relativistic nuclear collisions from FAIR to LHC
energies and the phase structure of QCD

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introduction and perspective
the hadron resonance gas(u,d,s) hadron production, Lattice QCD and the
QCD phase structure
quarkonia and heavy quark hadrons – window to understanddeconfinement
outlookTGSW 2017 workshop
Tsukuba, Japan
Sep. 25 - 27, 2017

phenomenology results obtained in collaboration with
Anton Andronic,
Krzysztof Redlich, and Johanna Stachel
hadron production data from the ALICE collaboration
at the CERN LHC
see, e.g., M. Floris,
Nucl.Phys. A931 (2014) 103-112
and references there

happy birthday from all of us

first PbPb collisions at LHC at √s = 5.02 A TeV
Run1: 3 data taking campaigns
pp, pPb, Pb—Pb> 135 publications
Run2 has started with 13 TeV pp
Pb—Pb runin November 2015
Now running with 13 TeV pp
Nov. 2016: pPb 5 TeV

and the funstartedparticle identification with the ALICE TPC
from 50 MeV to 50 GeV

hadron production and the QCD phase boundary
part 1: the hadron resonance gas

5duality between hadrons and quarks/gluons (I)Z: full QCD partition function
all thermodynamic quantities derive from QCD partition functions
for the pressure we get:comparison of trace anomaly from LQCD
Phys.Rev. D90 (2014) 094503
HOTQCD coll.
with hadron resonance gas prediction(solid line)
LQCD: full dynamical quarks with realisticpion massduality between hadrons and quarks/gluons (II)comparison of equation of state from
LQCD
Phys.Rev. D90 (2014) 094503
HOTQCD coll.
with hadron resonance gas predictions(colored lines)
essentially the same results also from
Wuppertal-Budapest coll.
Phys.Lett. B730 (2014) 99-104

pseudo-criticaltemperature

εcrit = (340 ± 45) MeV/fm3
εnucl = 450 MeV/fm3

duality between hadrons and quarks/gluons (III)in the dilute limit T < 165 MeV:

thermal model of particle production and QCD
partition function Z(T,V) contains sum over the full hadronic mass
spectrum and is fully calculable in QCD
for each particle i, the statistical operator is:particle densities are then calculated according to:from analysis of all available nuclear collision data we now know
the energy dependence of the parameters T, mu_b, and V over anenergy range from threshold to LHC energy and can confidently
extrapolate to even higher energies
in practice, we use the full experimental hadronic mass spectrum
from the PDG compilation (vacuum masses) to compute the'primordial yield'
comparison with measured hadron yields needs evaluation of allstrong decays

implementation

energy dependence of hadron production in central
Pb-Pb (Au-Au) collisions

total number of hadrons
produced
2.76 TeV Nhad = 25800
5.02 TeV Nhad = 32300

data from LHC run1 and run2

ALICE coll., Phys.Rev.Lett. 116 (2016) no.22, 222302

July 2017 update: excellent description of
ALICE@LHC data

proton discrepancy 2.8 sigma
fit includes loosely bound systems such as deuteron and hypertriton
hypertriton is bound-state of (Λ,p,n), Λ separation energy about 130 keV
size about 10 fm, the ultimate halo nucleus,
produced at T=156 MeV. close to an Efimov stateFrank Wilczek, QM2014 introductory talk

hypothesis:
all nuclei and hyper-nuclei are formed as compact multiquark states at the phase boundary. Then slow time
evolution into hadronic respresentation.
Andronic, pbm, Redlich, Stachel, in preparation
How can this be tested?
precision measurement of spectra and flow pattern for lightnuclei and hyper-nuclei
a major new opportunity for ALICE Run3and for CBM/NICA/JPARC/NA61

excellent agreement over 9 orders of magnitudeagreement over 9orders ofmagnitude with
QCD statisticaloperator
prediction

yield of light nuclei predicted in: pbm, J. Stachel, J.Phys. G28 (2002) 1971-1976,
J.Phys. G21 (1995) L17-L20

a note on the chemical freeze-out temperature
Tchem = 156.5 ± 1.5 MeV from fit to all particles
there is an additional uncertainty because of the poorly
known hadronic mass spectrum for masses > 2 GeV
for d, 3He, hypertriton and alpha, there is very little feedingfrom heavier states and none from high mass states in the
hadronic mass spectrum, for these particles thetemperature Tnuc can be determined 'on the back of anenvelope' :Tnuc = 154 ± 5 MeV, independent of hadronic mass
spectrumenergy dependence of temperature and baryochemical potential
energy range from SPS down to threshold (FAIR) is phase boundary ever reachedfor< 10 GeV?

