J/Ψ-suppression in the hadron resonance gas

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1 J/Ψ-suppression in the hadron resonance gas Dariusz Prorok Institute of Theoretical Physics University of Wroc law Wroc law, 17 February 2014 HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 1/31

2 All began in the early HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 2/31

3 Why J/Ψ? J/Ψ suppression as a signal for the QGP appearance in a heavy-ion collision. T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986) V (r) = σ r α r, T = 0 In the QGP (T T c ): V (r) = σ r D [1 exp r D = r D (T ) - screening radius { r }] αr { r exp r } D r D HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 3/31

4 Basic ingredients of our model Hadron resonance gas exists from the beginning (i.e. from t 0 ), the gas consists of all particles from PDG up to 2 GeV. The gas expands longitudinally and transversally. J/Ψ disintegration is due to inelastic scattering with constituents of the gas. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 4/31

5 Sketch of a central collision HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 5/31

6 Solution of hydro equations for n 0 B = 0 G. Baym, B. L. Friman, J. P. Blaizot, M. Soyeur and W. Czyż, Nucl. Phys. A407, 541 (1983) In the z = 0 plane the transverse expansion proceeds in the form of the rarefaction wave which moves inward with the sound velocity c s. Inside the temperature/density is constant (radial velocity v r = 0), in the narrow stripe of the rarefaction wave it decreases rapidly (radial velocity increases). In the z 0 plane and the moment t the transverse expansion looks the same as in z = 0 but at the moment τ = t 2 z 2. Longitudinal velocity v z = z/t. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 6/31

7 z = 0 plane Figure: View of an AA collision at impact parameter b. The region where the nuclei overlap has been hatched and its area equals S eff. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 7/31

8 J/Ψ inelastic scattering in a hadron gas Inspired by J. P. Blaizot and J. Y. Ollitrault, PRD39, 232 (1989), generalized in: DP and L. Turko, PRC 64, (2001) J/Ψ + h i D + D + X f t + v f = f l i=1 d 3 q (2π) 3 f i( r, q, t)σ i vrel i p ν q ν EE E = M 2 + p 2, E = m 2 i + q 2 HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 8/31

9 Formal solution of the kinetic equation f( r, p, t) = f 0 ( r v(t t 0 ), p) { exp t t 0 dt l i=1 } d 3 q (2π) 3 f i( r v(t t ), q, t )σ i vrel i p ν q ν EE p - momentum of J/Ψ v = p E - velocity of J/Ψ f 0 ( r, p) - initial distribution of J/Ψ at t 0 = 1 fm HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 9/31

10 Hadron distributions in the presence of a flow { qνu ν ( r,t) µ i ( r,t) T ( r,t) f i ( r, q, t) = (2s i + 1) 1 (2π c) 3 exp } ± 1 µ i ( r, t) = B i µ B ( r, t) + S i µ S ( r, t) u ν ( r, t) = 1 (t, 0, 0, z), T ( r, t) = T (z, t) = T (0, τ), τ µ B(S) ( r, t) = µ B(S) (z, t) = µ B(S) (0, τ) HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 10/31

11 J/Ψ survival factor in the hadron gas N HRG (y, b) = d 2 p T d 3 r F( r, y, p T, t) t= d 2 p T d 3 r F( r, y, p T, t) t=t0 F( r, y, p T, t) = M T cosh(y) f( r, p T, p L = M T sinh(y), t) f 0 ( r, p) = f 0 ( s) g 0 (p T ) h 0 (y), s S eff f 0 ( s) = T A( s)t B ( s b) T AB (b) HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 11/31

12 J/Ψ survival factor in the hadron gas, cont. N HRG (y, b) = 1 dpt M T g 0 (p T ) dp T M T g 0 (p T ) { tfinal exp dt t 0 l i=1 d 3 q (2π) 3 f p ν q ν } i i( q, t)σ i v rel,i EE i t final - average time of leaving the hadron medium by J/Ψ with the velocity v and produced in a collision at impact parameter b σ i = σ b for i = baryon, σ i = 2 3 σ b for i = meson HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 12/31

13 Full survival factor of J/Ψ Possible J/Ψ disintegration in the nuclear matter (pa data): N NA = exp { σb ρ 0 L } N th J/Ψ = N NA N HRG Only 60% of J/Ψ measured are directly produced during collision, so the realistic J/Ψ survival factor should read N = 0.6 N J/ψ N χ N ψ. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 13/31

14 J/Ψ suppression at SPS J/Ψ experimental survival factor only for midrapidity, y 0 N exp J/Ψ = ( Bµµσ J/ψ AB σ AB DY ( Bµµσ pp J/ψ σ pp DY ) ) Theoretical predictions: DP and L. Turko, PRC 64, (2001). HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 14/31

15 J/Ψ suppression for 17.2 GeV Figure: J/Ψ survival factor times B µµ σ pp J/ψ /σpp DY for n0 B = 0.25 fm 3 and T f.o. = 140 MeV: σ b = 4 mb (solid) and σ b = 5 mb (dashed). HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 15/31

