What to Expect When You're Expecting: Femtoscopy at the LHC

0.21 MB·English

by  Mike Lisa

MikeLisa 1
WhattoExpect WhenYou’re Expecting: Femtoscopy attheLHC
Mike Lisa1
1DepartmentofPhysics,OhioStateUniversity,1040PhysicsResearchBuilding,191WestWoodruffAve.,Columbus,OH43210,USA
Ahugesystematicsoffemtoscopicmeasurementshavebeenusedoverthepast20yearstocharacterizethe
systemcreatedinheavyioncollisions.Thesemeasurementscovertwoordersofmagnitudeinenergy,andwith
LHCbeamsimminent,thisrangewillbeextendedbymorethananother orderofmagnitude. Here,Idiscuss
theoretical expectations of femtoscopy of A+A and p+p collisions at the LHC, based on Boltzmann and
hydrodynamiccalculations,aswellasonnaiveextrapolationofexistingsystematics.
7 Keywords:LHC,HBT,femtoscopy,predictions,hydrodynamics,Boltzmanncascade,heavyions,RHIC
0
0
2 I. INTRODUCTION

n
a Whatdistinguishesultrarelativisticheavyionphysicsfrom
J
particle physics is its focus on geometrically large systems.

0 The desire is notto understandfundamentalprocesses, as in
2
the latter field, but to create and probe new states of matter

andaccesstheonlyphasetransitionassociatedwithafunda-
1
mental interaction (QCD). The geometrically-sensitive, bulk
v
8 propertiesare the crucialones, and these are reflected in the
5 soft(pT L QCD)sector.
∼
0 In soft sector observables, long-term baselines have been
1
established over a large energy range. Prior to first data at
0
RHIC,itwascommonlyspeculated(andhoped)thatlargede-
7
viationsfromthesesystematics(e.g. p 0/p ratios,sidewards
0 ±
/ flow,strangenessenhancement,totalmultiplicity)wouldsig- FIG.1: Thenumberofrefereed-journalpublicationsreportingnew
h
nalclearlythequalitativelydifferentnatureofthesystemcre- femtoscopyresultsinrelativisticheavyioncollisions. Beginningof
t
- ated there [1]. In femtoscopic systems, rather generic ar- availabilityofnewbeamsareindicatedinyellowboxes.
l
c guments led to expectations [2, 3] of a rapid increase, with
u √sNN,inthepion“HBTradii”Rout andRlong,reflectingrela-
n ery five years,” we may confidentlyexpecta barrage of new
tivelylongtimescalesofthetransitionfromdeconfinedQGP
: femtoscopicinformationtodigestwithinthenext5years.
v toconfinedhadronicmatter.
Here, we discuss predictions for femtoscopy at the LHC.
i Suchdramaticspeculationsarelargelyabsenttoday,inan-
X In the next Section, we consider the case of simple extrap-
ticipation of LHC collisions. Soft-sector, globalobservables
r olation of measured femtoscopic trends, with no reference
a atRHICareonlyquantitativelydifferentthantheyareatlower
to physics per se. In Section III, we consider predictions of
energies. Even in the high-p sector, where jet suppression
T Boltzmann/cascadetransportcalculations, and in Section IV
and partonicenergyloss measurementshave generatedhuge
those of hydrodynamicalmodels. Finally, we discuss spec-
excitement,energyscansatRHICrevealthatthedataindicate
ulationsonthephysicsbehindfemtoscopicmeasurementsin
moreofanevolutionthanarevolution.
p+pcollisions,whichwill, infact,bethefirstresultsavail-
Thisisalltothegood.Discoveriesviasharpjumpsa` lasu-
ableattheLHC.Attheendwesummarize.
perconductivityarenotourlot.Therealsciencebehindheavy
ion measurements (at very high energies as well as at much
II. NOTHINGNEWUNDERTHESUN(NNUS)SCENARIO
lowerones)liesinunderstandingthedetailsofthedata.
