UNIVERSITÀ DEGLI STUDI DI CATANIA INFN-LNS. inziale nel plasma creato nelle collisioni ad energie ultra-relativistiche

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1 UNIVERSITÀ DEGLI STUDI DI CATANIA INFN-LNS Anisotropie vn nello spazio degli impulsi e fluttuazioni di stato inziale nel plasma creato nelle collisioni ad energie ultra-relativistiche S. Plumari, L. Oliva, A. Puglisi, M. Ruggieri, F. Scardina, V. Greco

2 Outline Transport approach at fixed η/s Initial state fluctuations - role of η/s on the build-up of vn(pt): from RHIC to LHC - Correlations between εn (space eccentricities) and vn (collective flows) Conclusions

3 sketch of evolution of a HIC F. Gelis Int.J.Mod.Phys. E24 (2015) no.10, Initial out-of-equilibrium state: Glasma, namely, a configuration of longitudinal color electric and color-magnetic flux tubes.

4 η/s(t) around to a phase transition P. Kovtun et al.,phys.rev.lett. 94 (2005) L. P. Csernai et al., Phys.Rev.Lett. 97 (2006) R. A. Lacey et al., Phys.Rev.Lett. 98 (2007) Quantum mechanism Δ E Δ t 1 η/s 1 p τ > AdS/CFT suggest a lower bound η/s = 1/(4 π)~0.08 From pqcd: η/ s 1 g 4 ln (1 / g) η/ s 1 pqcd P.Arnold et al., JHEP 0305 (2003) 051. LHC RHIC LQCD some results approx. large error bars for quenched Quasi-Particle models seem to suggest a η/s~tα α ~ Chiral perturbation theory Meson Gas S. Plumari et al., J. Phys.: Conf. Ser (2013). arxiv: Intermediate Energies IE ( B>T)

5 Information from non-equilibrium: elliptic flow INITIAL OLD VIEW or s viscosity c2s=dp/d EoS-lQCD x y2 x2 y x 2 2 The v2/ measures efficiency in converting the eccentricity from Coordinate to Momentum space Can be seen also as Fourier expansion d3 N d2 N E = [ 1+ 2v 2 cos (2 ϕ)+ 2 v 4 cos ( 4 ϕ)+ ] 3 2 π p T dp T d η dp by symmetry vn with n odd expected to be zero (but event by event fluctuations) v2 cos2 p x2 p 2y px2 p y2

6 Information from non-equilibrium: vn(pt) or s viscosity c2s=dp/d EoS-lQCD r ϵ= n cos [ n( ϕ Φ n )] n n=2 r n n=3 The v2/ measures efficiency in converting the eccentricity from Coordinate to Momentum space ############################## n=4 n=5 n=6 Can be seen also as Fourier expansion 3 v n = cos [ n(ϕ Ψ n)] 2 d N d N E = [ 1+ 2v 2 cos 2 (ϕ Ψ 2 )+ 2 v 3 cos 3 (ϕ Ψ3 )+ ] 3 2 π p dp d η dp T T by symmetry vn with n odd expected to be zero (but event by event fluctuations) C. Gale et al., PRL 110, (2013).

7 Information from non-equilibrium: vn(pt) or s viscosity c2s=dp/d EoS-lQCD r ϵ= n cos [ n( ϕ Φ n )] n n=2 r n n=3 The v2/ measures efficiency in converting the eccentricity from Coordinate to Momentum space v n = cos [ n(ϕ Ψ n)] ############################## n=4 n=5 C. Shen, Z. Qiu, U. Heinz arxiv: n=6 Can be seen also as Fourier expansion 3 2 d N d N E = [ 1+ 2v 2 cos 2 (ϕ Ψ 2 )+ 2 v 3 cos 3 (ϕ Ψ3 )+ ] 3 2 π p dp d η dp T T by symmetry vn with n odd expected to be zero (but event by event fluctuations) n 5 6 7

