Color-neutral bound states above the QCD transition from
equilibrium and non-equilibrium processes Rene Bellwied (University
of Houston) Rene Bellwied (University of Houston) in collaboration
with Equilibrium: M. Cristoforetti (Trento), C. Ratti (U Torino)
Non-equilibrium: C. Markert (UT Austin), I. Vitev (LANL)
Slide 2
Are there bound states above T c ? Survival or formation a
question of perspective The deconfinement order parameter in lQCD:
Polyakov loop 2/28 Bazavov et al., arXiv:1105.1131 Low energy
collisions (AGS, SPS, RHIC scan, FAIR): survival of resonant states
High energy collisions (RHIC, LHC): formation of pre-hadronic
states survival formation
Slide 3
Are there bound states above T c ? A long standing question in
the literature Survival: Rapp et al. (arXiv:0901.3289) chiral
symmetry restoration signatures in the transition region (mass
shifts, width broadening, Brown-Rho scaling, etc. of surviving
resonant states in particular of heavy quarks) 3/28 Formation:
Shuryak (PRD 70 (2004)054507) colored bound states. Leads to phase
diagram with differing quark condensates
Slide 4
The fundamental questions How do hadrons form ? Parton
fragmentation or string fragmentation or recombination An early
color neutral object (pre-hadron) or a long-lived colored object
(quasi-particle or constituent quark) When do hadrons form ? Inside
the deconfined medium or in the vacuum ? Why investigate it now ?
1.) more precise lattice QCD calculations for the case of formation
out of equilibrium 2.) a better understanding of fragmentation
(non-equilibrium formation) 3.) better data from RHIC and LHC to
follow formation as a function of time, temperature and particle
momentum 4/28
Slide 5
Why distinguish between equilibrium and non-equilibrium ? There
is plenty of evidence for two components in the particle spectra at
RHIC and LHC. Breakdown of hydrodynamics at high pT, power law at
high pT Two component model: soft (bulk, equil.) / hard
(fragmentation, non-equil,) Kharzeev / Nardi scaling for yield:
Levi-Tsallis fit for spectra (exponential + power-law): 5/28
Slide 6
Is equilibrium and non-equilibrium production equally relevant
? Fragmentation will populate full spectrum Thus non-equilibrium
production surprisingly sizeable: 30% at RHIC, based on untriggered
correlation measurements (e.g. T.A. Trainor (
Phys.Rev.C80:044901,2009) Up to 50% at the LHC e.g. Eskola et al.
(hep-ph/0510019) 6/28
Slide 7
How to approach the problem ? Equilibrium Statistical
Hadronization Model (SHM) Hadronic resonance gas (HRG) Lattice QCD
(lQCD) 7/28 Recombination PNJL model Non - Equilibrium
Fragmentation Formation time Recent Work: Equilibrium: RB, M.
Cristoforetti, C. Ratti in preparation Non-equilibrium: RB, C.
Markert, Phys. Lett. B691, 208 (2010) C. Markert, RB, I. Vitev,
Phys. Lett. B669, 92 (2008)
Slide 8
The non-equilibrium case a short re-cap of my talk from the
Hadronization Workshop in Sardinia (2010) 8/28
Slide 9
The formation time of hadrons (for parton fragmentation in
medium) Can a hadron form inside the deconfined medium above T c ?
Three Scenarios: Is the energy loss in medium affected by the
formation of the hadronic state ? Are the properties of the
hadronic state affected by the formation in medium ? Signatures:
any early probe which is sensitive to the medium (e.g. energy loss
or v2) 9/28 A parton traverses the medium and fragments outside A
parton converts into a pre-hadronic state or a quasi-particle which
traverses the medium and fragments outside A parton fragments
inside the medium
Slide 10
The treatment of formation time There is per-se no reason to
believe that, in heavy ion collisions, a process such as
fragmentation, which does not thermalize with the surrounding
medium, would take more or less time than in vacuum. One could use
in-vacuum formation time. BUT there are two aspects to consider
in-medium: Lorentz boost : the higher the energy the longer the
formation time (based on Heisenbergs uncertainty principle, true
for string fragmentation) Energy conservation : the higher the
fractional momentum the shorter the formation time, since partons
lose energy through bremsstrahlung in medium (true for parton
fragmentation in medium). 10/28
Slide 11
Schematic Modeling of Hadronzation Inside-out cascade (boost) o
~ 1 fm/c : proper formation time in hadron rest frame E : energy of
hadron m: mass of hadron E/m = high energy particles are produced
later heavy mass particles are produced earlier Outside-in Cascade
(pre-hadron formation) large z (=ph / pq) = leading particle
shortens formation time C. Markert, RB, I. Vitev (PLB 669, 92
(2008)) 11/28 Bjorken (1976): The higher the energy and the lighter
the final state, the later the hadron will form (inside-outside
cascade) Kopeliovich (1979): A high z particle has to form early
otherwise the initial parton loses too much energy (outside-inside
cascade).
Slide 12
Formation Time of Hadrons in RHIC / LHC QGP (C. Mar kert, RB,
I. Vitev, PLB 669, 92 (2008)) RHIC LHC 12/28
Slide 13
A quasi-particle is a colored object, i.e. a dressed up quark
which has attained a thermal mass that can potentially exceed the
final state hadron mass and then decay into the hadronic state.