Femtoscopy[4],thegeometricmeasurementofsystemsat Femtoscopicmeasurementsdisplayrich,multidimensional
the fermi scale, has been used to characterize the freezeout and nontrivial systematic dependences upon kinematic (pT,
substructureof heavyion collisionsfortwo decadesin time, y, etc) variables and particle species [5, 7]. The depen-
and over two decadesin collision energy[5]. Soon, this en- denceuponglobalvariablessuchas√sNN andimpactparam-
ergyrangewillbeextendedbyanotherdecadeattheLHC. eter, however, appears significantly more trivial. Schemati-
cally characterizing the measured femtoscopic length scales
Itwillbeimportanttounderstandtheevolutionofthenon-
asamultidimensionalfunction,evidencethusfarindicatesan
trivialspace-timesubstructureofthebulksystemastheinitial
overallfactorization
conditions change dramatically with energy. In Figure 1 is
shown the number of refereed-journalpapers of experimen-
R √s ,A,B,~b,f ,y,m ,m ,m
talfemtoscopicresultsinrelativisticheavyioncollisions,asa (cid:16) NN | | T 1 2(cid:17)
fthuannctitohnisoFfipguubrelicaantidonRyeienahr.arEdvSentoacrkm’sedobwsietrhvantoiothnin[g6]mtohraet =Rg(cid:16)√sNN,A,B,|~b|(cid:17)·Fk(f ,y,mT,m1,m2) (1)
“HBT experiencesa renaissanceofnew insightsroughlyev- =R (M) F (f ,y,m ,m ,m ),
g k T 1 2
·
2 BrazilianJournalofPhysics,vol. ,no.,December,2006
extrapolatingM 0,butthisisnegligibleforhighmultiplic-
→
ity. Thisrelationmayreflectthataconstantfreezeoutdensity
200 GeV Au+Au PHENIX drivesthefemtoscopicscales[9],thoughthisneglectsanydy-
6 200 GeV Au+Au STAR
m) namiceffects. Assumingthatthissimpleproportionalitycon-
(fut4 tinues, then, we know Rg(M) and determining femtoscopic
Ro2 expectationsboilsdowntoanticipatingthemultiplicityatthe
LHC.
0
17.3 GeV Pb+Pb CERES A naive extrapolation [7, 8] of systematics suggests that
m)6 8.7 GeV Pb+Pb CERES dN/dy at the LHC will be 60% larger than that observed at
(fRside24 RatHtIhCe.LTHhuCs,wthiellzbereot1h7-%ord(e1r.6ex1/p3ec=ta1ti.o1n7i)sltahragtelrenthgathnstchaoleses
measured at RHIC, for all kinematic selections and particle
0
species,accordingtoEquation1.
4.8 GeV Au+Au E802
m)6 55..44 GGeeVV SSii++AAul EE880022 Going beyond simple extrapolation to include a physical
(fg4 picture, saturation-based calculations [15] give much higher
n
Rlo2 multiplicity–roughlytriplethatatRHIC.Thisleadstoexpec-
tationsoflengthscales45%higherthanthoseatRHIC.Thus,
0
0 2 4 6 8 0 2 4 6 8 10 Rlongforpionsatmidrapidityandlow pT incentralcollisions
N1p/a3rt (dNch/dh )1/3 wouldbe1.45 7fm=10fm.