16 J/Ψ suppression at RHIC J/Ψ experimental survival factor = J/Ψ nuclear modification factor N exp J/Ψ R AA = N coll dnj/ψ AA dy pp dnj/ψ dy Theoretical predictions: DP, L. Turko and D. Blaschke, Phys.Lett. B690, 352 (2010). HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 16/31

17 J/Ψ suppression for 200 GeV Figure: J/Ψ survival factor as a function of rapidity for a given centrality. Curves correspond to n 0 B = 0, σ b = 4 mb and T f.o. = 150 MeV, circles are the PHENIX data. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 17/31

18 J/Ψ suppression for 200 GeV Figure: J/Ψ survival factor as a function of rapidity for a given centrality. Curves correspond to n 0 B = 0, σ b = 4 mb and T f.o. = 150 MeV, circles are the PHENIX data. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 18/31

19 J/Ψ suppression for 200 GeV Figure: J/Ψ survival factor as a function of rapidity for a given centrality. Curves correspond to n 0 B = 0, σ b = 4 mb and T f.o. = 150 MeV, circles are the PHENIX data. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 19/31

20 J/Ψ suppression for 200 GeV Figure: J/Ψ survival factor as a function of rapidity for a given centrality. Curves correspond to n 0 B = 0, σ b = 4 mb and T f.o. = 150 MeV, circles are the PHENIX data. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 20/31

21 J/Ψ suppression at 200 GeV Figure: J/Ψ survival factor as a function of centrality for mid (solid) and forward (dashed) rapidity. Curves correspond to n 0 B = 0, σ b = 4 mb and T f.o. = 150 MeV, symbols are the PHENIX data. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 21/31

22 Conclusions 1. Up to RHIC energies the observed J/Ψ suppression might be explained without QGP. 2. In this model suppression at y 0 is stronger than for y = 0, as it is observed at RHIC. 3. It seems that geometry of the collision is responsible in great part for the pattern of J/Ψ suppression observed at SPS and RHIC. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 22/31

23 Sto Lat Ludwik! HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 23/31

24 How to obtain T (t), µ B (t) and µ S (t)? Inside the rarefaction wave only the Bjorken longitudinal expansion: s(t) = s 0t 0 t, n B (t) = n0 B t 0 t, n S = 0. Expressing left sides as corresponding densities in the Grand Canonical Ensemble: s = s(t, µ B, µ S ), n B = n B (T, µ B, µ S ), n S = n S (T, µ B, µ S ) and solving at each moment t the above equations, one obtains T (t), µ B (t) and µ S (t). HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 24/31

25 Sound velocity in the hadron gas T (t) = T 0 ( ) c 2 t0 s (T 0 ) t = putting T f.o. one obtains t f.o. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 25/31

26 Initial state scattering of gluons J. Hufner, Y. Kurihara and H. J. Pirner, PL B215, 218 (1988) S. Gavin and M. Gyulassy, PL B214, 241 (1988) J. P. Blaizot and J. Y. Ollitrault, PL B217, 392 (1989) The form proposed by S. Gupta and H. Satz, PL B283, 439 (1992): { } g(p T ) = 2p T exp p2 T p 2 T AB J/Ψ p 2 T AB J/Ψ p 2 T AB J/Ψ - the mean squared transverse momentum of J/Ψ gained in an A-B collision HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 26/31

27 Taking into account the shadowing E. G. Ferreiro et al., arxiv: with Fits to PHENIX d-au data chose the extrinsic scheme with the EPS08 model and σ abs = 3.6 mb. NNS AuAu (y) RdAu F erreiro ( y, σ abs = 0) NJ/Ψ AuAu th = N NA NNS AuAu N HRG HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 27/31

28 J/Ψ suppression with shadowing included Figure: J/Ψ survival factor as a function of rapidity. Curves correspond to n 0 B = 0, σ b = 3.6 mb and T f.o. = 150 MeV, circles are the PHENIX data for 200 GeV. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 28/31

29 J/Ψ suppression with shadowing included Figure: J/Ψ survival factor as a function of rapidity. Curves correspond to n 0 B = 0, σ b = 3.6 mb and T f.o. = 150 MeV, circles are the PHENIX data for 200 GeV. HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 29/31

30 Phys. Lett. 477, 28 (2000) NA50 announcement Bσ(J/ψ) / σ(dy) Pb - Pb 1996 Pb - Pb 1996 with Minimum Bias Pb - Pb 1998 with Minimum Bias E T (GeV) Figure 6: Comparison between our data and several conventional calculations of J/ψ suppression. Figure: Evidence for deconfinement of quarks and gluons from the J/Ψ suppression pattern measured in Pb-Pb collisions at the CERN-SPS HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 30/31

31 Definitions Rapidity Pseudorapidity y = 1 2 ln E + p L = 1 E p L 2 ln 1 + v L 1 v L ) η = ln ( tan θ 2 = 1 2 ln p + p L p p L N = d 3 p f( p) = dy d 2 p T Ef = dy d 2 p T d 2 N 2πp T dp T dy d 2 { N 2πp T dp T dy = E f = A m T cosh(y) exp m } T cosh(y) µ T m T = m 2 + p 2 T, E = m T cosh(y), p L = m T sinh(y) HECOLS workshop and XXXII Max-Born Symposium Dariusz Prorok 31/31