Collective effects in light-heavy ion collisions

Collective effects in light-heavy ion collisions

Björn Schenke and Raju Venugopalan Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA
Abstract

We present results for the azimuthal anisotropy of charged hadron distributions in A+A, p+A, d+A, and He+A collisions within the IP-Glasma+music model. Obtained anisotropies are due to the fluid dynamic response of the system to the fluctuating initial geometry of the interaction region. While the elliptic and triangular anisotropies in peripheral Pb+Pb collisions at are well described by the model, the same quantities in p+Pb collisions underestimate the experimental data. This disagreement can be due to neglected initial state correlations or the lack of a detailed description of the fluctuating spatial structure of the proton, or both. We further present predictions for azimuthal anisotropies in p+Au, d+Au, and He+Au collisions at . For d+Au and He+Au collisions we expect the detailed substructure of the nucleon to become less important.

keywords:
heavy ion collisions, fluctuations, fluid dynamics
volume:

00 \journalnameNuclear Physics A \runauthB. Schenke and R.Venugopalan \jidnupha \jnltitlelogoNuclear Physics A

1 Introduction

For the physical interpretation of observables in heavy ion, proton/deuteron-heavy ion and (high-multiplicity) proton+proton collisions, the existence of a sophisticated description of the multi-particle production mechanism and event-by-event fluctuations is essential. In the high energy limit the color glass condensate (CGC) framework Gelis et al. (2010) is the proper effective theory of quantum chromodynamics (QCD) that provides such description.

One particular implementation of the CGC is the IP-Glasma model Schenke et al. (2012a, b). It combines the IP-Sat dipole model Kowalski and Teaney (2003); Kowalski et al. (2008), which parametrizes the impact parameter and -dependence of the saturation scale, with the classical dynamics of produced gluon fields Krasnitz and Venugopalan (2000, 2001); Lappi (2003). With its parameters constrained by inclusive and diffractive deeply inelastic scattering (DIS) data from e+p scattering at HERA, the IP-Glasma model correctly describes the bulk features of various collision systems over a wide range of energies Schenke et al. (2014).

After briefly introducing the IP-Glasma model and the employed relativistic fluid dynamic simulation music, we present results for the azimuthal anisotropy of charged hadrons produced in peripheral Pb+Pb collisions, and p+Pb collisions of comparable multiplicity. We compare to experimental data from the CMS collaboration Chatrchyan et al. (2013). We then present predictions for the systematics of the transverse momentum dependent anisotropy coefficients in p+Au, d+Au, and He+Au collisions at top RHIC energies.

2 IP-Glasma + MUSIC

The IP-Glasma model Schenke et al. (2012a, b) relates the DIS constrained nuclear dipole cross-sections to the initial classical dynamics of highly occupied gluon fields produced in a nuclear collision. Given an initial distribution of color charges in the high energy nuclear wave-functions, the strong multiple scatterings of gluon fields are computed by event-by-event solutions of Yang-Mills equations. Both fluctuating distributions of nucleons in the nuclear wave-functions and intrinsic fluctuations of the color charge distributions are included. This results in “lumpy” transverse projections of the gluon field configurations that vary event to event. The scale of this lumpiness is given on average by the nuclear saturation scale which corresponds to distance scales smaller than the nucleon size Kowalski et al. (2008).

The IP-Glasma model provides the initial conditions for fluid dynamic calculations at a given time . The initial energy density and flow velocities , are extracted from the gluon fields’ energy-momentum tensor at every transverse position via the relation . In the results presented below, the viscous part of the energy momentum tensor is set to zero at the initial time of the fluid dynamic simulation. This is done because the gluon field strength tensor is very anisotropic (the longitudinal pressure is approximately zero). A full 3+1 dimensional simulation including quantum fluctuations could provide a mechanism for isotropization via instabilities Berges et al. (2014); Epelbaum and Gelis (2013).

We employ the viscous relativistic fluid dynamic simulation music Schenke et al. (2010, 2011a, 2011b), which is a 3+1 dimensional simulation. However, because the initial conditions from the IP-Glasma model are boost-invariant, it is used in its 2+1 dimensional mode.

3 p+Pb collisions at the LHC

Figure 1: Multiplicity dependence of the root-mean-square elliptic (left) and triangular (right) flow coefficients in Pb+Pb (open symbols) and p+Pb collisions (filled symbols) from the IP-Glasma+music model (connected triangles) compared to experimental data by the CMS collaboration Chatrchyan et al. (2013). Figure from Schenke and Venugopalan (2014).

