Heavy Ions at the LHC: First Results Thomas Schaefer North Carolina State University
Heavy ion collision: Geometry R Au /γ y R Au x b z rapidity : y = 1 2 log ( E + pz E p z ) transverse momentum : p 2 T = p 2 x + p 2 y
Bjorken expansion Experimental observation: At high energy ( y ) rapidity distributions of produced particles (in both pp and AA) are flat dn dy const Physics depends on proper time τ = t 2 z 2, not on y All comoving (v = z/t) observers are equivalent Analogous to Hubble expansion
Bjorken expansion τ =const t η =const hadrons QGP pre equilibrium projectile target z
Bjorken expansion: Hydrodynamics Boost invariant expansion u µ = γ(1,0,0, v z ) = (t/τ, 0,0, z/τ) solves Euler equation (no longitudinal acceleration) µ (su µ ) = 0 Solution for ideal Bj hydrodynamics s(τ) = s 0τ 0 τ d dτ [τs(τ)] = 0 T = const τ 1/3 Exact boost invariance, no transverse expansion, no dissipation,...
Numerical estimates Total entropy in rapidity interval [y, y + y] S = sπr 2 z = sπr 2 τ y = (s 0 τ 0 )πr 2 y R Use S/N 3.6 s 0 τ 0 = 1 πr 2 S y z = τ y s 0 = 3.6 ( dn πr 2 τ 0 dy ) Bj estimate Depends on initial time τ 0. Assume QGP equation of state s 0 = 2π2 45 N dt 3 0 Fixes initial temperature (and energy density)
BNL and RHIC
Multiplicities 400 Au+Au 19.6 GeV 600 Au+Au 130 GeV dn ch /dη 300 200 dn ch /dη 400 100 200 0-5 0 5 η 0-5 0 5 η 800 0-6% 6-15% Au+Au 200 GeV 25-35% 35-45% dn ch /dη 600 400 15-25% 45-55% 200 0-5 0 5 η Phobos White Paper (2005)
Bjorken expansion
LHC: Pb+Pb s NN = 2.76 TeV
Predictions: Limiting fragmentation
Result vs Predictions: mini-jets, color glass,...
Alice results: Scaling with energy
What does it mean? Factor 2.2 in multiplicity: factor 2.85 in energy density, factor 1.3 in temperature (at fixed τ 0 ) AA pp: extra multiplicity per participant pair. Simple saturation works better than improved saturation.
Chemical equilibrium at freezeout Ratio 1 s NN =130 GeV T (MeV) 250 200 crossover quark gluon plasma end 10-1 150 point 10-2 10-3 π - π + Data Model T=165.5, µ b =38 MeV - K K + p p Λ Λ Ξ Ξ Ω Ω K + π + - K π - p π - Λ π - Ξ π - Ω π - φ K - * K K - 100 50 NA49 SIS, AGS RHIC hadrons 0 0 500 1000 µ B (MeV) Andronic et al. (2006)
Collective behavior: Radial flow Radial expansion leads to blue-shifted spectra in Au+Au Au+Au p+p 1/(2π) d 2 N / (m T dm T dy) [c 4 /GeV 2 ] 10 2 10 STAR preliminary Au+Au central s NN = 200 GeV K - π - 1/(2π) d 2 N / (m T dm T dy) [c 4 /GeV 2 ] 1 10-1 K - STAR preliminary p+p min. bias s NN = 200 GeV π - p 10-2 p 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 m T - m 0 [GeV/c 2 ] m T - m 0 [GeV/c 2 ] v T 0.6c! m T = p 2 T + m2
Collective behavior: Elliptic flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy Parameter v 2 0.3 0.2 0.1 0 Hydro model π K p Λ PHENIX Data π + +π - + - K +K p+p STAR Data 0 K S Λ+Λ b 0 2 4 6 Transverse Momentum p T source: U. Heinz (2005) dn p 0 d 3 p = v 0 (p ) (1 + 2v 2 (p ) cos(2φ) +...) pz =0 (GeV/c)
Elliptic flow II: Multiplicity scaling v 2 /ε 0.25 HYDRO limits 0.2 0.15 0.1 E lab /A=11.8 GeV, E877 E lab /A=40 GeV, NA49 0.05 E lab /A=158 GeV, NA49 s NN =130 GeV, STAR s NN =200 GeV, STAR Prelim. 0 0 5 10 15 20 25 30 35 (1/S) dn ch /dy source: U. Heinz (2005)
