Mass tomography at different momentum ranges in quark-gluon plasma

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by  Magdalena Djordjevic

Mass tomography at different momentum ranges in Quark-Gluon Plasma
Magdalena Djordjevic,1 Bojana Blagojevic,1 and Lidija Zivkovic1
1Institute of Physics Belgrade, University of Belgrade, Serbia
Wehereshowthatatlowermomentum(i.e. p⊥ ∼10GeV)singleparticlesuppressionfordifferent
typesofprobesexhibitaclearmasshierarchy,whichisadirectconsequenceofthedifferencesinthe
energyloss,ratherthanthedifferencesintheinitialdistributions. Ontheotherhand,wepredictthat
themasshierarchyisnotexpectedathighmomentum(i.e. p⊥ ∼100GeV);i.e. whilewesurprisingly
predict that suppression for charged hadrons will be somewhat smaller than the suppression for
heavymesons,wefindthatthisdifferencewillbeaconsequenceoffragmentationfunctions,notthe
finite mass effects. That is, apart from the fragmentation functions, the probes of different masses
6
1 exhibit nearly the same suppression in the high momentum region. We also argue that the same
0 insensitivity on the probe types also appears for jets. In particular, the experimental data in the
2 momentumregions wherethey exist for both typesof probes, showsimilar suppressions of charged
hadrons and inclusive jet data. Interestingly, we also find that our state-of-the-art suppression
v
predictionsforhighmomentumsingleparticlesarealsoinagreement withthejetsuppressiondata,
o
where the reasons behind this agreement yet remain to be understood. Finally, the available jet
N
data also show (though with large error bars) an overlap between b-jets (heavy) and inclusive jets
(light)probes. Consequently,ourresultssuggestthatsingleparticlesinthemomentumregionbelow
3
50 GeV present an excellent tool for mass tomography, while high momentum single particles and