It was shown in Schenke and Venugopalan (2014) that experimental data from heavy ion collisions is well described by the IP-Glasma+music model out to fairly peripheral centrality bins. The natural question that arises is how the model does in describing data from p+A collisions that produce similar multiplicities. Fig. 1 shows the multiplicity dependence of and in peripheral Pb+Pb collisions and p+Pb collisions with comparable multiplicity. While the agreement with experimental data from the CMS collaboration Chatrchyan et al. (2013) is fairly good in the Pb+Pb case, for p+Pb collisions is under-predicted by approximately a factor of 4. In p+Pb agrees for the lower multiplicities studied, but has a rather flat multiplicity dependence and underestimates the experimental data at the higher multiplicities.

One reason for the disagreement could be that all initial state correlations that lead to an elliptic anisotropy111When including fluctuations initial state correlations should also contribute to odd harmonics. Dusling and Venugopalan (2012, 2013a, 2013b, 2013c); Gyulassy et al. (2014); Dumitru and Giannini (2014); McLerran and Skokov (2014) are neglected. Additionally, the description of the proton in the IP-Glasma model is over-simplified. The proton shape is approximated by a sphere, and any deviations from that are due to the small scale color charge fluctuations. Since the interaction region in p+Pb collisions is dominated by the shape of the smaller projectile, initial geometries in p+Pb collisions have very small eccentricities. This inevitably leads to small coefficients. If there is indeed a large contribution to coefficients in p+Pb collisions from collective effects, our result indicates that the shape of the proton fluctuates significantly more than assumed in the IP-Glasma model. One could envision a description where the small gluon distributions are still concentrated around large valence quark positions, leading to much larger eccentricities and fluctuations. In this case p+A collisions could be used to determine the shape and fluctuations of gluon distributions in the proton at high energies.

4 p+Au, d+Au, and He+Au collisions at RHIC

To determine whether final state collective effects provide the dominant contribution to the measured azimuthal anisotropy, RHIC is now studying He+Au collisions that on average generate more triangular initial state configurations compared to p+Au or d+Au. If collectivity is the physical explanation for the observed anisotropies, we expect a larger in He+Au collisions compared to p+Au and d+Au collisions at the same energy. To make this expectation more quantitative, we present predictions from the IP-Glasma+music framework.

For deuteron-gold collisions (d+Au) we compute the nucleon distribution in the deuteron using the Hulthen form of its wave function Miller et al. (2007); Bzdak et al. (2013). For He, we use the same nucleon configurations as employed in Nagle et al. (2013). They are obtained from Green’s function Monte Carlo calculations using the AV18 + UIX model interaction Carlson and Schiavilla (1998).

For this comparative study we do not perform a detailed centrality selection, but instead sample the impact parameter between 0 and in all systems. We then compute the initial state distribution of the energy density and flow velocity at time and evolve the system using viscous fluid dynamics with until freeze-out at .

We present typical configurations of the initial energy density distribution in the transverse plane and final results for the transverse momentum dependent azimuthal anisotropy coefficients to in Fig. 2. While we find very small values for through in p+Au collisions, the additional nucleons and their position fluctuations generate larger in d+Au and He+Au collisions. The odd harmonics and are noticeably larger in He+Au collisions compared to d+Au collisions. This qualitative prediction can be compared to future measurements at RHIC.

Figure 2: Typical configurations of the initial energy density distribution for p+Au, d+Au and He+Au collisions (upper panel). Azimuthal anisotropy coefficients in the three collision systems (lower panel).

5 Conclusions

We have demonstrated that experimental results for and in proton-heavy ion collisions at the LHC are not well described by the IP-Glasma+music model. Reasons for this could be the neglected initial state correlations and/or the lack of a detailed description of the fluctuating subnucleonic structure of the proton. Our results for p+A collisions differ significantly from those in Bozek and Broniowski (2013); Werner et al. (2014); Kozlov et al. (2014); Bzdak and Ma (2014), suggesting that the details of the initial shape in small systems are of paramount importance.

We predict an increase of both and in He+Au collisions compared to d+Au collisions, while the even harmonics are comparable in both systems. The detailed substructure of the nucleon is expected to be less important for the initial state geometry in these collisions compared to p+A collisions.

Acknowledgments We thank Jamie Nagle for providing us with the He nucleon configurations. This work was supported under DOE Contract No. DE-AC02-98CH10886. BPS acknowledges support from a DOE Office of Science Early Career Award. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the DOE Office of Science under Contract No. DE-AC02-05CH11231.

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