Viscous Corrections Longitudinal expansion: Bj expansion solves Navier-Stokes equation ( 4 entropy equation 1 ds s dτ = 1 3 1 η + ζ ) τ stτ Viscous corrections small if 4 3 η s + ζ s (Tτ) early Tτ τ 2/3 η/s const η/s < τ 0 T 0 late Tτ const η T/σ τ 2 /σ < 1 Hydro valid for τ [τ 0, τ fr ]
Viscous corrections to T ij (radial expansion) T zz = P 4 3 η τ T xx = T yy = P + 2 3 increases radial flow (central collision) decreases elliptic flow (peripheral collision) Modification of distribution function δf = 3 8 Correction to spectrum grows with p 2 Γ s T 2 f 0(1 + f 0 )p α p β α u β η τ δ(dn) dn 0 = Γ s 4τ f ( p T ) 2
Elliptic flow III: Viscous effects v 2 (percent) 25 20 15 10 ideal η/s=0.03 η/s=0.08 η/s=0.16 STAR 5 0 0 1 2 3 4 p T [GeV] Romatschke (2007), Teaney (2003)
Elliptic flow IV: Systematic trends Deviation from ideal hydro increases for more peripheral events increases with p source: R. Snellings (STAR)
Elliptic flow V: Predictions for LHC 0.25 0.5 e p /e x ( v 2 /e x ) 0.2 0.15 0.1 0.05 η/s = 10-4 η/s = 0.08 η/s = 0.16 RHIC Glauber RHIC CGC LHC Glauber LHC CGC PHOBOS/CGC PHOBOS/Glauber 0 10 20 30 40 50 60 70 80 (1/S overlap )(dn ch /dy)[fm -2 ] Romatschke, Luzum (2009) Busza (QM 2009)
Elliptic flow VI: Recombination quark number scaling of elliptic flow Anisotropy Parameter v 2 0.3 0.2 0.1 0 Hydro model π K p Λ PHENIX Data STAR Data π + +π - + - h +h + - K +K K 0 S p+ p Λ+ Λ 0 2 4 6 Transverse Momentum p T (GeV/c) v 2 /n 0.08 0.06 0.04 0.02 0 Polynomial Fit π + +π - 0 K S p+ p Λ+Λ STAR Preliminary + - K +K Ξ+Ξ (qq) (mes) p mes = 2pqu Data/Fit 1.5 1 0.5 (qqq) (bar) p bar = 3pqu 0 0.5 1 1.5 2 2.5 p T /n (GeV/c)
Alice flow
Flow excitation function
What does it mean? Hydro rules! RHIC data not an accident. Differential v 2 exactly equal to RHIC (!?) Integrated v 2 somewhat high: mean p T increase? acceptance?
Jet quenching R AA = n AA N coll n pp source: Akiba [Phenix] (2006)
Jet quenching II Disappearance of away-side jet φ) dn/d( φ) dn/d( 1/N 1/NTRIGGER Trigger 0.2 0.1 d+au FTPC-Au 0-20% p+p min. bias Au+Au Central 0-1 0 1 2 3 4 φ (radians) source: Star White Paper (2005)
Jet quenching III: The Mach cone azimuthal multiplicity dn/dφ (high energy trigger particle at φ = 0) wake of a fast quark in N = 4 plasma Chesler and Yaffe (2007) source: Phenix (PRL, 2006), W. Zajc (2007)
Jet quenching: Theory 10.0 energy loss governed by RHIC data ˆq = ρ q 2 dq 2 dσ dq 2 q (GeV 2 /fm) 1.0 0.1 pion gas QGP 0.01 1 10 100 (GeV/fm 3 ) 0.1 cold nuclear matter larger than pqcd predicts? relation to η? (ˆq 1/η?) also: large energy loss of heavy quarks source: R. Baier (2004)
ATLAS mono-jet Event display of a highly asymmetric dijet event, with one jet with E T > 100 GeV and no evident recoiling jet, and with high energy calorimeter cell deposits distributed over a wide azimuthal region. Only tracks with p T > 2.6 GeV.
What does it mean? Jets can be identified in AA environment. E T > 100 GeV jet is stopped! Proof of principle, detailed analysis needed.