtained by solving,
Eq. (2) is the conservation equation for the energy–momentum tensor, , ε, p and u being the energy density, pressure and fluid velocity respectively. is the shear
Viscous effects on elliptic and triangular flow
For fluid viscosity to entropy ratio , 0.04, 0.08, 0.12 and 0.16, we have simulated Pb + Pb collisions. collisions approximately corresponds to 30–40% collision. In viscous evolution, entropy is generated. To account for the entropy generation, the Gaussian density was reduced with increasing viscosity, such that in ideal and viscous fluid, on the average, multiplicity remains the same. In each event, Israel-Stewartʼs hydrodynamic equations are solved and from the
Conclusions
In a simple model of fluctuating initial states, we have studied fluctuations in elliptic and triangular flow in ideal and viscous fluid evolution. It is shown that fluctuations in triangular flow can be very large. Large fluctuation reduces the sensitivity of flow coefficients to viscosity. For example, fluctuations of elliptic flow make it insensitive to variation of viscosity to entropy ratio in the range . Fluctuations in triangular flow are even larger and viscosity to entropy
References (31)
Nucl. Phys. A
(2006)Nucl. Phys. A
(2005)Nucl. Phys. A
(2005)Phys. Lett. B
(2009)- et al.
Phys. Lett. B
(2011) - et al.
Phys. Lett. B
(2011) Phys. Lett. B
(2011)Phys. Lett. B
(2010)- et al.
Phys. Rev. C
(2010) - et al.
Phys. Rev. C
(2008)
Phys. Rev. Lett.
Phys. Rev. C
Phys. Rev. C
Phys. Rev. C
Phys. Rev. Lett.
Cited by (12)
Integrated dynamical approach to relativistic heavy ion collisions
2013, Progress in Particle and Nuclear PhysicsEvent-by-event viscous hydrodynamics for Cu-Au collisions at sNN=200GeV
2012, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsInfluence of α-clustering nuclear structure on the rotating collision system
2018, Nuclear Science and TechniquesCollective flows of α -clustering <sup>12</sup>C + <sup>197</sup>Au by using different flow analysis methods
2018, European Physical Journal ANuclear cluster structure effect on elliptic and triangular flows in heavy-ion collisions
2017, Physical Review C