(e.g. Cassing et al. (DQPM model) or Ratti et al. (lattice QCD)) A
pre-hadron is a color neutral object that approaches the final
hadronic wave function during its evolution, i.e. quark content
fixed but not all hadron properties fixed (e.g. Kopeliovich or
Accardi or RB/CM) A colored object will continue to interact and
not develop a hadronic wave function early on (constituent quark or
quasi-particle) A color-neutral object will have a reduced size and
interaction cross section (color transparency) and develop wave
function properties early Only a color neutral state can exhibit
hadronic features (e.g. can pre- resonance decay prior to pion
hadronization ?) Quasi-particle or pre-hadron ? Is their a
difference ? 13/28
Slide 14
The equilibrium case Recent work with M. Cristoforetti (Trento)
& C. Ratti (Torino) 14/28
Slide 15
Evolution of the phase transition as a function of finer
lattice spacing smaller quark masses (the cross-over becomes
smoother = a longer mixed phase ?) 15/28 new old
Slide 16
Lattice QCD inspired quasi-particle mass calculations (Evidence
for massive states above T c ) Levai & Heinz, PRC 57, 1879
(1998) Ratti, Greco et al., arXiv:1103.5611 Slight difference in
temperature dependence of the quasi-particle masses for two lattice
QCD actions Important is the general trend just above T c.
Quasi-particle masses increase and exceed the constituent quark
masses. 16/28
Slide 17
But could there be color-neutral bound states ? A
re-interpretation of the Polyakov Loop in lattice QCD (measure of
deconfinement) 17/28
Slide 18
An interpretation pushed early on in a slightly different
variation (Shuryak & Zahed, hep-ph/0403127) 18/28 Bound states
above T c Due to exclusion of color-neutral states above T c by
early lattice calculations, the authors focused on colored, mostly
gluonic, bound states
Slide 19
New lattice results: diagonal and non-diagonal correlators in
limited T-range above T c (Ratti et al., QM 2011) 19/28 diagonal
correlators non-diagonal correlators
Slide 20
Recent work: how much of this is due to fluctuations in the
deconfined medium rather than bound states Comparison of lattice to
PNJL (RB, M.Cristoforetti, C.Ratti) 20/28 PNJL variations PNJL-MF:
pure mean field calculation PNJL-PL: mean field plus Polyakov loop
fluctuations PNJL-MC: mean field plus all fluctuations (incl.
chiral and Kaon condensate fluctuations) Conclusion: even the
inclusion of all possible flucutations is not sufficient to
describe lattice data above Tc. There has to be a contribution from
bound states
Slide 21
Can we estimate the contribution of bound states above the
critical temperature ? 21/28 The ratio between PNJL and lattice
results tells us the percentage of bound state in the QGP mixed
phase It agrees with the lattice continuum estimate for the
Polyakov loop. ~50% bound states at 1.5 Tc ! L ren
Slide 22
Properties of bound states above T c : Flavor dependence even
in the light sector 22/28 The heavier the quark the longer the
mixed phase More strange bound states than light bound states above
T c ?
Slide 23
Properties of bound states above T c : Baryon-meson dependence
in correlator 23/28 Upswing in lattice correlator shows that baryon
contribution rises with T, but the correlator never turns positive
-> the contribution of bound states above T c must be
predominantly of mesonic nature until final deconfinement C. Ratti,
Hadronic resonance gas (HRG) calculation: Baryonic bound states
dominate at T>190 MeV.
Slide 24
Experimental Signatures Reduction in p T broadening of final
state due to color transparency in medium (verified in HERMES
results) Medium modification of early produced resonances due to
chiral restoration in medium (project at LHC) Reduction of v2 at
high p T due to early formation and color transparency (masked by
loss of collectivity at high p T ) Reduction in energy loss due to
color transparency of color-neutral pre- hadrons in medium
(evidence at RHIC and LHC) 24/28
Slide 25
Predictions for energy loss RB & C. Markert (PLB 691, 208,
2010)) 25/28
Slide 26
Flavor dependence at the LHC 26/28 QM 2011: Simone Schuchmann,
Harry Appelshaeuser (ALICE) Data can be described with differing
formation time for baryons and mesons, if one assumes rather short
existence of pre-hadron in mixed phase (late formation). (CM &
RB, 2011) Alternative: recombination
Slide 27
The latest evidence: R AA at the LHC 27/28 Data: ALICE, PLB
696, 30 (2011) An explanation based on color-neutral states and
color transpareny The color-neutral state (in this case labeled
color dipole) will form the earlier the higher the fractional
momentum. No distinction between pre-hadrons of different flavor.
All charged hadrons are based on the same color dipoles which
traverse the medium and exhibit color transparency. Alternative:
strong shadowing Theory: Kopeliovich et al., PRC83, 021901
(2011)
Slide 28
Summary 28/28 There is evidence for flavor and mass dependent
color-neutral bound state formation in the medium above the QCD
phase transition based on lattice QCD and fragmentation studies. A
comparison of lattice QCD to HRG and PNJL calculations allows us to
quantify the relative abundance of the confined and deconfined
states in the equilibrated mixed phase around the critical
temperature as a function of T. Experimental studies of p T, width,
mass broadening, nuclear suppression, yields and ratios of
identified particles and resonances give us a unique tool to answer
fundamental questions of hadron formation.