×
Multiplicity predictions based on Boltzmann/cascade cal-
FIG.2: PionHBT radii plotted versus thenumber of participating culations can be significantly higher yet. Selecting two
nucleons(left)andversusthechargedparticlemultiplicity(right)for for which femtoscopic predictions also exist (Section III),
collisionsofvaryingcentralityandawiderangeofenergies. Com- A Multi-Phase Transport (AMPT) calculation [16] and the
pilationfrom[5]. HadronicRescatteringModel(HRM)[17]predict5 and7
× ×
RHIC multiplicity, respectively. Thus, femtoscopic scales at
LHCmaybeasmuchas90%higherthanatRHIC.Depending
whereF isadimensionlessfunctioncontaining,e.g.decreas- onthefinal-stateinteractionwhichproducesthetwo-particle
k
ing“HBTradii”withparticlem . ThedimensionalscaleR is correlationfunction,measuringlengthscalesof 15fmmay
T g
∼
determinedby globalobservables. However,asindicatedby challenge experimental two-track resolutions. For two-pion
thesecondequalityofEquation1,togoodapproximationthe correlations,suchscalesarewithinthecapabilitiesoftheAL-
onlyrelevantglobalobservableis the totalmultiplicity M of ICEdetector[18].
the collision. In fact, this multiplicitydominancewell apply
toallsoft-sectorobservables[8].
III. BOLTZMANNTRANSPORTCALCULATIONS
There are at least three caveats to the above statement.
Firstly,theCERES[9]collaborationhasshownthatthescale More interesting than simple scaling relations are mod-
depends also on the freeze-out chemistry (baryon-to-meson els with real physics and dynamics, such as transport calcu-
ratio) in addition to the multiplicity. This is important at lations. Boltzmann/cascade transport models generally re-
low (AGS) energies. For collisions above top SPS energy, produce “HBT radii” at RHIC better than do hydrodynamic
√sNN 17 GeV, the chemicalevolutionis sufficientlyweak calculations [5]. The reasons behind this include different
∼
thatonemayconsidermultiplicityonly. Secondly,asseenin physics in the models, a more detailed description of the
Figure 2, there is some residual dependence of the outward kinetic freezeout, and the use of more appropriate methods
radius on √sNN in addition to multiplicity; in this Section, of calculating the radii [19]. Predictions of pion HBT radii
we ignore this potentially important detail. Finally, the az- witheachofthetransportcalculationsdiscussedinSectionII
imuthal(f p, asdeterminedrelativetothereactionplane)de- reveal predictions more subtle than the simple multiplicity-
pendence [10, 11, 12, 13] likely at some point violates the scalingdiscussedabove.
factorization. While it has not been experimentally tested, Foraninfiniteandboost-invariantsystem(onlyanapprox-
two collisions producingthe same multiplicity, one very pe- imation of reality, of course), the longitudinal HBT radius
ripheral (i.e. spatially anisotropic in the entrance channel) R is proportional to the system evolution time (i.e. be-
long
at high energyand the other verycentralat low energy, pre- tweeninterpenetrationoftheionsandkinematicfreezeoutof
sumablygeneratefreezeoutdistributionswithdifferentspatial theproducts)[5,20]. Naturally,thisisnotaunique,system-
anisotropy,whichisthenreflectedintheazimuthally-sensitive widetime,butadistribution. AnexampleisseeninFigure3,
femtoscopy[14]. SeeSectionIVforfurtherdiscussion. inwhichthepionfreeze-outtimedistributionforcollisionsat
These caveats stated, however, the factorization of Equa- RHIC and LHC are compared in the HRM calculation. The
tion1isprobablyourbest,zero-new-physicsguidetosimple LHCtimescalesareroughlydoublethoseatRHIC.Although
extrapolationoffemtoscopictrendsmeasuredovertwoorders HRMisnotexplicitlyaboost-invariantmodel,weseeinFig-
of magnitudein √sNN and from from the lightest (p+p) to ure4thatRlong reflectsthistimescale increase, roughlydou-
the heaviest (Pb+Pb) systems. Figure 2 suggests a simple bling when the energy is increased from RHIC to LHC en-
formR (M)(cid:181) M1/3;thisignoresthefiniteoffset 1fmwhen ergies. The 70% increase in R is roughly consistent,
g long
∼ ∼
MikeLisa 3
1.2 10
ot normalized) 00..681 Prieosnc afrteteerzienogu, tb t=im8 fem d LRicsHHetCInrC iP tbArbuau++PltiAibtouyn radius parameter (fm) 2468 rescatteringR, bT =si8de f m cLReHHnCICt rP aAblui+t+PyAbu RT out
n
y ( 0 0.8
Probabilit 00..2400 20 40 60 80 radius parameter (fm) 2468 RLong llll 000...756
t
0 0.4
0 200 400 600 800 0 200 400 600 800 1000
p (MeV/c) p (MeV/c)
T T
FIG.3: ThefreezeouttimedistributionfromtheHadronicRescat-
teringModelofHumanic[17]forRHICandLHCconditions.
