Initial Energy Density of √s = 7 and 8 TeV p–p Collisions at the LHC

Máté Csanád,Ze-Fang Jiang,Tamás Csörgő,Chun-Bin Yang

doi:10.3390/universe3010009

Abstract

Results from the Relativistic Heavy Ion Colloder (RHIC) and the Large Hadron Collider (LHC) experiments show that in relativistic heavy ion collisions, a new state of matter, a strongly interacting perfect fluid, is created. Accelerating, exact and explicit solutions of relativistic hydrodynamics allow for a simple and natural description of this medium. A finite rapidity distribution arises from these solutions, leading to an advanced estimate of the initial energy density of high energy collisions. These solutions can be utilized to describe various aspects of proton–proton collisions, as originally suggested by Landau. We show that an advanced estimate based on hydrodynamics yields an initial energy density in s = 7 and 8 TeV proton–proton (p–p) collisions at the LHC on the same order as the critical energy density from lattice Quantum Chromodynamics (QCD). The advanced estimate yields a corresponding initial temperature that is around the critical temperature from QCD and the Hagedorn temperature. The multiplicity dependence of the estimated initial energy density suggests that in high multiplicity p–p collisions at the LHC, there is large enough initial energy density to create a non-hadronic perfect fluid.

Highlights

The first years of data taking in the experiments at the Relativistic Heavy Ion Collider (RHIC)resulted in the discovery of a new state of matter produced in s NN = 200 GeV gold–gold (Au+Au) collisions [1,2,3,4], the so-called strongly coupled quark–gluon plasma, the “perfect liquid of quarks”: it consists of deconfined quarks, but behaves like an almost perfect fluid.The RHIC experiments achieved the following “milestones” [5,6,7,8,9,10,11] among others in discovering and characterizing this new state of matter
The advanced estimate yields a corresponding initial temperature that is around the critical temperature from Quantum Chromodynamics (QCD) and the Hagedorn temperature
Resulted in the discovery of a new state of matter produced in s NN = 200 GeV gold–gold (Au+Au) collisions [1,2,3,4], the so-called strongly coupled quark–gluon plasma, the “perfect liquid of quarks”: it consists of deconfined quarks, but behaves like an almost perfect fluid

Summary

Introduction

The first years of data taking in the experiments at the Relativistic Heavy Ion Collider (RHIC). The LHC heavy ion experiments confirmed the existence of this new state of matter (see e.g., References [16,17,18,19]), meaning that at collision energies that are two orders of magnitude higher, the created matter behaves very an intriguing result in itself. The equations of hydrodynamics are highly nonlinear, so they are frequently solved via simulations, where suitable initial conditions have to be assumed, and the equations of hydrodynamics are solved numerically, see details for example in the recent reviews of References [20,21] Besides these efforts, there is an interest in models where exact, explicit and parametric solutions of the hydrodynamical equations are used, and where the initial state may be inferred directly from matching the parameters of the solution to the data.

Rapidity Distributions from Hydrodynamics

Energy Density Estimation

Initial Energy Densities in 7 and 8 TeV LHC p–p Collisions

Uncertainty of the Estimate

Summary