Non-thermal p/pi ratio at LHC as a consequence of hadronic final state interactions

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by  Jan Steinheimer

Non-thermal p/π ratio at LHC as a consequence of hadronic final state interactions
∗
Jan Steinheimer
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA and
Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universita¨t,
Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main
J¨org Aichelin
SUBATECH, UMR 6457, Universit´e de Nantes, Ecole des Mines de Nantes,
IN2P3/CNRS. 4 rue Alfred Kastler, 44307 Nantes cedex 3, France and
Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universita¨t,
Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main
3 Marcus Bleicher
1 Institut fu¨r Theoretische Physik, Johann Wolfgang Goethe-Universita¨t,
0 Max-von-Laue-Strasse 1, 60438 Frankfurt am Main and
2 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universita¨t,
Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main
n
a
RecentLHCdataonPb+Pbreactionsat√s =2.7TeVsuggeststhatthep/π isincompatible
J NN
with thermal models. We explore several hadron ratios (K/π, p/π, Λ/π, Ξ/π) within a hydrody-
8
namic model with hadronic after burner, namely UrQMD 3.3, and show that the deviations can
2
be understood as a final state effect. We propose the p/π as an observable sensitive on whether

final state interactions take place or not. The measured values of the hadron ratios do then allow
]
h togauge thetransition energy density from hydrodynamicsto theBoltzmann description. We find
t that thedata can be explained with transition energy densities of 840 150 MeV/fm3.
- ±
l
c
u
I. INTRODUCTION productsnotallowingforanexperimentalreconstruction
n
of the resonances.
[
WiththestartoftheLHCphysicsprogramthreeyears At LHC energiesthis is different. Here, twoof the ele-
2
ago, the field of high energy nuclear physics, and espe- mentary ratios, the p/π and p/π-ratios,show clear devi-
v
ciallyheavyionphysics,hasgoneintoanewera. Itisnow ationsfromthe predictions ofthe thermalmodel[13,16]
2
possible to explore the properties of Quantum-Chromo- whose parameters are fitted to other particle ratios. It
0
3 Dynamics(QCD)atunprecedentedparticledensitiesand has been proposed that this deviation can be due to dif-
5 temperatures. ThethreelargescaleexperimentsALICE, ferent hadronization temperatures of light and strange
. ATLASandCMShaveprovidednoveldataonthetrans- quarks[17](howeversuchaneffectshouldbe visiblealso
3
0 verse expansion dynamics, e.g. elliptic flow, jet attenu- at lower energies).
2 ation far beyond the reach of RHIC, high quality charm In this letter we suggest that this deviation is due to
1 and bottom data and the suppression of quarkonia [1– out of equilibrium final state interactions of the hadrons
v: 4]. Many of these data could be understood in terms after the break-up of the thermal fireball. Discussions
i ofpQCDinspiredmodels, partoncascadesandhydrody- on hadronic final state interactions are ongoing since
X
namic approaches [5–10]. hadronic afterburners where first introduced. It is the
r Alongstandingalternativeapproachtointerpretbulk primaryaimofourpapertoshowthewayhowthisques-
a
hadron multiplicities is based on the statistical or ther- tion can be settled by a detailed analysis of the experi-
mal model of hadron yields [11–15]. Here one assumes mental data, i.e. the p/π ratio. Final state interactions
the production of a thermalized fireball with a common are, at lower energies, too weak to largely distort this
temperature, T,a commonbaryo-chemicalpotentialµB, ratio, though a recent investigation within the statisti-
and a fixed volume. Under these assumptions one can cal model suggests that hadronic final state interactions
extract the fireball parameters T and µB from the mea- should not be neglected for anti-particle yields even at
sured hadron ratios. At energies below the current LHC SPS and RHIC energies [18]. We will furthermore show
energy a very large number of measured hadron ratios thatthis ratioallowsforthe experimentaldetermination
is compatible with the assumptionthat hadronsare pro- ofone ofthe keyquantitiesinpresentdaytransportthe-
duced from such a thermalized source. Deviations from ories at this energy: The energy density at which the
the thermal predictions, as seen for resonances,could be systems ceases to be able to maintain a local equilib-
interpreted as due to rescattering of one of the decay rium and passes to the phase of non-equilibrium final
state interactions. This energy density is called freeze
out or transition energy density. In the hydrodynamical
approaches this is the energy density where hadrons are
∗ [email protected] formed. We elucidatethis ideabyemployingacombined
2
hydrodynamic plus hadronic cascade model.

