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

Abstract

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.

Charged-particle multiplicities in proton–proton collisions at $$\sqrt{s} = 0.9$$ s = 0.9 to 8 TeV

“…Based on the Bjorken formula [85], a characteristic collision energy density can be estimated, which increases by the same factor. For a qualitative estimate, assuming that the average energy density in pp collisions at √ s = 7 TeV is of the order of 1 GeV/fm 3 (see for example [78]), a density of 10 GeV/fm 3 should be reached with high multiplicity pp collisions, similar to the energy density of Au-Au central collisions at RHIC [86]. When LHC runs at its nominal centre-of-mass energy of 14 TeV, high multiplicity proton-proton collisions will provide further direct comparisons of nuclear matter properties for interacting systems with similar energy densities but very different volumes.…”

“…In |η| < 0.5 and |η| < 1, the observed multiplicity reaches 10 times the mean multiplicity. It is expected that the average energy density in proton collisions at the LHC, at √ s = 14 TeV, is about 5 to 15 times smaller than energy densities reached in gold ions at RHIC [78]. Therefore, in proton-proton collisions of multiplicity exceeding 10 times the average multiplicity, energy densities should overlap with those of heavy ion collisions at RHIC, allowing to compare properties of systems with very different collision volumes (two to three orders of magnitude) but the same energy density.…”

1+1 dimensional relativistic magnetohydrodynamics with longitudinal acceleration

“…It has been pointed out that in realistic situations the energy density at mid-rapidity decreases faster than in the Bjorken flow. Although the Bjorken-estimation for the initial energy density is widely used, the longitudinal expansion dynamics of hydrodynamics seems [28][29][30][31] to be able to offer a more realistic estimation for the initial energy density estimation and the final state description. Acceleration effects are important in the estimation of the initial energy density even at mid-rapidity, if the expanding system is finite: even the most central fluid element exert a force on the volume elements closer to the surface, and this work decreases the internal energy of cells even at mid-rapidity.…”

Pseudo-rapidity distribution from a perturbative solution of viscous hydrodynamics for heavy ion collisions at RHIC and LHC

“…There has been tremendous theoretical and numerical work [27][28][29][30][31] in solving relativistic hydrodynamic equations, and those works not only simulate the fluid's dynamical evolution but also play an important role in extracting the transport properties of the strongly coupled matter. In our previous papers [32,33], a series of exact solutions for the relativistic accelerating perfect fluid were presented and served as a reliable reference to study the longitudinal acceleration effect, pseudorapidity distributions and the initial state properties for colliding systems at RHIC and at LHC [15,17,19,32,33].…”

“…In this paper, we expand the current knowledge of accelerating hydrodynamics [17,32] by including the first-order viscous (Navier-Stokes limit) corrections in the relativistic domain.…”