FIG.4: HBTradiifromfitstopioncorrelationfunctionsfromthe
HadronicRescatteringModel ofHumanic[17]forRHICandLHC
conditions.
then, with expectations from both a timescale and from the
multiplicity-scalingpointofview. Thisiscertainlynotaco-
incidence,astheincreasedtimescaleisdueinlargeparttothe joyedhugesuccessinreproducingmomentum-spaceobserv-
increasedmultiplicity. ables such as elliptic flow. Furthermore, the conditions at
On the otherhand, there is more going on. The predicted LHCarelikelyto provideanevenbetterapproximationthan
p -dependenceofbothR andR aresteeperattheLHC atRHIC to the zero-mean-free-pathassumptionsof purehy-
T long side
than atRHIC. Also, the increase in R is significantlyless drodynamics. Finally, the direct connection between hydro-
side
than90%.Bothoftheseeffectsareconsistentwithafreezeout dynamics and the Equation of State of strongly-interacting
scenariowithsignificantlyincreasedtransverseflow[14]. In- matter (color-confined or not) remains a compelling reason
deed, transversemomentumdistributionspredictedby HRM toexploresoft-sector,bulkconsequencesofthemodel.
are significantlyharder (less steep) at the LHC than those at
RHIC.Sincethe p dependenceofHBTradii[5]andspectra
T A. SourceLengthScales
in the soft sector are observed to change very little between
√sNN =20 200 GeV, it will be interesting to see whether Recently, Eskola and collaborators [22] coupled a
thistrendis÷brokenattheLHC,aspredictedbyHRM. pQCD+saturation-based prediction for initial conditions at
The HRM model is a deliberate effort to use the simplest LHC to their 1+1-dimensional hydro calculation. The
(often criticized as too simplistic) physics picture, free of Equation-of-State featured a first-order phase transition be-
novel phases like QGP. It is a pure hadron-based transport tween an ideal QGP at high temperature and a hadron reso-
calculation, though the initial conditionsmay be taken from nancegasatlowtemperature.
Pythia or Saturation-basedscenarios[17]. On the other side AsshowninFigure5,theinitialenergydensityatwhichhy-
ofthe“simplicityspectrum”isAMPT,anattempttodescribe drodynamicsis assumed to take overexpectedto roughlyan
the various stages of the system’s evolution in terms of the orderofmagnitudelargerattheLHCthanatRHIC,dueboth
mostappropriatemodelforthatstage[21]. toincreasedgluonproductionandtoshortersystemformation
Similar to HRM, AMPT predicts stronger transverse flow (thermalization)timet 0 atthehigherenergy.Sincetheinitial
at the LHC, as compared to RHIC, leading to steeper p - transversescalechangesonlylittle,thepressuregradientswill
T
dependence of HBT radii. In terms of scale, the transverse likewise be much higherat LHC, leading to increased trans-
(longitudinal)radii are predicted to increase by 10% (30%). verse flow. These effects place competing pressures on the
This is more modest than the predictions of HRM (30% space-time evolution of the system, and on the femtoscopic
and 70%, respectively), and much more modest than pure- scalesatfreezeout,asdiscussedbelow.
