Viscous Hydrodynamic Predictions for Nuclear Collisions at the LHC
Matthew Luzum, Paul Romatschke
TL;DR
The paper addresses predicting collective flow in heavy-ion and small-system collisions at LHC energies using viscous hydrodynamics, with $v_2$ as a probe of the QCD medium's transport properties. It extends a RHIC-validated viscous-hydrodynamics framework to $\sqrt{s}=5.5$ TeV Pb+Pb and $\sqrt{s}=14$ TeV p+p, solving $D_\mu T^{\mu\nu}=0$ with a lattice-inspired EoS, constant $\eta/s$, and a Cooper-Frye freeze-out at $T_f=0.14$ GeV. Key findings include a ~10% increase of integrated $v_2$ at the LHC for Pb+Pb with RHIC-like viscosities, and a predicted near-zero $v_2$ in minimum-bias $p+p$ at $\sqrt{s}=14$ TeV unless $\eta/s<0.08$, which would imply a breakdown of the gradient expansion. The results relate the elliptic flow to the initial spatial eccentricity through $v_2/e_x$, highlighting the role of initial conditions (Glauber vs CGC) and providing a path to constrain $\eta/s$ and the initial geometry from future LHC data.
Abstract
Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v_2 in sqrt(s)=5.5 TeV lead-lead and sqrt(s)=14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v_2 from RHIC to Pb+Pb at LHC, and v_2 ~ 0 in p+p collisions unless eta/s < 0.08.