Anisotropic flow in a Boltzmann kinetic approach at fixed /s(T) V. Greco UNIVERSITY of CATANIA INFN-LNS S. Plumari M. Ruggieri F. Scardina nfQCD 2013 Kyoto, 2-6 December 2013 Outline Two main results for HIC Two main results for HIC: Elliptic flow from Color Glass Condensate (fKLN) going beyond x and implementing also going beyond x and implementing also the p-space with the Qs saturation scale the p-space with the Qs saturation scale Are there hints of /s(T) ? Transport Kinetic Theory at fixed /s : Motivations How to fix locally /s Relativistic Boltzmann-Vlasov approach Collisions -> 0 Field Interaction (EoS) Free streaming One can expand over microscopic details ( 2 2,2 3 ), but in a hydro language this is irrelevant only the global dissipative effect of C[f] is important! f(x,p) is the one-body distribution function -C[f eq + f] 0 deviation from ideal hydro ( finite or /s ) -We map with C[f] the phase space evolution of a fluid at fixed /s ! Starting from 1-body distribution function f(x,p) and not from T : -Include off-equilibrium at high and intermediate p T -Implement non-equilibrium implied by CGC-Qs scale (beyond x ) -Relevant at LHC due to large amount of minijet production -freeze-out self-consistently related with /s(T) Its not a gradient expansion /s: - valid also at high /s -> LHC ( T>>T c ) or cross-over region (T T c ) - valid also at high /s -> LHC ( T>>T c ) or cross-over region (T T c ) Appropriate for heavy quark dynamics ( next week talk ) Motivation for Transport approach Collisions -> 0 Field Interaction Free streaming Simulate a fixed shear viscosity Usually input of a transport approach are cross-sections and fields, but here we reverse it and start from /s with aim of creating a more direct link to viscous hydrodynamics g(a=m D /2T) correct function that fixes the relaxation time for the shear motion Chapman-Enskog agrees with Green-Kubo! Chapmann-Enskog S.Plumari et al., PRC86(2012) CE good one ! Chapmann-Enskog Viscosity from Green-Kubo Correlator estimate in a Box at fixed T Simulate a fixed shear viscosity =cell index in r-space Space-Time dependent cross section evaluated locally Transport code Viscosity fixed varying Usually input of a transport approach are cross-sections and fields, but here we reverse it and start from /s with aim of creating a more direct link to viscous hydrodynamics g(a=m D /2T) correct function that fix the relaxation time for the shear motion Chapman-Enskog agrees with Green-Kubo Chapmann-Enskog G. Ferini et al., PLB670 (2009) S.Plumari et al., PRC86(2012) CE good one ! Chapmann-Enskog Transport at fixed /s vs Viscous Hydro in 1+1D Knudsen number -1 Comparison for the relaxation of pressure anisotropy P L /P T Huovinen and Molnar, PRC79(2009) In the limit of small /s ( factor 2 larger tot is needed respect to isotropic case cross section Keep same /s means: /s or details of the cross section? cross section /s is really the physical parameter determining v 2 at least up to GeV microscopic details become relevant at higher p T First time /s v 2 hypothesis is verified! for m D =0.7 GeV -> factor 2 larger tot is needed respect to isotropic case 4 /s=1 Keep same /s means: /s or details of the cross section? for m D =1.4 GeV -> 25% smaller tot for m D =5.6 GeV -> 40% smaller tot cross section /s is really the physical parameter determining v 2 at least up to GeV microscopic details become relevant at higher p T First time /s v 2 hypothesis is verified! Keep same /s means: /s or details of the cross section? cross section /s is really the physical parameter determining v 2 at least up to GeV microscopic details become relevant at higher p T First time /s v 2 hypothesis is verified! Differences arises just where in viscous hydro f becomes relevant No Fine tuning! Employed the relaxation time approximation! Natural extension from low to high p T Boltzmann transport describes rise and fall of v 2 (p T ) Transition between low and high p T in a unified framework! partons Highly non-pQCD Disappearing of non-pQCD pQCD limit S. Plumari and VG, AIP1422(2012)- arXiV: [hep-ph] s =0.3 and m D =0.7 GeV pQCD limit, but with s =0.3 - No Q 2 dependence & - No radiative part Renormalize to fix /s 4-5 GeV, fixed by /s What about Color Glass condensate initial state? - Kinetic Theory Q