multiplicityscalingsofSectionII. Theincreasedenergydensity(directlyassociatedwith en-
Thus the dynamical physics, in these models, lead to ex- tropy density and thus multiplicity) tends to produce longer
pected details significantly beyond simple extrapolation of timescalesattheLHC. Longitudinalexpansiontendsto cool
lower-energyresults. thesystemtowardsfreezeoutconditions.However,especially
attheLHC,thelargetransverseflowgeneratedbytheintense
pressure gradients cannotbe ignored. Eskola and collabora-
IV. HYDRODYNAMICALCALCULATIONS
tors[22],estimatethatthetimerequiredtocoolfromthemax-
As mentioned, hydrodynamical models tend to repro- imum energydensity (at r=0 in Figure 5 to the critical en-
duce femtoscopicmeasurementsmore poorlythan do Boltz- ergydensity(e =1.93GeV/fm3)wouldbe6fm/c(20fm/c)
c
mann/cascadecalculations. Ontheotherhand,theyhaveen- at RHIC (LHC), due to longitudinalexpansionalone. How-
4 BrazilianJournalofPhysics,vol. ,no.,December,2006
2500
s1/2=5500AGeV
2000 ss511//%22==m12o30s00tcAAeGGnteerVVal t (fm/c)15 IPES y (fm)10
10 RHIC1 C 1
0
3]1500 HI
m R
eV/f Pb+Pb 5 y=0 −10
[G1000 A0ef=f=0.11903fm/c 0 x=0 IPES
0 5 10 15 −10 0 10
Au+Au x or y (fm) x (fm)
500 A =181
eff
=0.17fm/c
0
FIG.6: Left: freeze-outspace-timehypersurfaceincollisionswith
0 0=0.19fm/c finite impact parameter calculated by Heinz and Kolb [23]. The
0 1 2 3 4 5 6 7 8
“IPES”calculationisanestimateofthesystemcreatedattheLHC.
r[fm]
The impact parameter is defined to lie in the xˆ-direction. Right:
time-,z- and momentum-integrated freeze-out shapes in the trans-
verseplane.
FIG. 5: Initial energy density distribution in the transverse plane,
calculatedbyEskolaetal[22].
parameter,boththespatialconfigurationoftheentrancechan-
nelandtheresultingmomentumdistributionintheexitchan-
ever, when transverse dynamics are included, the cooling nel are anisotropic. In particular, the initial state is spatially
times become 5 fm/c (7.5 fm/c) at RHIC (LHC). The evo- extended out of the reaction plane, and the resulting flow is
lutiontime to kinematicfreezeout–say untilT 140MeV– strongerinthereactionplane(ellipticflowv2>0).
ist 12 14fm/cinbothcases; thisisthetim≈escalemost Due to the preferential in-plane expansion, as the system
0
∼ −
directly probed by femtoscopy. This is dramatic– the effect evolvesthespatialconfigurationshouldbecomeincreasingly
of transverse flow on cooling timescales can almost be ne- in-planeextended(equivalently,decreasinglyout-of-planeex-
glectedatRHIC,whileitisdominantattheLHC.Thisisrem- tended). Thus, knowledge of the entrance-channel shape
iniscent of the cascade calculations discussed in Section III; (e.g.thoughGlaubermodelcalculations)andmeasurementof
themuchstrongerflow maywellleadto deviationsfromthe theexit-channelshape(throughfemtoscopy)provide“bound-
trends(e.g. p -dependenceofpionHBTradiibeingindepen- ary conditions”on the dynamicalspacetime evolutionof the
T
dentof√sNN)establishedsofaratlowerenergy. Thisaspect anisotropic system, and probe the evolution timescale. The
of the NNUS scenario may finally be violated. The qualita- extracted timescale is model-dependent, requiring in princi-
tive difference is apparent from the freezeout hypersurfaces ple a detailed time evolutionof the flow. However, a simple
atRHIC andLHC, shownin Figure6. The Figureis froma estimate [25] of the timescale extracted through shape mea-
calculationbyKolbandHeinz[23],butissimilartoEskola’s. surementsand thatextractedfromblast-wavefits [14, 26] to
Itwouldbeveryinterestingtoknowwhethertheotheras- azimuthally-integratedHBTradiiareroughlyconsistent.
