Collective and non-flow correlations in event-by-event hydrodynamics Institute of Nuclear Physics Kraków WPCF 22-2.9.22
3 -D viscous hydrodynamics T T h /- v 3 [%] 25 2 5 5 2 5 5 2 5 5 ideal, e-b-e η/s=.8, e-b-e η/s=.6, e-b-e.5.5 2 2.5 3 p T [GeV] -5% central -2% central 3-4% central first 3D visc. : B.Schenke et al. c s 2.3.2. lqcd Wuppertal-Budapest dn/dη PS ] -2 dy) [GeV dp dn/(2 π p 6 5 4 3 2 Au-Au 2GeV 8 PHOBOS c=-6%,...,45-55% BRAHMS c=-5% 7-6 -4-2 2 4 6 3 - -3-5 η PS Au-Au 2GeV PHENIX data π -5% visc. hydro ideal fluid 2 4 6 8 T [MeV] lqcd Hadron Gas -7 ideal fluid visc. hydro 4-5% -9.5.5 2 2.5 3 p [GeV] T η/s =.8(.6)
Τ fmc high multiplicity p-pb event 5 4 3 2 4 2 2 4 y fm Event-by-event hydrodynamics Glauber initial conditions Au-Au 2GeV Cu-Au 2GeV p-pb 4.4TeV d-pb 3.3TeV
p-pb, d-pb @ LHC dn 8 dη PS 2 6 4 2 ALICE Pb-Pb 2.76TeV 7-8% 6-7% d-pb 3.TeV p-pb 4.4TeV d-pb 6.22TeV CMS 7TeV p-pb 8.8TeV 2 3 4 5 6 7 8 9 TeV s NN large multiplicity - large fireball - collective expansion?
Fireball in p-pb ) part P(N.6 p-pb Glauber Monte-Carlo.4.2..8.6.4.2 8 N Part (32-49%) N Part (4-32%) 7 8 N Part (-4%) 5 5 2 25 3 N part ε.8.6.4.2 p-pb Glauber Monte-Carlo ε 2 ε 3 5 5 2 25 3 35 N part
v 2.2..8.6.4.2 p-pb 4.4TeV 8 N part N part 7 8 N part v 3.2..8.6.4.2 p-pb 4.4TeV 8 N part N part 7 8 N part.5.5 2 2.5 p [GeV].5.5 2 2.5 p [GeV] elliptic flow in p-pb triangular flow
d-pb v 2.25.2.5 d-pb 3.TeV dn 4 dη PS 2 8 6 4 2 d-pb 3.TeV large elliptic flow 27 6 N part N part N part 26 5 p-pb 8 N part -4-2 2 4 η PS y fm 3 2 2..5 27 N part 6 N part 26 5 N part.5.5 2 2.5 p [GeV] 3 32 2 3 x fm
v 2.2..8.6.4.2 ALICE Pb-Pb hydro p-pb hydro d-pb 2 4 6 8 2 4 dn/dη collective flow effects peripheral Pb-Pb can be observed p-pb (d-pb) is not p-p superposition only p-p as baseline PS
Au Au Au d d d Event by event Cu-Au@2 GeV 2.5 2.5.5 -.5 - -.5 F F F -F F F -5-4 -3-2 - 2 3 4 5 d-au (Bialas Czyz) fη.8.6.4.2 f Η fη f Η f Η f Η 5 2.5 2.5 5 Η dn ch dη PS 4 3 2 Cu-Au 2GeV -5% 2-3% -4-2 2 4 η PS
Directed flow Cu-Au@2GeV. (%) v -. -.2 -.3 Cu-Au 2GeV v {RP} η/s=.8 v {RP} η/s=.6-4 -2 2 4 η PS - odd and even component - even component from fireball asymmetry 6 (%) 5 Cu-Au 2GeV c=2-3% v 4 v {EP} 3 2 v {EP} η/s=.6 v {RP} (even) v {RP} (odd) -.5.5 2 p [GeV] T fluctutations increase v
Directed flow in Au-Au@2 GeV (%) v.5 STAR c=5-4% τ =.2fm/c τ u x = xp p ǫ = x(p 2 3 p ǫ η τ ) -.5 3D hydro η/s=.8 η/s=.6-4 -2 2 4 η PS τ Y = ηp τ(p ǫ) = η(p 4 3 τ(p ǫ) η τ ) pressure anisotropy
Size fluctuations p fluctuations - v 6 N w r 2 2 3.4fm p 563MeV 6 N w r 2 2 2.38fm p 622MeV y fm 3 y fm 3 3 a 3 b 6 6 6 3 3 6 6 3 3 6 x fm x fm proposed by Broniowski et al. Phys.Rev. C8 (29) 592 : two-shots calculation
> (GeV) <p T.7.68.66.64.62.6.58.56.54 N w w=.52 2 2.2 2.4 2.6 2.8 3 3.2 3.4 <r> (fm) (p i p )(p j p ) /2 p
PHENIX data vs. hydro. p Ti p Tj 2 pt 5 4 3 2 2 3 4 5 6 7 c p Ti p Tj 2 pt 3.5 3. 2.5 2..5..5..5..5 2. 2.5 3. 3.5 p max T GeV
HBT of fluctuating fireballs Τ fmc 7.5 5 2.5 single event smooth i.c. 7.5 5 2.5 2.5 5 7.5 x fm can the lumpy surface be observed?