s saturation scale x y z pxpx pypy Unintegrated distribution functions (uGDFs) Saturation scale Qs depends on: 1.) position in transverse plane; 2.) gluon rapidity. Nardi et al., Nucl. Phys. A747, 609 (2005) Kharzeev et al., Phys. Lett. B561, 93 (2003) Nardi et al., Phys. Lett. B507, 121 (2001) Drescher and Nara, PRC75, (2007) Hirano and Nara, PRC79, (2009) Hirano and Nara, Nucl. Phys. A743, 305 (2004) Albacete and Dumitru, arXiv: [hep-ph] Albacete et al., arXiv: [nucl-th] Factorization hypothesis: convolution of parton distribution functions in the parent nucleus. fKLN realization of CGC pTpT dN/d 2 p T Q sat (s) p-space x-space x (fKLN)=0.34 x (Glaub.)=0.29 CGC-KLN x 30% larger than Glauber T. Hirano et al., PLB636(06) Kharzeev et al., PLB561, 93 (2003) Nardi et al., PLB507, 121 (2001) Drescher et al, PRC75, (2007) Hirano et al., PRC79, (2009) Albacete and Dumitru, arXiv: V 2 from KLN in Hydro What does it KLN in hydro? 1) r-space from KLN (larger x ) 2) p-space thermal at t 0 fm/c - No Q s scale, Well call it fKLN- Th Glauber /s = 0.08 CGC-KLN /s=0.16 Larger x - > higher /s to get the same v 2 (p T ) See also: Alver et al., PRC 82, (2010) Heinz et al., PRC 83, (2011) Luzum and Romatschke PRC78(2008) Thermalization in less than 1 fm/c, in agreement with Greiner et al., NPA806, 287 (2008). Not so surprising: /s is small -> large effective scattering rate -> fast thermalization. Implementing KLN p T distribution Using kinetic theory we can implement full KLN (x & p space) - x =0.34, Qs =1.4 GeV KLN only in x space ( like in Hydro) x =0.341, Qs=0 -> Th-KLN GeV 20-30% Glauber in x & thermal in p x =0.289, Qs=0 -> Th-Glauber M. Ruggieri et al., Phys.Lett. B727 (2013) 177 Longitudinal and transverse pressure P L /P T show also a very fast equilibration ( isotr 0.3 fm/c )! However it is not this that makes a difference for v 2 : isotropization time very similar for all the cases t=1/Qs0.1 fm/c -> P L /P T > 0 Gelis & Epelbaum arXiV: Longitudinal and transverse pressure For /s > 0.3 one misses fast isotropization in P L /P T ( 2 fm/c ) For /s pQCD no isotropization Semi-quantitative agreement with Florkowski et al., PRD88 (2013) our is 3+1D not in relax.time but full integral but no gauge field pQCD 80% level of isotropization Hydro - likeFull x & p GeV When implementing KLN and Glauber like in Hydro we get the same of Hydro When implementing full KLN we get close to the data with 4 /s =1 : larger x compensated by Q s saturation scale (non-equilibrium distribution) Results with kinetic theory M. Ruggieri et al., Phys.Lett. B727 (2013) [nucl-th] We clearly see that when non-equilibrium distribution is implemented in the initial stage ( 1 fm/c) v 2 grows slowly respect to thermal one What is going on? Evolution with Centrality The difference fKLN, Th-fKLN and Th-Glauber disappears at central collisions ( like in hydro for Th-fKLN and Th-Glauber ) In peripheral collisions fKLN would even be lower than Th-Glauber due to non-equilibrium impact Applying kinetic theory to A+A Collisions. x y z pxpx pypy Part II - Impact of /s(T) on the build-up of v 2 (p T ) vs. beam energy /s increases in the cross-over region, realizing a smooth f.o. self- consistently dependent on h/s: /s increases in the cross-over region, realizing a smooth f.o. self- consistently dependent on h/s: Different from hydro that is a sudden cut of expansion at some T f.o. Different from hydro that is a sudden cut of expansion at some T f.o. Terminology about freeze-out Freeze-out is a smooth process: scattering rate < expansion rate /s(T) for QCD matter lQCD some results for quenched approx. ( large error bars ) A. Nakamura and S. Sakai, PRL 94(2005) H. B. Meyer, Phys. Rev. D76 (2007) Quasi-Particle models seem to suggest a /s~T , ~ 1 1.5. S.Plumari et al., PRD84 (2011) M. Bluhm, Redlich, PRD (2011) Chiral perturbation theory ( pT) M. Prakash et al., Phys. Rept. 227 (1993) J.-W. Chen et al., Phys. Rev. D76 (2007) Intermediate Energies IE ( B >T) W. Schmidt et al., Phys. Rev. C47, 2782 (1993) Danielewicz et al., AIP1128, 104 (2009) (STAR Collaboration), arXiv: [nucl- ex]. 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) Impact of /s(T) vs s NN 4/s=1 during all the evolution of the fireball -> no invariant v 2 (p T ) -> smaller v 2 (p T ) at LHC. Initial minijets relevant at LHC for p T >1.5 GeV ! LHC: almost insensitivity to cross-over ( 5%) : v 2 from pure QGP Without /s(T) increase TTc we would have v 2 (LHC)3 with an ev.