pectofNNUS,namelythemultiplicityscalingshowninFig- MeasurementsofthefreezeoutshapeattheAGS[11]and
ure 2, is satisfied by the hydro models. Unfortunately, Es- RHIC [12, 13] indicate an out-of-plane-extendedconfigura-
koladidnotcalculatepion“HBTradii,”andHeinzandKolb tion.Consistentwiththefactthatpreferentialin-planeexpan-
did not calculate multiplicity, so a consistent estimate of the sion(i.e. ellipticflow)isstrongeratRHIC,theconfiguration
scalingcannotbe checked. However,the formerpredictthat atthehigherbombardingenergyisrounder. Thisisshownin
the multiplicity at LHC will be approximately triple that at Figure 7, in which the transverse anisotropyis characterized
RHIC, corresponding to a 40% increase in HBT radius un- bye (R2 R2)/(R2+R2)(xisinthereactionplane).
≡ y− x y x
der NNUS scaling. Heinz and Kolb [23] do, in fact, predict The anisotropic shapes and corresponding azimuthally-
roughlythisincreaseinthetransverseradii,but–remarkably– selected HBT radii have been calculated in two dynamical
theyalso predicta significantdecreaseinRlong atLHCrela- models. At the AGS, the transport code RQMD [27] repro-
tivetoRHIC![35] ducestheoverallscale[28]andtheanisotropy[10,11]ofthe
sourcereasonablywell, asshown in Figure7. At RHIC, the
2+1hydrocode[23]reproducestheshapequitewell,while
B. SourceShape
missingthescale. AttheLHC,thelattercalculationpredicts–
Azimuthally-sensitive pion interferometry– the measure- again– a qualitative change in the freezeoutdistribution. As
mentofspatialscalesasafunctionofemissionanglerelative shownintherightpanelofFigure6thesourceisexpectedto
tothereactionplane–probestheshapeofthefreezeoutcon- evolvetoanin-planeconfiguration(e <0).
figuration,inadditiontoitsscale[10,14,24]. Atfiniteimpact However,again,thishugeflowhasotherdramaticandqual-
MikeLisa 5
1.8
pion HBT from LHC p+p
-1<y<1, mult>300
e 0.4 E895 STAR ALICE 1.6
0.3
1.4
0.2 m)
0.1 R (f 1.2
0 ?? ! or 1
-0.1 RQMD
hydro
-0.2 0.8
1 10 102 103 104 !, "=0.1 fm/c
R, "=0.1 fm/c
√sNN (GeV) 0.6 !R,, ""==11..00 ffmm//cc
FIG. 7: Transverse spatial freezeout anisotropy e as afunction of 0.2 0.4 0.6 0.8
collisionenergy, asestimated withazimuthally-sensitive pion fem- p (GeV/c)
toscopy,forcollisionswithimpactparameter 7fm.Roundsources T
correspondtoe =0;e >0indicatesanout-of-∼plane-extendedsource.
Measurements at the AGS [11] and RHIC [13] are compared with FIG. 8: Full markers: predicted pT-dependence of Rinv and
l from Gaussian fits to calculated correlation functions in a
RQMDandhydrodynamiccalculations,respectively, andtheshape
Pythia+hadronic rescattering model [31]. Here, the hadronization
predictedbyhydroattheLHCisshown.
time was set to t = 0.1 fm/c, the value required to reproduce
E735 [32] data at the Tevatron. Also shown in open markers are
thefemtoscopicparameterscorrespondingtoalongerhadronization
itatively new implications: the decreasedRlong mentionedin time.Inthiscase,thereislittleveryhadronicrescatteringandthusa
SectionIVA; andanactualsigninversionoftheoscillations muchweaker pT-dependenceofRinv.
oftheHBTradiiwith p [14,23].