8 Motivation for a kinetic approach: ν p {p + [ p ν F + M M ] } f (x, p)=s 0 + C 22+ Free streaming Field Interaction 3P Souce term: Collisions particle creation η 0 Starting from 1-body distribution function and not from T ν: - possible to include f(x,p) out of equilibrium. M. Ruggieri, F. Scardina, S. Plumari, V. Greco PLB 727 (2013) 177. M. Ruggieri, A. Puglisi, L. Oliva, S. Plumari, F. Scardina, V. Greco PRC 92 (2015) extract information about the viscous correction δf to f(x,p) S.Plumari,G.L. Guardo, V. Greco, J.Y. Ollitrault NPA (2015) 87 It is not a gradient expansion in η/s. Valid at intermediate pt out of equilibrium. Valid at high η/s (cross over region): + self consistent kinetic freeze-out

9 Applying kinetic theory to A+A Collisions. p {p + M M } f ( x, p)=c Impact of /s(t) on the build-up of vn(pt) vs. beam energy - role of EoS on the vn(pt) - including the Initial state fluctuations

10 Initial State Fluctuations: Monte Carlo Glauber Not almond shape smooth distribution n=2 n=3 n=4 n=5 n=6 Characterization of the initial profile in terms of Fourier coefficients r n cos [n( ϕ Φ n )] ϵ n= r n r = x2 + y2, r n sin ( n ϕ) 1 Φ n= arctan n n r cos( n ϕ) ϕ=arctan ( y / x ) G-Y. Qin, H. Petersen, S.A. Bass and B. Muller, PRC82, (2010). H.Holopainen, H. Niemi and K.J. Eskola, PRC83, (2011).

11 Initial State Fluctuations: role of the EoS on <vn> and vn(pt) ϵ=t 0 0 p= 1 T ii 3 i For massless case the system is more efficient in converting the initial anisotropy in coordinate space. The effect of the EoS is to reduce the <vn>. The elliptic flow show a mass ordering typical of hydro expansion where at low pt the v2(pt) pt - <β < T> m T Different <vn> probes different value of p/ε during the expansion of the fireball.

12 Initial State Fluctuations: vn(pt) for central collisions LHC RHIC At low pt vn(pt) ptn. v2 for higher pt saturates while vn for n>3 increase linearly with pt. For central collisions viscous effect are more relevant. For n>2 the vn(pt) are more sensitive to the η/s ratio in the QGP phase.

13 Initial State Fluctuations: vn vs εn LHC: (20-30)% S. Plumari, G. L. Guardo, F. Scardina, V. Greco Phys.Rev. C92 (2015) no.5, At LHC vn are more correlated to εn than at RHIC. v2 and v3 linearly correlated to the corresponding eccentricities ε2 and ε3 rispectively. C(4,4) < C(2,2) for all centralities. v4 and ε4 weak correlated similar to hydro calculations: F.G. Gardim, F. Grassi, M. Luzum and J.Y. Ollitrault NPA904 (2013) 503. H. Niemi, G.S. Denicol, H. Holopainen and P. Huovinen PRC87(2013) For central collisions vn are strongly correlated to εn: vn εn for n=2,3,4. n=2,3,4 LHC: (0-0.2)%

14 Initial State Fluctuations: vn vs εn S. Plumari, G. L. Guardo, F. Scardina, V. Greco Phys.Rev. C92 (2015) no.5, Equation of State and collision energy play a role on the build up of <vn> in central collisions. The effect of the EoS is to reduce the final <vn>. At RHIC energies the <vn> are smaller than those LHC and for more realistic η/s(t) v2 > v3 > v4... At LHC energies and ultra-central collisions the <vn> keep more information about the initial eccentricities <εn>.

15 From fields (Glasma) to particles (QGP) dn [ p + p ν F ] f (x, p)= + C 22 + d Γ ν ν We solve self-consistently Boltzmann-Vlasov F =J and Maxwell eq. (abelian approx.) ν p SCHWINGER MECHANISM Classical fields decay to particles pairs via tunneling due to vacuum instability. Longitudinal Chromo-Electric fields decay in gluon pairs and quark-antiquark pairs. For 4πη/s=1: Fast thermalization in about 1 fm/c Pressure isotropization in about 1 fm/c Pure field with negative longitudinal pressure Focus on a single flux tube