1.3 1.3
II. URQMD HYBRID APPROACH
)
o
For the present calculations we employ the UrQMD dr1.2 1.2
3.3 hybrid model to centralPb+Pbreactions at the cur- y
h
rentLHC energyof√s=2.75TeV.The UrQMDhybrid d(1.1 1.1
approachextendspreviousansatzestocombinehydrody- el
namic and transport models for relativistic energies by /Yi1.0 1.0
)
combining these approaches into one single framework al
for a consistent description of the dynamics [9, 19–27]. n
fi0.9 0.9
The simulations starts from a PYTHIA generated ini- d(
tial condition [25, 27] which is mapped onto a hydrody- el
namic energy momentum tensor assuming local equili- Yi0.8 eCF [e0]: 0.8
bration. In the next step the ideal hydrodynamic equa- 3
tions are solved [28] until a local transition criterion is 0.7 5 0.7
7
reached. Thetransitioncriterionfromthehydrodynamic
9
description to the transport stage is defined by the lo-
0.6 0.6
_ _ _ _
cal energy density in the rest frame of the cells, i.e. + - + -
K K n p p
ǫtransition = n ǫ0, with ǫ0 being the groundstate energy
∗
density, the parameter n has usually been set to a value
of n = 5. By Monte-Carlo sampling of the Cooper-Frye
distribution,thelocaldensitiesarethantransformedinto FIG. 1. (Color online) Ratios of particle multiplicities in the
hadronsand evolvedin the hadronic cascadeuntil allre- finalstatescaledbytheparticlemultiplicitydirectlyafterthe
hydrodynamic stage for central Pb+Pb reactions at √s =
actions cease. For a detailed description of the model
2.75 TeV. The different symbols denote different transition
and how it can be extended to LHC energies we refer to
energy densities in units of ǫ0.
[7, 29–32]
III. EFFECT OF THE CASCADE STAGE dominantly disintegrate into two particles and therefore
can maintain their equilibrium distribution for a longer
time. The small change in the Λ yield can therefore be
Figure 1 shows the ratios of particle multiplicities
explained by regenerationthrough resonance excitations
in the final state scaled by the particle multiplicity
in the final state, a process that is not allowed for
directlyafterthehydrodynamicstageforcentralPb+Pb
protons which have to be created as a p-p pair. With
reactions at √s = 2.75 TeV. In both cases the hadron
this, our results agree with previous calculations, where
yields include the feed down from all resonances in the
the UrQMD model was used for the final state of a
model. The different symbols denote different transition
energy densities in units of ǫ0 = 145MeV/fm3. One hydrodynamical calculation [40].
observes a dependence of the yields on the transition
energy density. For early transitions, i.e. at a higher Inpreviousstudies[33–36]theimportanceofthemulti
energy density, the modifications are stronger than for meson fusion reaction for describing anti-baryon yields
a later transition, i.e. a lower energy density. While at the SPS (and lower) energies was pointed out. At
the meson yields are only modified on a 10% level, for those energies the net baryon number is still consider-
transition energy densities between 3 9ǫ0, a stronger ably large and the number of protons larger than that
−
effect can be observed for (anti-)protons. Λ’s on the of the anti-protons. The pion density at hadronization,
other hand are not as much modified. This indicates, however, should not change considerably from the SPS
that the dominant process in the decoupling phase, to LHC as the transition temperature T increases only
c
following the Cooper-Frye transition, is the annihilation very slowly with beam energy. Because the inverse reac-
process,reflectedin the strongdependence ofthe proton tion 5π p+p is proportional to the fifth power of the
→
final yield on the transition density. It is expected piondensity,wecanexpecttherelativecontributionfrom
that in an expansion the annihilation processes are multipionscatteringtothe anti-protonyieldtodecrease
the first which signal that the systems leaves chemical with beam energy, as there are considerably more anti-
equilibrium [33–36]. Usually a baryon-anti baryon anni- protons produced, at hadronization,at the LHC than at
hilation creates a couple of pions (n 5) [37, 38] and the SPS.