Tlim = 159 +/- 3 MeV

Tlim = 159 +/- 3 MeV ismaximum hadronic temperature

Tc = 154 +/- 9 MeV
from lattice

energy dependence of hadron production described
quantitatively

together with known energy dependence of charged hadron production in Pb-Pb collisions
we can predict yield of all hadrons at all energies with < 10% accuracy

no new physics needed to describe K+/pi+ ratio
including the 'horn'

is multiplicity dependence described bycanonical thermodynamics?

main features, but not details, are captured well – needs further study
arXiv:1512.07227 ALICEthe QGP phase diagram, LQCD, and hadronproduction data

quantitative agreement ofchemical freeze-out parameterswith LQCD predictions for baryochemical potential < 300 MeV

charmonium as a probe for the properties of theQGPthe original idea: (Matsui and Satz 1986) implant
charmonia into the QGP and observe their modification,in terms of suppressed production in nucleus-nucleus
collisions with or without plasma formation – sequential
melting
new insight (pbm, Stachel 2000) QGP screens all
charmonia, but charmonium production takes place atthe phase boundary, enhanced production at colliders –signal for deconfined, thermalized charm quarks
production probability scales with N(ccbar)2
reviews: L. Kluberg and H. Satz, arXiv:0901.3831
pbm and J. Stachel, arXiv:0901.2500
both published in Landoldt-Boernstein Review, R. Stock, editor,
Springer 2010nearly simultaneous: Thews, Schroeder, Rafelski 2001
formation and destruction of charmonia inside the QGP

n.b. at collider energies
there is a complete
separation of time scales
tcoll << tQGP < tJpsi
implanting charmonia
into QGP is an
inappropriate notion
this issue was alreadyanticipated by Blaizot
and Ollitrault in 1988

the idea
heavy quarks are not thermally produced, since their mass m >> Tat collider energies, heavy quarks are copiously produced through QCD
hard scattering
the developing hot fireball formed in the collision thermalizes the heavy
quarksall charmed hadrons and charmonia are deconfined near Tc
the fireball expands and cools until it reaches the phase boundary
there, charmonia are formed with thermal/statistical weights
since charmonium formation scales with N(ccbar)2 and since the charmcross section increases strongly with energy, we expect enhanced
charmonium production at collider energy
this brings the thermal model into the heavy quark era with a large
heavy quark fugacity

note: mass of charm quark is about 300 times heavier
than mass of light quarks

quarkonium as a probe for deconfinement at theLHC
the statistical (re-)generation picture

charmonium enhancement as fingerprint of color
screening and deconfinement at LHC energypbm, Stachel, Phys. Lett. B490 (2000) 196
Andronic, pbm, Redlich, Stachel, Phys. Lett. B652 (2007) 659

less suppression when increasing the energy density

discovery of new production
mechanism by ALICE coll.
in LHC run1

ALICE data
arXiv:1311.0214
Phys.Lett. B734 (2014) 314-327

from here to here more than factor of 2 increase in energy
density, but RAA increases by more than a factor of 32007 prediction impressively confirmed by LHC data

predictions from 2000/2007 beautifully confirmed by RHIC
and LHC data

ALICE coll.,
arXiv:1606.08197

dependence on transverse momentum (1)forward rapidity

ALICE coll., arXiv:1606.08197

dependence on transverse momentum (II)mid-rapidity vs forward rapidity

indication of J/psi enhancement at low pt near mid-rapidity

elliptic flow of charmonium

arXiv:1709.05260

most recent LHC Run2 result,charm quarks participate in the hydrodynamical evolution of the QGP fireballsupport for statistical hadronization of deconfined charm quarks

J/psi flow at mid-rapidity and forward rapidity

J/psi flow larger than expected
at high transverse momentum
transition from hydrodynamic flow
to energy loss?

arXiv:1709.05260

summary
overall the LHC data provide strong support for chemical
freeze-out driven by the phase transition at Tc = 156 MeV
the full QCD statistical operator is encoded in the nuclear collision data on
hadron multiplicities
success to describe also yields of loosely bound states: are they produced as
virtual multi-quark states?
statistical hadronization model describes hadrons including charmonia
formed from deconfined charm quarks
knowledge of hadron mass spectrum up to 2.5 GeV is important for
description → connection to hadron physics community
connection between LQCD and dataexperimental evidence for:
QCD phase boundary
deconfinement of charm quarks

additional slides

The Hypertriton
mass = 2.990 MeV
Lambda sep. energy. = 0.13 MeV
molecular structure:(p+n) + Lambda

2-body threshold: (p+p+n) + pi- = 3He + pirms radius = (4 B.E. Mred)-1/2 = 10.3 fm =rms separation between d and Lambda
in that sense: hypertriton = (p n Lambda) =(d Lambda) is the ultimate halo state
yet production yield is fixed at 156 MeV temperature(about 1000 x separation energy.)