T
V. PROTONCOLLISIONS
the physics implications might be dramatic. We do not dis-
Beforeheavy ionsare acceleratedat the LHC, protoncol- cussthishere,butsimplyobservethattheNNUSscenariois
lisions at √s=1.4 TeV will be measured. While the thrust alikelybaselineexpectationfor p+patLHC.
of the p+p program is towards Higgs physics, it is well- The increase of HBT radii with multiplicity has also been
recognizedthat p+pcollisionsserveasavaluablereference observedpreviouslyin p p¯collisionsbytheE735Collabo-
to heavy ion analyses in the “hard” (high-pT) sector, where ration[32]. WhileinA+−Acollisions,thisisnaturallyrelated
one looks for the effects of the medium on particles coming toincreasinglengthscalesintheentrancechannelgeometry,
fromwell-calibratedfundamentalprocesses. Paic´ and Skowron´ski[33] postulate thatjet dynamics, rather
Soft-sectoranalyses,too,shouldbeperformedforsystems than bulk properties, drivethis dependencein the p+p¯ sys-
from the smallest to the largest, and the results compared. tem. Withinasimplemodelofhadronization,theycanrepro-
Since such analyses are assumed to measure the bulk prop- ducetheE735multiplicitydependence,andmakepredictions
erties, one might well hope for qualitative differences when ofsimilar multiplicitydependencefor p+pcollisionsatthe
comparingresultsfor p+ptoPb+Pbcollisions. top LHC energy. However, since the expectationof increas-
WhilepionHBTmeasurementshavebeencommoninboth inglengthscaleswithmultiplicityseemstoberathergeneric
the high-energyand heavy-ioncommunitiesfor manyyears, toallscenarios,itwillbeinterestingtosee thesepredictions
a direct“apples-to-apples”comparisonbetween results from expanded to more differential measures– say, the multiplic-
A+A and p+p collisions has not been possible until very ity and p dependence, probing both aspects of Equation 1.
T
recently. The STAR Collaborationat RHIC hasreportedthe Thisshouldallowamorediscriminatingcomparisonbetween
firstdirectcomparisonofpionHBTradiiinAu+Au,Cu+Cu, models,allowingsometoberuledout.
d+Au, andp+pcollisions, usingthe samedetector, sameen-
Such differential predictions have very recently
ergy, identical techniques (event mixing, etc) to create the
been performed by Humanic [31], in the context of a
correlation function, identical coordinate systems and iden-
Pythia+hadronic rescattering (through HRM) scenario. It is
tical fitting techniques [29]. Remarkably, Gaussian fits to
found that, contrary to some expectations, hadronic rescat-
the correlation functions return “HBT radii” which factor-
teringiscrucialtounderstandtheM p dependenceofthe
ize according to Equation 1; i.e. Fk, which quantifies the E735 data. Reproducing the data r⊗equTires the assumption
dynamically-generatedsubstructure,isidenticalin p+pand
of a surprisingly short hadronization timescale ( 0.1 fm);
A+A collisions. However, the STAR data show significant ∼
longertimescalesdonotallowsufficienthadronicrescattering
non-femtoscopicstructures[29], whichmustbe properlyac-
needed to describe the p -dependence. The prediction of
countedfor[30]beforedrawingfirmconclusions. Ifthefac- T
the model for the highest multiplicity p+p collisions at
torizationis unchangedafter a moresophisticated treatment,
√s=1.4TeVareshowninFigure8.
6 BrazilianJournalofPhysics,vol. ,no.,December,2006
VI. SUMMARY relativetoRHICvalues,thelongitudinalonesshouldexpand
little,andmayevendecrease.