≈
therefore the inverse process is highly density dependent In the following we want to clarify the differences and
and a high density is required to maintain chemical the apparent conflict of our work with that of Rapp and
equilibrium [39]. This is in contrast to resonances which Shuryak [33, 34, 36]. The relevance of the annihilation
3
anditsbackreactionisdeterminedbythedynamicalevo-
lution of the phase space densities of the involved parti- <TCF >[MeV]
cles. In the work of Rapp and Shuryak this evolution 133 141 148 152
0.7 0.7
is simplified to a certain degree, and therefore, already
+ +
the annihilation rate is significantly overestimated. A 3 K/
+
previous investigation with our model showed that anti- 10 p/
- +
100 /
protonabsorption, at top SPS energies, can very well be 0.6 - + 0.6
500 /
described and does not lead to such a drastic depletion
o
of anti-protons as predicted by Rapp and Shuryak [18]. ti
a
Consequently,due tothe overestimatedannihilation,the r

pion phase space in their work turns out over saturated. cle 0.5 0.5
As the backreactionisproportionalto the fifth powerof ti
r
the pion density it is also largely overestimated to com- a
p
pensate the too large annihilation rate. The final value
0.4 0.4
fortheanti-protonyield,obtainedbyRappandShuryak,
turns out to be not much different from the results with
our model, presented in [18]. Considering that the SPS
data, referred to in [33], have been corrected since, to 0.3 0.3
accommodate weak decays, by roughly a factor of 0.5,
the back reactiondoes not play such a significantrole as
3 4 5 6 7 8 9
previously proposed.
e [e ]
CF 0
To give a quantitative bound on the systematic error
of our result, due to lack of detailed balance, we investi-
FIG. 2. (Color online) Hadron ratios as a function of the
gatedthe protonlossina staticsystem, withinUrQMD.
transitionenergydensityforcentralPb+Pbreactionsat√s=
For this we initialized systems in chemical equilibrium,
2.75TeV.Thesymbolsdenotethecalculations,thelinedepict
corresponding to the average densities/temperatures
theexperimental data.
at our different transition criteria. We then let the
system evolve in a static box, i.e. without expansion,
and observe a depletion of the proton yield in that
box (without resonance decays), due to lack of detailed
balance. Wecanobservealossofprotonsproportionalto Figure 2 shows the final hadron ratios (scaled for vis-
the time which is largest at the highest temperature, as ibility) as a function of the transition energy density for
expected. Fromtheseresultsweextractthetemperature central Pb+Pb reactions at √s = 2.75 TeV. The aver-
dependent proton loss due to lack of detailed balance ageproductiontemperature T ,correspondingtothe
CF
h i
dN /dt(T). Because the system created at the LHC is transitionenergydensityboundaryisshownontheupper
p
fast expanding it remains at the highest temperature axisoffigure2. Thesymbolsdenotethecalculations,the
only for a short time. An estimate on the time evolu- solidlinesdepicttheexperimentaldata(thedashedlines
tion of the density/temperature can be obtained from correspond to the experimental errors in the Ω/π) [16].
