KINETIC MODEL RESULTS FOR HEAVY-QUARK COALESCENCE

R. L. THEWSUNIVERSITY OF ARIZONA

Characterization of the Quark Gluon Plasma with Heavy Quarks

25-28 JUNE 2008Physikzentrum Bad Honnef

IN-MEDIUM FORMATION(REGENERATION)

HIGH ENERGY EVOLUTION OF MATSUI-SATZ:

Rplasma screening < Rquarkonium SUPPRESSION in a static medium, or

KHARZEEV-SATZ: Ionization with deconfined gluons

Charm pair diffuse away, will not recombine during deconfinement phase or at hadronization

NEW SCENARIO AT COLLIDER ENERGIES

Multiple ccbar pairs in high energy AA Collisions

10-15 from extrapolation of low energy 20 from PHENIX electrons 40 from STAR electrons and K

( 0) 30 ( ) ppcc ccN b mb

CENTRAL VALUES AT RHIC:

AND AT LHC: 100-200??

PROBE REGION OF COLOR DECONFINEMENT WITH

MULTIPLE PAIRS OF HEAVY QUARKS

Two Distinct Physical Scenarios:

(1) Form Quarkonium in the Medium, where it competes with Suppression, and/or

(2) Form Quarkonium during the Hadronization Transition

QUARKONIUM FORMATION MODELS IN REGION OF COLOR DECONFINEMENT

STATISTICAL HADRONIZATION: P. Braun-Munzinger, J. Stachel, Phys. Lett B490 (2000) 196 [nucl-th/0007059].

KINETIC IN-MEDIUM FORMATION:

R. L. Thews, M. Schroedter, J. Rafelski, Phys. Rev. C63 (2001) 054905 [hep-ph/0007323].

COLOR DECONFINEMENT ALLOWS THE INCOHERENT RECOMBINATION OF ALL PAIRS OF HEAVY QUARKS

,

2

Probability for charm quark to combine with anticharm:

/ /

Since << 1, sum for each c:

/

Average over fluctuations:

/ ( 1) /

Centrality dependence in

c u d cc ch

quarkonium cc ch

cc cc ch

N N N N

N N N

J N N N

13

p

1

1

terms of participants N :

Parameterize ,

/ / ( )

ch p

cc p p

N N

J N binary aN bN

D

k

k

32

3 6

2 12

20

1 2

03 2

05

/ /( / )

( / )

MANY THEORETICAL INPUT PARAMETERS

dN

dv N v N

J

F c c D g J

/

/

Gold-plated signature for Regeneration

SEARCH FOR J/PSI with xF > 1

OFF-DIAGONAL PAIRS POPULATE X_F > 1.0

FORMED J/PSI ALSO POPULATES X_F > 1.0

THE P_T DISTRIBUTION IS PEAKED NEAR ZERO

BUT THEY ONLY APPEAR NEAR THE RAPIDITY BOUNDARY

R. L. Thews and M. L. Mangano Phys. Rev. C73, 014904 (2006) [nucl-th/0505055]

1. Generate sample of ccbar pairs from NLO pQCD (smear LO qt)

2. Supplement with kt to simulate initial state and confinement effects

3. Integrate formation rate using these events to define particle distributions (no cquark-medium interaction)

4. Repeat with cquark thermal+flow distribution (maximal cquark-medium interaction)

CAN Y AND PT SPECTRA ALONE PROVIDE SIGNATURES OF IN-

MEDIUM FORMATION?

/ /3 3

1 1/ /

( )

( )

cc ccN NJ i j J

reli jJ J

d N d p p p Xd tv

d p V t d p

•All combinations of c and cbar contribute

•Total has expected (Nccbar)2 / V behavior

•Prefactor is integrated flux per ccbar pair

•Do the J/Psi spectra retain a memory of the underlying charm quark spectra?

No REGENERATION FOR ppJ/Psi, DIAGONAL PAIRS ALONE SHOULD FIT SPECTRA

EXTRACT ALLOWED <kT

2> = .75 GeV2

DIAGONAL PAIRS – NO EXTRA PARAMETERS

Use dAu broadening to determine nuclear kt2 2 1.3 0.3 GeVt AAk (Minimum Bias)

Central rapidity data exhibits anti-broadening!

S. Gavin and M. Gyulassy, Phys. Lett. B214 (1988)

2 2 2{ 2}T AB T pp A Bp p n n Nuclear broadening from Initial state parton scattering, extract 0.56 +/- 0.08 GeV2 for Au-Au at RHIC, compare with 0.12 +/- .02 GeV2 at fixed-target energy. Note: and n are correlated within given nuclear geometry.

Proceed with analysis for muon data only:

Collision numbers nbar correlated with centrality

Initial lambda estimate disfavors Direct Production

Revised lambda value allows 100% Direct Production

Regeneration is almost independent of centrality and lambda , and magnitude consistent with initial PHENIX data.

Comparison with Thermal + Transverse Flow c-Quark Distributions

(Blast Wave)

max max

0 120

sinh( ) cosh( )[ [ ]

R T T T T

TT

r rp y m ydN R Rm r dr I K

dp T T

K.A.Bugaev, M. Gazdzicki, M.I.Gorenstein, Phys.Lett.B544,127(2002)

S.Batsouli, S.Kelly, M.Gyulassy, J.L.Nagle, Phys.Lett.B557,26 (2003)

Determine fraction of regeneration using y=0 data

Consider combination of Direct and Regeneration (pQCD) with weights (1- and match data at y = 0

Predict pT Spectra which are in agreement with Data

Comparison with coalescence model: V Greco, C. M. Ko, R. Rapp, Phys. Lett. B595:202 (2004)

WHERE IS FORMATION FROM THERMAL CHARM?

In-Medium Formation (AKA regeneration, coalescence, recombination) as a mechanism for J/ production in central Au-Au at RHIC must reflect the underlying charm quark distributions.

We find that normalized pT and y spectra alone can provide signatures of in-medium formation,

independent of the absolute magnitude of recombination processes. We show that variation of <pT

2> with centrality provides characteristic signals.

Baseline tests using pp and pA collisions provides a connection with initial pQCD charm quark

distributions.

SUMMARY

Centrality dependence and shapes of spectra

are consistent with a 10 – 20% fraction produced in-medium from recombination of pQCD charm quarks.

PHENIX measurements of y spectra in AA collisions now exhibit some narrowing as predicted

for in-medium formation.

pT spectra do not indicate an obvious contribution from recombination of thermalized charm

Robust predictions require complete set of constraints from pp and pA.