Size fluctuations of the initial source and event-by-event transverse momentum fluctuations in relativistic heavy-ion collisions

Abstract

We show that the event-by-event fluctuations of the transverse size of the initial source, which follow directly from the Glauber treatment of the earliest stage of relativistic heavy-ion collisions, cause, after hydrodynamic evolution, fluctuations of the transverse flow velocity at hadronic freezeout. This in turn leads to event-by-event fluctuations of the average transverse momentum, pT . Simulations with GLISSANDO for the Glauber phase, followed by a realistic hydrodynamic evolution and statistical hadronization carried with THERMINATOR, lead to agreement with the RHIC data. In particular, the magnitude of the effect, its centrality dependence, and the weak dependence on the incident energy are properly reproduced. Our results show that bulk of the observed event-by-event pT fluctuations may be explained by the fluctuations of the size of the initial source. We propose a new mechanism for generating the transverse-momentum fluctuations in relativistic heavyion collisions, based on the fluctuations of the initial size of the formed system and its subsequent hydrodynamic evolution. It is well established that a successful description of the physics of relativistic heavy-ion collisions is achieved with the help of relativistic hydrodynamics [1,2,3,4,5,6,7,8,9,10,11,12], effective at proper times ranging typically from about a fraction of a fm/c to a few fm/c, where statistical hadronization takes over. Numerous observables can be reproduced that way, such as the momentum spectra, elliptic flow, or the HBT correlation radii [11,12], measuring the system's space-time extension. The initial condition for hydrodynamics is usually obtained from the Glauber approach, leading to the wounded-nucleon picture [13] (a wounded nucleon is a nucleon, that has collided inelastically at least once) or its variants [14,15]. When the initial condition is obtained via Glauber Monte Carlo simulations, its shape fluctuates, simply reflecting the randomness in positions of the nucleons in the colliding nuclei.In this paper we show that the event-by-event fluctuations of the initial size are substantial, even when we consider the class of events with a strictly fixed number of the wounded nucleons, N w . The fluctuations are then carried over by hydrodynamics to the fluctuations of the transverse flow velocity at the hadronic freeze-out, which in turn generate the event-by-event fluctuations of the average transverse momentum, p T , * Supported in part by the Polish Ministry of Science and Higher Education, grants N202 034 32/0918 and N202 249235. of the produced hadrons. The mechanism is very simple: a more squeezed initial condition leads to faster expansion, larger flow, and, consequently, higher p T , while, on the conrary, a more stretched initial condition leads to slower expansion, lower flow, and lower p T . The event-by-event p T fluctuations have been a subject of intense theoretical and experimental studies

Eccentricity fluctuations in an integrated hybrid approach: Influence on elliptic flow

“…The density profiles are not smooth, but there are peaks in the transverse and the longitudinal direction. There are impact parameter fluctuations within one specific centrality class leading to multiplicity fluctuations and differences in the initial geometry [10]. Furthermore, the nuclei do not necessarily collide in the event-plane given by the laboratory system, but might also have a rotated reaction plane.…”

Correlations in the Monte Carlo Glauber model

“…In particular, comprehensive studies have been devoted to fluctuations of the average transverse momentum p T , both from the theoretical [34][35][36][37] and experimental side [38][39][40][41], as these fluctuations may reflect critical phenomena expected at the phase transition. Much progress has been made in understanding the response to initial fluctuations [11,[42][43][44][45][46]: typically, elliptic flow is proportional to the initial eccentricity [7]; triangular flow is proportional to the initial triangularity [10]; finally, p t fluctuations arise as a natural consequence of initial-state (size) fluctuations [47]. Eventually, the study of fluctuations essentially boils down to the study of the initial fluctuations.…”

Continuous description of fluctuating eccentricities

“…Since the eccentricities are linear in δρ, their variances can be easily determined in terms of the two-point function of the probability distribution, defined as (13) Eq. (10) yields…”

“…They leave observable traces in particle distributions after the hydrodynamical evolution [1]. They are for instance responsible for elliptic flow fluctuations [2,3] triangular flow [4][5][6][7] and higher harmonics [8,9], directed flow near midrapidity [9][10][11][12], and may also explain [13,14] observed transverse momentum fluctuations [15][16][17][18]. Considerable experimental and theoretical efforts are presently devoted to pin down the details of these fluctuations [19][20][21][22] and their various correlations [5,23,24].…”