Transport Model Description of Flow

Transcription

1 Transport Model Description of Flow Che-Ming Ko Texas A&M University Transport model (AMPT) Parton coalescence Elliptic flow Collaborators: Z.W. Lin, S. Pal, B. Zhang, B.A. Li: PRC 61, (00); 64, (01); NPA 698, 375c (0) V. Greco, P. Levai: PRL 90, 010 (003); PRC 68, (003) L.W. Chen 1

2 A multiphase transport model Initial conditions: HIJING Hard minjet partons and soft strings Parton evolution: ZPC Default: Minijet partons String melting: Minijet partons and soft partons Hadronization: Default: Lund string model String melting: quark coalescence or recombination Hadronic transport: ART PRC 61, (00); 64, (01); NPA 698, 375c (0)

3 Parton collision rate Default: 800 collisions for 1600 partons, i.e., about one collision per parton String melting: both parton and collision numbers increase by ten, i.e., about ten collisions per parton 3

4 Softening of equation of state 4

5 Rapidity distributions 130 AGeV Data from BRAHMS Solid lines: default HIJING Dashed lines: AMPT prediction 5

6 Transverse mass distributions 6

7 Two-Pion Correlation Function Lin, Ko & Pal, PRL 89, (00) 130 AGeV Need string melting and large parton scattering cross section 7

8 Emission Function Shift in out direction Strong correlation between out position and emission time Large halo due to resonance ( ) decay ω and explosion non-gaussian source 8

9 Elliptic flow in 00 AGeV Lin & Ko, PRC 65, (00) 9

10 130 AGeV 10

11 Jet quenching in quark-gluon plasma r E 0 E = C dτ ρ( τ, x( τ))( τ - τ0)ln( ) 0 τ µ L Gyulassy, Levai, Vitev, PRL, 85, 5535 (000) Screening mass µ ~ 0.5GeV Path length L ~ 4 fm C ~

12 Transverse positions of minijet partons at freezeout n parton ( τ f ) =1fm -3 1

13 Parton azimuthal distribution 13

14 Parton elliptic flow 14

15 The coalescence model Dover et al., PRC 44, 1636 (1991) N = g M f q (x p 1, p dσ 1 )f q p (x dσ M 1 1, p )f 3 d p E M 1 1 (x 1 3 d p E, x ; p 1, p ) Quark distribution function Spin-color statistical factor Coalescence probability function g f q M (x, p) e.g. 3 d p p dσ f 3 q (x, p) = (π) E g = gk = 1/36 π N g = g * ρ q K = 1 /1 fm(x1, x;p1,p) f(x1 x;p1 p) 15

16 Coalescence probability function f (x 1 x ; p 1 exp{[( p 1 p ) = p ) exp[( x (m 1 1 x m ) ) / ] / x p ] } Coalescence radii x p h Quark mass (x (p r r 1 x ) = τ [1 cosh( η 1 η )] (r1 r ) 1 p) = m1t + mt m1t mt cosh(y 1 y) (p1t pt) r r 16

17 Monte-Carlo method Introduce quark probabilities P q (i) according to their transverse momentum and spatial distributions dn r d p M T = g M f M i, j (x i P q, x j (i)p ; p i q, p ( j) j ) δ ( ) r (p T r p it r p jt ) dn r d p B T = g B f B i j k (x i P q, x j (i)p, x k q ( j)p ; p i q, p j (k) δ, p k ) () r (p T r p it r p jt r p kt ) 17

18 Minijet partons Gyulassy, Levai, Vitev, PRL, 85, 5535 (000) dn r d p dn r dp jet T jet T 1 r r r r r r r = d bd rt Au(r)t Au(b r) dxadx bd k atd k σtot a,b r r g(k at)g(k bt )fa / Au(xa,Q )fb / Au(x b,q ) ab ŝ dσ δ(ŝ + tˆ + û) π dtˆ L / λ= 3.5 After jet quenching using opacity parameter = A B B + p T n A(10 4 / GeV ) g u,d u, d s, s B(GeV) n bt 18