extending the hydro simulation after the transition. We Depending on the transition energy density, i.e. on the
use the time dependence of the temperature, down to lifetime of the hadronic stage, the baryon/meson ratios
130 MeV, to estimate the upper bound on the total are systematically modified. The higher the transition
numberofprotonslostduetolackofdetailedbalanceby energy density the higher the density and therefore the
integrating dN /dt(T) over the evolution of the system. moreprobablethatthebaryonsfindanannihilationpart-
p
We find it to be around8% ofthe starting value (for the ner. In a rapidly expanding system the inverse reaction
highest transition temperature), considered that 50% becomes rare and therefore the deficit with respect to
of all protons come from resonance decays. From this thermal model prediction remains. The lower the tran-
we conclude that our results, presented in figure 1, are sition energy density the lower is the density and the
qualitatively robust and quantitatively off by less than shorter is the life time of the hadronic stage. Therefore
8%. itismoredifficultforthe baryonsto findanannihilation
The contribution from the backward reaction should partnerandtheratiosapproachthevaluesexpectedfrom
even be smaller, considering that the system is not a thermal distribution at the transition energy density.
static but fast expanding with a large collective velocity Allratiosapproachthe experimentalvaluesifthe transi-
which drives the particle freeze out and should suppress tion energy density is around ǫ = 6ǫ0, close to our stan-
the multi pion reactions. This has been shown in [34] dard value (ǫ=5ǫ0).
where the chemical relaxationtimes for the anti-protons From this investigations, we conclude that the apparent
quicklyexceededthefireballslifetimebecausemulti-pion inconsistencyofexperimentalp/π-ratiowiththethermal
annihilation is not frequent enough to counteract the modelpredictionscanbe explainedbythe hadronicfinal
p+p annihilation. stateinteraction,whichmodifiesthehadronyields. Even
4
more,theirvaluesascomparedtothethermalmodelpre- Evenmoreimportantourfindingsimposeabenchmark
dictions allows for an experimental determination of the to every simulation model and narrows down therefore
transition energy density. By comparison to the experi- the uncertainties of the predictions of allpresently avail-
mental data we can fix the transition energy density in able transport models. In the light of our findings a
the UrQMD hybrid model to 840 150 MeV/fm3. thorough investigation of the importance of final state
±
annihilations at all beam energies is in order. At the
SPS, data is compatible with considerable anti-particle
annihilation [18]. At the RHIC the situation is not so
IV. SUMMARY clear. Three experiments have published data and show
an ambiguous picture. STAR data for example suggests
nodepletionofthethermalmodelyieldbuthasnotbeen
The apparentnon-thermal p/π ratio observedat LHC
corrected for weak decays which have shown to be im-
has been investigated. We found that the p/π- ratio is
portant. Once a meaningful analysis can be done it will
strongly modified due to the late stage hadronic effects.
be an important step toward a better understanding of
Inthisstagethehadronsfalloutofequilibriumuntilthey
the RHIC and LHC physics.
finally decouple. One can summarize the main points of
our findings as:
V. ACKNOWLEDGMENTS
ThedescriptionoftheLHCdatarequirestheinclu-
•
sion of an out-of-equilibrium final hadronic stage. ThisworkhasbeensupportedbyGSIandHessianini-
tiative for excellence (LOEWE) through the Helmholtz
International Center for FAIR (HIC for FAIR), by the
Signals on where this transition takes place are
• European Network I3-HP3 Turic and by the agence na-
not washed out completely during this out-of-
tional de recherche (ANR) program ”hadrons@LHC”.
equilibrium final hadronic stage.
J. S. acknowledges a Feodor Lynen fellowship of the
Alexander von Humboldt foundation. This work was
This signalcan and has to be used to calibrate the supported by the Office of Nuclear Physics in the US
•
different models. It determines where in a given DepartmentofEnergy’sOfficeofScienceunderContract
model(andifconsistencybetweendifferentmodels No. DE-AC02-05CH11231. Thecomputationalresources
can be achieved in anture) the transition between were provided by the LOEWE Frankfurt Center for Sci-
the eq. and the out-of-eq. phase takes place. entific Computing (LOEWE-CSC).
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