-by-ev. analysis put even stronger constraints Plumari, Greco,Csernai, arXiv: However for a definite statement needed hadronization + EoS-lQCD Development of kinetic at fixed /s(T) : Verified that up to GeV: v 2 /s, cross section microscopic details irrelevant For a fluid at /s P L /P T > 0.8 at isotr Non-equilibrium implied by Qs damps v 2 (p T ) compensating the larger x -> v 2 (p T ) can be described by 4 /s 1 also for fKLN v 2 (p T ) can be described by 4 /s 1 also for fKLN Summary Outlook for the kinetic theory approach Include initial state fluctuations to study v n : more constraints on /s(T) and initial state? something more or new at p T 2-4 GeV ? pA Endeavor already undertaken. Hadronization: statistical model +Cooper-Frye vs. coalescence + fragm. Field Dynamics: Realistic EoS: M(T) + Bag mean field dynamics [Done!] Next step Include Initial State Fluctuations (Preliminary results) Monte Carlo Glauber = 0.5 fm G-Y. Qin, H. Petersen, S.A. Bass and B. Muller, PRC82, (2010) H.Holopainen, H. Niemi and K.J. Eskola, PRC83, (2011) v 2 and v 3 linearly correlated to the corresponding eccentricities 2 and 3 Initial State Fluctuations: v n vs n ( Preliminary ) C(2,2)=0.93 C(3,3)= /s=1 5 v 4 and 4 weak correlated similar to hydro calculations: F.G.Gardim,F.Grassi,M.Luzum and J.Y.Ollitrault NPA904 (2013) 503. Niemi, Denicol, Holopainen and Huovinen PRC87(2013) Initial State Fluctuations: v n vs n ( Preliminary ) C(2,2)= /s=1 5 C(3,3)=0.23 General agreement with hydro Niemi et al. PRC87(2013), but: /s not constant (include cross-over increase) -3+1 D not 2+1D =0.5 fm not 0.8 fm (if relevant at all!) Like in viscous hydro the data of v n (p T ) at RHIC energies are described with 4/s=1 5 Data taken from: A. Adare et al. [PHENIX collaboration], Phys.Rev. Lett. 107, (2011). Initial State Fluctuations: v n (p T ) ( Preliminary ) Fluctuations allows to extend the studies on impact of CGC-Qs, /s(T) and study pA Distribution function & occupation number f >1 need of Bose-Einstein statistics (1+f) terms needed in the collision integral -> possibility of Bose Condensate induced by CGC J. -P. Blaizot et al., arXiv: [hep-ph]; J. - P. Blaizot et al., Nucl. Phys. A , 829c (2013). At LHC and low p T it could be there and CYM helps! f >1 at p T > 0.5 our effect manifest at larger p T Longitudinal expansion lowers average density by -1 but f(p) goes down slowly at p T 1.5 GeV Effect non-negligible Impact of minijets on v 2 (p T ) Larger sensitivity on /s (T) at LHC Effect larger respect to viscous hydro, but this depends also on f Sensitivity in transport using same /s(T) Hydro-Niemi Viscous Hydrodynamics An Asantz (Grad) - at p T ~3 GeV !? f/f 5 - this implies RTA and not CE it violates causality, I0 Navier-Stokes, but it violates causality, II 0 order needed -> Israel-Stewart Problems Problems: dissipative correction to f -> f eq + f neq just an ansatz f neq /f at p T > 1.5 GeV is large f neq /s implies a RTA approx. (solvable) (t 0 ) =0 -> discard initial non-eq (ex. minijets) p T -> 0 no problem except if /s is large K. Dusling et al., PRC81 (2010) Transport at fixed /s vs Viscous Hydro a test in 3+1D Changing M of partons one gets different EoS c s (T) v 2 / x (0) decrease with c s Time scales, trends and value quite similar to hydro evolution An exact comparison under the same conditions has not been done tot =15 mb r-space: standard Glauber model p-space: Boltzmann-Juttner T max = T c [ p T 2-3GeV ] T max0 = 340 MeV T =1 -> =0.6 fm/c We fix maximum initial T at RHIC 200 AGeV Then we scale it according to initial 62 GeV200 GeV2.76 TeV T0T0 290 MeV340 MeV580 MeV fm/c0.6 fm/c0.3 fm/c Typical hydro condition Discarded in viscous hydro r-space: standard Glauber condition p-space: Boltzmann-Juttner T max =2(3) T c [ p T 2-3GeV ] Risultati di Heinz da hadron production Larger x - > higher /s to get the same v 2 (p T ) Uncertainty on initial conditions implies uncertainty of a factor 2 on /s V 2 from KLN in Hydro What does it KLN in hydro? 1) r-space from KLN (larger ex) 2) p-space thermal at t 0 0.8 fm/c - No Q s scale, Well call it fKLN-Th Heinz et al., PRC 83, (2011)