HBT of fluctuating fireballs R out [fm] 6 4 (a) c=-5% Τ fmc 7.5 R side [fm] 6 4 Au-Au 2GeV STAR Data (b) 5 single event smooth i.c. 2.5 7.5 5 2.5 2.5 5 7.5 x fm can the lumpy surface be observed? R long [fm] R out /R side ev-by-ev average (c).5 (d).5.2.3.4.5 k T [GeV]
Charge balancing local charge conservation charge balance function _ p u _ p 2 Bass et al. (2)
Non-flow effect on v n v 2.4.2..8.6.4.2 v.22 2.2.8.6.4.2..8.6.4.2 PHENIX c=-% STAR v 2 v 2 ch. balan. hydro ch. balan. η/s=.6.2.4.6.8.2.4.6.8 2 p [GeV] T PHENIX c=3-4% STAR.2.4.6.8.2.4.6.8 2 p T a) hydro ch. bal. hydro b) hydro ch. balan. η/s=.6 [GeV] ] -3 [ v 2 n.9.8 (a) -5%.7.6.5.4.3.2. -2 -.5 - -.5.5.5 2 η (LS) 2 v 2 (CI)-v -3 7 6 STAR Data 5 4 3 2 hydro hydro ch. balan. hydro ch. balan. η/s=.6-2 3 4 5 6 7 8 dn/dη event-by-event
v - charge and momentum conservation transverse-momentum conservation lowers v 2 cos(φ φ 2 ) v 2 2..5..5 c 34 c 5 c 67x 3...2.4.6.8. P T tot GeV 3 2.5 (b) 3-4% 2.5.5 -.5 - -.5-2 -.5 - -.5.5.5 2 η comparison to the STAR data Borghini, Dinh, Ollitrault
CME signals cos(φ φ 2 ) cosαβ 3 5 4 3 2 PT not conserved STAR (-)-() Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 2 3 4 5 6 c LCC charge splitting C.I. - momentum conservation Pratt, Schlichting (2), Bzdak, Koch, Liao (2) cosαβ 3 cosαβ 3 6 5 4 3 2 PT not conserved charge indep. STAR Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 2 3 4 5 6 2.5 2..5..5. PT con served STAR c Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 2 3 4 5 6 c
CME signals cos(φ φ 2 2φ c ) cosαβ2γ 6 8 6 4 2 PT not conserved STAR Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 2 3 4 5 6 c LCC charge splitting charge indep.?? - momentum cons. for 3-part. - momentum cons. - part of the effect - flow cannot explain cos 2 (φ ) sin 2 (φ ) - η η 2 early correlations cosαβ2γ 6 cosαβ2γ 6 8 6 4 2 2 8 6 4 2 2 charge indep. PT not conserved STAR Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 2 3 4 5 6 PT c con served STAR Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 2 3 4 5 6 c
CME signals cos(2φ 2φ 2 4φ c ) 8 8 cosαβ2γ 6 6 4 2 PT not conserved STAR Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV cos2α2β4γ 6 PT not conserved 6 Η s.6, T f 5 MeV Η s.6, T f 4 MeV Η s.8, T f 5 MeV Η s.8, T f 4 MeV 4 2 2 2 3 4 5 6 2 3 4 5 6 c c negligible charge splitting for the quadrangular observable
Summary Ev-by-ev hydro for ppb, CuAu, AuAu Flow coefficients : v, v, v 2, v 3... size matters, p fluctuations from size fluctuations v2, v 3 : hydro non-flow - non-flow increases v n - η dependence directed flow - v - (odd) early expansion, sensitive to pressure asymmetry - (even) fluctuations (AuAu); asymmetryfluct. (CuAu) - strong non-flow : momentum conservation LCC small effect on HBT ashbt CME signals - local charge conservation charge splitting - momentum conservation explains partly the magnitude Collectivity (FSI) in ppb@lhc