16 Conclusions Transport at fixed η/s: Enhancement of η/s(t) in the cross-over region affect differently the expanding QGP from RHIC to LHC. LHC nearly all the v n from the QGP phase. At LHC stronger correlation between vn and εn than at RHIC for all n. Ultra central collisions: - vn εn for n=2,3,4 strong correlation C(n,n) 1 - vn(pt) much more sensitive to η/s(t) - degree of correlation increase with the collision energy and the relative strenght of <vn> depend on the colliding energies. - correlations in (vn,vm) reflect the initial correlations in (εn,εm) Relativistic transport theory permit to study early dynamics of HIC - Initial color-electric field decays in about 1 fm/c - Thermalization and Isotropization in about 1 fm/c

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18 From fields (Glasma) to particles (QGP): (1+1D evolution) dn [ p + p ν F ] f (x, p)= + C 22 + dγ ν ν We solve self-consistently Boltzmann-Vlasov F =J and Maxwell eq. (abelian approx.) ν p SCHWINGER MECHANISM Classical fields decay to particles pairs via tunneling due to vacuum instability Focus on a single flux tube LONGITUDINAL CHROMO-ELECTRIC FIELDS DECAY IN GLUON PAIRS AND QUARKANTIQUARK PAIRS Casher, Neuberger and Nussinov, PRD 20, 179 (1979) Glendenning and Matsui, PRD 28, 2890 (1983) ABELIAN FLUX TUBE MODEL negligible chromo-magnetic field abelian dynamics for the chromoelectric field longitudinal initial field Schwinger mechanism

19 From Glasma to Quark Gluon Plasma: (1+1D evolution) 1+1 D expansion For 4πη/s=1: Field decays quickly with a power law Fast thermalization in about 1 fm/c Pressure isotropization in about 1 fm/c M. Ruggieri, et al., PRC 92 (2015) For large η/s: Field decays faster in about 0.5 fm/c and for t > 0.5 fm/c plasma oscillations Particle spectra different from a thermal one Less efficient isotropization Pure field with negative longitudinal pressure

20 From Glasma to Quark Gluon Plasma: (3+1D evolution) Electromagnetic probes are an efficient tool to investigate the initial state of heavy ion collisions and the properties of quark-gluon plasma. Schwinger simulations take into account of pre-equilibrium effects: Total Theoretical models can be used to identify these sources and their relative importance photon number enhanced of 30% in the spectrum mainly at high pt

21 Boltzmann Transport Equation ν p {p + [ p ν F + M M ] } f (x, p)=s 0 + C 22+ To solve numerically the Boltzmann-Vlasov eq. we use the test particle method 1 C 22= 2 E1 d3 p2 1 3 (2 π) 2 E 2 ν d 3 p'1 d3 p'2 3 3 ( 2 π) 2 E ' 1 (2 π) 2 E ' 2 2 f ' 1 f ' 2 M 1 ' 2 ' 1 2 ( 2 π) 4 δ(4) ( p ' 1+ p ' 2 p1 p2 ) For the numerical implementation of the collision integral we use the stochastic algorithm. ( Z. Xu and C. Greiner, PRC (2005) ) 1 η( x, t)/ s= p τ η 15 1 p 1 σ = 15 g (m D /2T)n η/ s η/ s tot σ is evaluated in such way to keep fixed the η/s during the dynamics according the Chapman-Enskog equation. (similar to D. Molnar, arxiv: [nucl-th]) - We know how to fix locally η/s(t) - We have checked the Chapmann-Enskog (CE): - CE good already at 1st order 5% - Relaxation Time Approx. severely understimates η S. Plumari et al.,prc86 (2012) A. El, Z. Xu, C. Greiner PRC 81 (2010) results of BAMPS

22 Initial State Fluctuations: vn(pt) and η/s LHC RHIC vn(pt) at RHIC is more sensitive to the value of the η/s at low temperature. v4(pt) and v3(pt) are more sensitive to the value of η/s than the v2(pt). At LHC energies vn(pt) is more sensitive to the value of η/s in the QGP phase (compare solid and dot-dashed lines).

23 Initial State Fluctuations: vn(pt) and η/s LHC RHIC vn(pt) at RHIC is more sensitive to the value of the η/s at low temperature. v4(pt) and v3(pt) are more sensitive to the value of η/s than the v2(pt). At LHC energies vn(pt) is more sensitive to the value of η/s in the QGP phase (compare solid and dot-dashed lines).