19 Quark-gluon plasma dn q r dyd p T = g q τπr (π) 3 m T m T µ exp T q Light quarks g 6, m 300 MeV, u,d = u,d = µ u, d = 10 MeV Strange quarks g s = 6, m s = 475 MeV, µ s = 10 MeV Gluons g = 16, mg = 300 MeV, g g µ = 0 Take T=170 MeV u / u = d / d = 0.89, s / s = 1 s / u = 0.7 p / p = 0.7, K / K + = 89, K / π = 0.4 as in experimental data 19

20 Parton transverse momentum distributions Thermal QGP p T GeV Power-law minijets p T GeV Choose R = 8.3 fm τ = 4 fm, y 0.5 de dy V = 900 fm T = y GeV Consistent with data (PHENIX) 0

21 Other inputs or assumptions Minijet fragmentation via KKP fragmentation functions dn r d p had jet dn dz d p = r jet D had / jet z (z, Q ), z = p p had jet Gluons are converted to quarks and antiquarks with flavor probabilities similar to quarks in QGP Quark-gluon plasma is given a transverse collective flow β = 0.5c velocity of, so partons have an additional velocity v(r) = β(r / R) Minijet partons have current quark masses m u,d = 10 MeV, m s = 175 MeV -1 p = x = 0.4 GeV Use coalescence radii for mesons -1 p = x = 0.45 GeV for baryons 1

22 Pion spectrum including rho decays 00 AGeV Dash-dotted: minijets Dashed: QGP+minijets Solid: QGP+minjets+soft-hard coalescence Filled circles: data Inset: ratio of with and without soft-hard coalescence Reproduce data at all momenta Hard+hard coalescence negligible

23 Antiproton spectrum including antidelta decays 00 AGeV Dash-dotted: minijets Dashed: QGP+minijets Solid: QGP+minijets+soft-hard coalescence Filled squares: data (PHENIX) Inset: ratio of with and without soft-hard coalescence Reproduce data at low momenta Soft+hard coalescence more important than in pions Soft +hard and 3hard coalescence negligible 3

24 Antiproton to pion ratio Dashed: without soft-hard coalescence Solid: with soft-hard coalescence Filled squares: data (PHENIX) Reproduce data at low and intermediate momenta Small ratio at high momenta due to minjets 4

25 Kaon spectrum including K* decays 00 AGeV Dash-dotted: minijets Dashed: QGP+minijets Solid: QGP+minijets+sof-hard coalescence Filled diamonds: data (PHENX) Inset: ratio of with and without soft-hard coalescence Reproduce data at low momenta 5

26 Elliptic flows of pions and protons 00 AGeV Elliptic flow of light quarks is extracted from fitting measured pion elliptic flow Proton elliptic flow is then predicted and agrees with data (STAR) 6

27 Elliptic flows of kaons, lambdas and omegas 00 AGeV Elliptic flow of strange quarks is extracted from fitting measured kaon elliptic flow. Predicted lambda elliptic flow agrees with data (STAR) Omega elliptic flow is predicted to be smaller than that of lambda 7

28 Charm production 00 AGeV e - charm quark D meson charmonium 8

29 Charm flow 9

30 Pentaquark Theta+ flow ( uudd s ) quark 30

31 Summary Transport model can describe rapidity and transverse momentum distributions as well as two-particle correlations. Large elliptic flow is obtained in transport model that includes scattering of soft partons from melted strings. Radiative energy loss of minijet partons in QGP leads to appreciable elliptic flow at high momenta. Quark coalescence can explain elliptic flow of identified hadrons and large baryon/pion ratio at intermediate transverse momenta. Elliptic flow of D meson and J/psi based on quark coalescence are sensitive to charm quark collective dynamics. 31