the hadron mass spectrum and lattice QCD

S. Duerr et al., Science 322 (2008) 1224-1227

details on thermal description

156.5

chi^2 curves in (T,V) for fit

for the special case of uncorrelated emission (Skellam distribution) and net
baryon number N = B, the susceptibility is related to the total mean numberof baryons + anti-baryons via

in this limit, we can make a direct comparison between the susceptibility
from LQCD, and the experimentally measured total mean number ofbaryons and anti-baryons.
for N = strangeness S or charge Q, similar expressions, with |q| = (1,2)
and |q| = (1,2,3) hold:within this approach, a direct link between ALICE LHC data and LQCD
predictions can be established
LQCD predictions from:multiplicity dependence of yield ratios
approach to grand-canonical limit observed

grand-canonicalOmega/pi
arXiv:1606.07424
ALICE

...more details

excluded volume correction:

equilibration at the phase boundary
statistical model analysis of (u,d,s) hadron production: an
important test of equilibration of quark matter near the phaseboundary, no equilibrium → no QGP matterno (strangeness) equilibration in hadronic phasepresent understanding: multi-hadron collisions near phaseboundary bring hadrons close to equilibrium – supported bysuccess of statistical model analysis
this implies little energy dependence above RHIC energy
analysis of hadron production → determination of Tc
pbm, Stachel, Wetterich,
Phys.Lett. B596 (2004) 61-69

at what energy is phase boundary reached?

a few remarks about analysis of higher momentsof conserved charges
already for second moments there is a delicate balance between influenceof conservation laws (at large acceptance) and trivial fluctuations (at small
acceptancefor small acceptance, delta_eta << 1, probability distributions become
Poisson and are not sensitive to critical behavor.
in this limit all efficiencies are binomially distributed.
for large acceptance, delta_eta > 1, effect of conservation laws becomeslarge. Efficiencies are not anymore binomially distributed. But data aresensitive to dynamical behavior.
corrections for baryon number conservation become mandatory
for large values of mu_b, impact parameter (volume) fluctuations
become largest source of 'trivial' fluctuations, very unpleasant for searchfor critical endpoint (details see below)
for higher moments, situation becomes more difficult.
effect of purity in PID needs to be carefully studied, crucial for higher
moment analysis

a few remarks about analysis of higher momentsof conserved charges
volume fluctuations
independent source model:
for N: total number of particles, N_s: number of sources, n: number ofparticles from a single source
stay tuned for more
results inAnar Rustamov's talkon Friday
2 limits:(i) <n> = N_p low energy limit, fluctuations dominated by trivial
volume fluctuations(ii) <n> = <N_p – N_pbar> = 0high energy (LHC) limit, volume
fluctuations drop out

also ALICE higher
moments results soon

major advantage at LHC energy: EbE measurements ofconserved quantities sensitive to dynamical fluctuations

quark-gluon plasma and hadron yields in central nuclear
collisions
QCD implies duality between (quarks and gluons) – hadrons
hadron gas is equilibrated state of all known hadrons
QGP is equilibrated state of deconfined quarks and gluons
at a critical temperature Tc a hadronic system converts to QGP
consequence:

QGP in central nuclear collisions if:
1. all hadrons in equilibrium state at common temperature T
2. as function of cm energy the hadron state must reach a limiting
temperature Tlim
3. all hadron yields must agree with predictions using the full QCD
partition function
at the QCD critical temperature Tc = Tlim

The size of loosely bound molecular objects
Examples: deuteron, hypertriton, XYZ 'charmonium
states, molecules near Feshbach resonances in cold
quantum gases

Artoisenet and Braaten,
arXiv:1007.2868

evolution of the early universe and the QCD
phase diagram

QCD phase boundary

homogeneous Universe inequilibrium, this matter can
only be investigated in nuclear collisions
charge neutrality
net lepton number = net baryon number
constant entropy/baryon
neutrinos decouple and light nuclei begin to be formed

The QGP phase transition drives chemical equilibration forsmall  b
Near phase transition particle
density varies rapidly with T.
For small  b, reactions such as
KKK    Nbar bring multi-strange
baryons close to equilibrium.
Equilibration time   T-60 !
All particles freeze out within the samevery narrow temperature window.

are there similar mechanisms forlarge  b?

pbm, J. Stachel, C. WetterichPhys. Lett. B596 (2004) 61
nucl-th/0311005

temperature dependence of meson masses
in a NJL model

Mesonic correlation functions at finite temperature and density in the Nambu-Jona-Lasinio model with a Polyakov loop
H. Hansen, W.M. Alberico (INFN, Turin & Turin U.), A. Beraudo (Saclay, SPhT), A. Molinari, M. Nardi (INFN, Turin &Turin U.), C. Ratti (ECT, Trento & INFN, Trento). Sep 2006. 26 pp.
Published in Phys.Rev. D75 (2007) 065004