Two decades’ worth of femtoscopic systematics [5] in
heavyioncollisionsrevealsastrikinglyconsistentandsimple Theevolutiontimescalemayalsobeprobedbymeasuring
structure. The kinematic and particle-species dependences, the anisotropic shape of the source in coordinate space, for
whichreflectdynamicsubstructure,decouplefromtheglobal non-centralcollisions. Here again,a qualitativedifferenceis
scale,whichdepends(almost)solelyonmultiplicity. Theas- predicted by hydrodynamicsbetween RHIC and LHC colli-
sumptionthatthefactorizationofEquation1persists–i.e.that sions. Inparticular,thegreatlyincreasedflowandsomewhat
F remainsunchangedattheLHC–togetherwiththeassump- increasedevolutiontimeleadtopredictionsofanin-planeex-
k
tionR (M) √3M,istheessenceoftheNNUSscenario. tendedsource,producingHBTradiusoscillations180 outof
g ◦
∼
In the NNUS picture, all femtoscopic length scales mea- phasewiththoseseenatlowerenergy.
sured at RHIC will be reproduced at LHC, only scaled up
Probablyasimportantassoft-physicsanalysesinheavyion
by 20-90%, dependingon the multiplicity prediction. Thus,
systems are parallel ones for p+p collisions. First prelim-
the “pionHBT radius”R atlow p mightbe expectedin
long T inary “apples-to-apples” comparisons of Gaussian HBT ra-
the range (1.2 1.9) (7fm)=8.4 13fm, while the aver-
÷ × ÷ diusmeasurementsatRHICsuggestthatNNUSfactorization
ageshiftbetweenpionsandkaons(about6fmatRHIC[34])
continuestoholdevenforthesesmallestsystems; itremains
would be in the range 7.2 11.5 fm. However, dynamical
÷ to be seen whether this conclusion survives more sophisti-
models generally predict interesting violations of NNUS at
cated treatment of non-femtoscopic correlations in the data,
theLHC.Thesignificantdispersionbetweenpredictionsholds
presentlyunderway.Inthecontextoftwosimplemodels,pion
outthepossibilitythatthedatawilleliminatesomemodels.
HBT radii at the LHC depend strongly on the hadronization
In the HRM and AMPT Boltzmann/cascade calculations,
scenario. Both predict an increase in femtoscopic freezeout
increased rescattering due to the higher density at the LHC
scaleswithincreasingmultiplicity,whichinitselfwillnotdis-
generates much stronger global space-momentum correla-
tinguishthesemodelsfromanyother.However,inone,thep
tions. Thisleadstoflatter p spectraforhighmassparticles, T
T dependenceisfoundtodependstronglyonthehadronization
and to a steeper p -dependence of the femtoscopic length
T timeanddegreeofsubsequenthadronicscattering.Suchscat-
scales; that is, F would pick up a √s dependence,violating
k teringisusuallyignoredintreatmentsof p+pcollisions;in-
NNUSfactorization. Transverse(longitudinal)scalesareex-
deed,thelackofsignificantrescatteringisbelievedtobetheir
pectedtoincrease10-30%(30-70%),relativetoRHICvalues.
primary virtue as a reference measurement. As hinted at by
Inhydrodyanamicalcalculations,muchhigherenergyden-
thefirstRHICmeasurements,maybetheyarenotsodifferent
sities andpressuregradientsattheLHCmaygeneratequali-
fromA+A collisionsafter all. Moredetailed measurements
tativelynewfemtoscopicsignals. Contrarytothesituationat
at the LHC may, in fact, spur a re-evaluationof ideas of the
RHIC, the transversely explosive nature of the source at the
spacetimeevolutionofbothheavyionandhadroniccollisions.
LHCseverelyshortensthetimeuntilfreezeout.Thefreezeout
hypersurfaceisofaqualitativelydifferentshapeintransverse Inanycase,wemayconfidentlyexpectconsiderableactiv-
positionandtime;whiletransverseradiimayincreaseby40% ityandexcitementasthenextmountainformsonFigure1.
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