1. 1 Hadron multiplicities, p T -spectra and net-baryon number in central Pb+Pb collisions at the LHC Kari J. Eskola, Department of Physics, University of Jyväskylä Helsinki Institute of Physics based on: K. J. Eskola, H. Honkanen, H. Niemi, P. V. Ruuskanen and S. S. Räsänen, Phys. Rev. C 72 (2005) 044904 [arXiv:hep-ph/0506049] Heavy Ion Collisions at the LHC: Last Call for Predictions, CERN, 28 June, 2007

2. 2 pQCD + saturation + hydrodynamics (EKRT) framework 1. Initial conditions from pQCD+saturation : - pQCD minijets in A+A [Eskola, Kajantie, Lindfors, Nucl.Phys.B323(1989)37] collinear factorization, p T ≥ p 0 LO; K = 1.6 for RHIC, 2.3 for LHC [from ET in NLO, hep-ph/0002008] nPDFs: EKS98 - saturation of produced gluons (interaction vertices)  p sat = p 0 = 1.1 GeV … 2.0 GeV central Au+Au at RHIC Pb+Pb at LHC τ form = 1/p sat = 0.17 fm... 0.10 fm  average ε (τ form ) = E T (p sat )/(  R A 2 τ form ) n B (τ form ) = N B (p sat )/(  R A 2 τ form ) - for ε(τ form,r) & n B (τ form,r) assume binary profiles [ EKRT, hep-ph/9909456 ] hep-ph/0506049

3. 3 2. Hydrodynamics - Fast & full thermalization : τ 0 = τ form - Longitudinal boost-invariance: v z = z/t - Transverse expansion; initially v r ( τ 0 ) = 0 - EoS: QGP: ideal gas, N f = 3, m=0, B 1/4 = 239 MeV, T C = 165 MeV HRG: ideal gas, m < 2 GeV - Cooper-Frye dec. with single T dec = 150 MeV from RHIC data; use this for LHC - Resonance decays included - Ideal 1+2 d hydro: evolution isentropic  initial N AA ~ final N AA  predicted [hep-ph/9909456] correctly RHIC N ch (η=0) for central Au+Au at 56, 130, 200 GeV. hep-ph/0506049 nucl-th/0008014 hep-ph/0111223

4. 4 Early LHC prediction from pQCD+saturation+ hydrodynamics dN ch /dη = 2560 for 6 % most central Pb+Pb collisions Eskola, Ruuskanen, Räsänen, Tuominen, hep-ph/0104010 hep-ph/0104010

5. 5 Works at RHIC with T dec = 150 MeV. hep-ph/0506049 RHIC: charged hadrons at η = 0

6. 6 - Reproduce pi & K p T -spectra and p multiplicities well with T dec = 150 MeV. - Proton p T -spectra need more detailed decoupling, recombination, … - Comparison with pQCD + FF + E-losses  Hydrodynamic region p T < 3 GeV RHIC: pi, K, p at y=0 hep-ph/0506049 ~

7. 7 LHC predictions at η = y = 0 [ hep-ph/0506049] - Hydrodynamic region p T < 4…5 GeV; larger than at RHIC ~ η = 0 y = 0 K.J. Eskola et al T dec =150 MeV

8. 8 For further LHC predictions with input from pQCD + saturation + hydrodynamics, see Harri Niemi: Minimum bias v 2 (p T ) Thorsten Renk: Charged hadron R AA (p T )

9. 9 Extra slide: T dec dependence of integrated observables Our LHC predictions here [hep-ph/0506049]