] (possibly) jets are rather insensitive to thedetails of theinteraction with Quark-Gluon Plasma.
h
t
-
l INTRODUCTION aconsequenceofaserendipitousinterplaybetweenen-
c
u ergy loss and fragmentationfunctions. Below 10 GeV,
n there exists a small difference in the RAAs between
Quark-gluon plasma (QGP) is a new state of mat-
[ D mesons and charged hadrons; however, this differ-
ter [1, 2] consisting of interacting quarks, antiquarks
ence in the suppressions is both small and somewhat
2
and gluons. Such new state of matter is created
v influenced by the fragmentation functions [11], so it
in ultra-relativistic heavy ion collisions at Relativistic
2 is, unfortunately, not suitable for extracting any re-
5 HeavyIonCollider(RHIC)andLargeHadronCollider liable conclusions. Furthermore, at high momentum,
8 (LHC). Rare high momentum probes, which are cre-
recent jet measurements indicate (though with large
7 ated in such collisions and which transverse QGP, are
error bars) the same suppression for b-jets [12], and
0
excellent probes of this extreme form of matter [3–5].
. inclusive (light) jets [13, 14]. Consequently, there is a
1 Astheseprobeshavedifferentmassesandconsequently
nontrivialquestionofwhatexactlyprobesandmomen-
0 interact with the medium in a different manner, such
tum ranges canbe used for obtaining new information
6
masstomographyallowsinvestigatingpropertiesofthe
1 onprobe-mediuminteractions. Addressingthiswill,in
interactions with the medium [6–8]. Furthermore, as
: turn, allow optimally exploiting experimental efforts
v higher momentum ranges become increasingly avail-
i andprovidefurthertestsofourunderstandingofQCD
X able at the LHC experiments, there are both different
matter. Systematically testing the mass tomography
probes and a wide range of their momentum, which
r effects, for different probes, and at wide momentum
a become available for such mass tomography. However,
ranges, will be the main goal of this paper.
there is now a question whichexactly probes,and mo-
mentum ranges, are optimal for such tomography, i.e.
To achieve this goal, we will here use our state-of-
willleadtodifferentbehaviorthatcanprovidenewin-
the-artdynamicalenergylossformalism[15,16],which
formationaboutinteractionswiththemedium. Toad-
removes a widely used static approximation and takes
dressthisquestion,wewillinthispaperconcentrateon
into account interactions of the probe with the mov-
the nuclear modification factor (R ), as suppression
AA ing (dynamical) medium constituents. Through this,
istraditionallyconsideredtobeanexcellentobservable
it consistently treats both radiative [15, 16] and col-
for mass tomography.
lisional [17] energy loss, which has been shown to be
As an example, it was previously widely expected crucial for quantitatively and qualitatively explaining
that such clear distinction between the suppression the experimental data [18]. Additionally, the formal-
patterns will be provided by the measurements of ism also takes into account finite magnetic mass [19]
charged hadron (light) and D meson (heavy) probes and running coupling [20], and is integrated in an
(see e.g.[7, 8]). However,as shownby both the exper- up-to-date numerical procedure, which includes path-
imental data [9, 10] and theoretical predictions [11], length [21] and multi-gluon [22] fluctuations. The for-
these two probeshavethe samesuppressionatleastin malismwaspreviouslyshowntobeconsistentwiththe
themomentumregionbetween10and50GeV,whichis wide range of suppression data corresponding to dif-
2
ferent probes and experimental conditions [11, 20, 23]. lisions, scaled by the number of binary collisions Nbin:
Importantly, no free parameters areusedincomparing
predictions with the experimental data. The same pa- RAA(p⊥)= dNAA/dp⊥ (1)
rameter set, corresponding to the standard literature NbindNpp/dp⊥
values,willbeusedinthispaper,sothatthegenerated
Tocalculatethequenchedspectraoflightandheavy
predictions will be also constrained by an agreement
probes, we use the generic pQCD convolution, which
with a wealth of previous data.
consists of the following steps:
WewillheregeneratesingleparticleR predictions
AA
3 3
amtobmoetnhtluomwe(ri.me.omp⊥en∼tu1m00(i.Ge.eVp⊥) r∼eg1io0nGs.eVO)uarnpdrehdigich- Edfp3⊥d,fσ = Eiddp3⊥σ(,iQ) ⊗P(Ei →Ef)⊗ (2)
tions are applicable for both 2.76 TeV and 5.02 TeV
D(Q H ) f(H J/ψ). (3)
Q Q
collision energies, since we here predict the same sup- ⊗ → ⊗ →
pression at these two collision energies for light flavor, Here”i”and”f”subscriptscorrespond,respectively,to
while we previously [24] predicted the same suppres- ”initial” and ”final”, E is energy, p⊥ is momentum, Q
sion at these energies for heavy flavor. Comparing denotes partons(quarks andgluons),and the terms in
these predictions with single particle RAA measure- the equation correspond to the following:
mentswillallowinvestigatinghowsuppressiondepends
i) E d3σ(Q)/dp3 denotes the initial parton spec-
on the mass hierarchy in different momentum regions, i ⊥,i
trum. For lightquarksand gluons,the spectrum
particularly since high precision single particle R
AA
is extracted from [25], while for charm and bot-
measurements are (or will soon become) available at
tom quarks,the spectrum is extracted from [26].
both lower and high momentum ranges. In the high
momentumrange,wewillgeneratepredictionsfor5.02
ii) P(E E ) is the energy loss probability. The
i f
TeV collision energy, where preliminary experimental →
probability is generalized to include both colli-
data are currently becoming available. The high mo-
sional[17]andradiative[15,16]energylossinthe
mentumsingleparticlepredictionsarenotavailablefor
same framework (i.e. realistic finite size dynam-
2.76 TeV, so in this range, we will compare our sin-
ical QCD medium), which abolishes the widely
gle particle predictions for 5.02 TeV (which are also
used approximation of static scattering centers.
applicable to 2.76 TeV, see above) with the available
It is also recently improved to include path-
jet measurements. The comparisonof the single parti-
length [21] and multi-gluon [22] fluctuations, as
cle predictions with the available jet data is motivated
well as running coupling [20] and finite magnetic
by the fact that, in the momentum region where both
mass [19].
(limited) single particle and jet R data exist, these
AA
two observables show the same suppression within the iii) D(Q HQ) is the parton to hadron HQ frag-
→
errorbars,as we present below. This observationleads mentation function. For light hadrons, D and
to a question of how the leading particle R predic- B mesons we use DSS [27], BCFY [28] and
AA
tions,donewithstate-of-the-artdynamicalenergyloss KLP [29] fragmentation functions, respectively.
model,comparewiththe wholejetR ,whichwewill Note, however, that for heavy flavor, fragmenta-
AA
hereaddress. Consequently,wewillhereprovideasys- tionfunctionsdonotinfluencethesuppressionof
tematic investigationof howthe predicted suppression heavy mesons [11]. That is, heavy mesonRAA is
depends on the probe type, the momentum and colli- a true probe of heavy quark RAA.
sion energy range, and how these predictions compare
with various available data. iv) Fornon-promptJ/Ψ,wealsohavetoincludethe
decay of B meson to J/ψ, which is represented
by the function f(H J/ψ) and obtained ac-
Q
→
cording to [26].
METHODS
Togeneratethesuppressionpredictionsforlightand
heavy flavor observables in Pb+Pb collisions at the
Thenumericalframeworkforgeneratingsuppression
LHCexperiments,weusedthefollowingparameterset:
predictions is presented in detail in [20]. We below
QGPwithperturbativeQCDscaleofΛ =0.2GeV
QCD
briefly outline the main steps in this procedure.
and effective light quark flavors n =3. In the calcu-
f
We study the angularaveragednuclearmodification lations, as a starting point we use an effective tem-
factor R , which is established as an excellent probe perature of 304 MeV for 0-40% centrality Pb+Pb col-
AA
for studying the interaction of high-momentum parti- lisions at the LHC [30] experiments (as extracted by
cles with QGP. R is the ratio of the quenched spec- ALICE); the average temperature for every central-
AA
trum in A+A collisions to the spectrum in p+p col- ity region is then determined according the procedure
3
given in [23]. Also, for every centrality region, we use data.
different path-length distributions, which areprovided Clear distinction in predictions between lower and
to us by [37]. The light quark mass is assumed to be high p⊥ rangesare observed. In addition, for lowerp⊥
dominated by the thermal mass M=µE/√6, where (the left panel of Fig. 1), it is obvious that the light
temperature dependent Debye mass µE is obtained and heavy flavor suppressions are significantly differ-
from [31]. The gluon mass is mg = µE/√2 [32], while ent. On the other hand, in the high p⊥ 100 GeV
∼
the charm and the bottom masses are, M=1.2GeV range (the right panel of Fig. 1), the predictions for
and M=4.75GeV, respectively. Magnetic to elec- all the probes (both light and heavy) almost overlap
tric mass ratio is 0.4 < µM/µE < 0.6, as extracted with each other. From pQCD perspective, a reason
from several independent non-perturbative QCD cal- for similar suppressionsat high momentum is that the
culations[33–36],sotheuncertaintyinthepredictions, mass of the probe becomes small compared to its mo-
presentedinthenextsection,willcomefromthisrange mentum, so the relevance of mass effects should also
ofscreeningmassesratio. Notethatourmodelusesno become small in this region. However, while plausi-
free parameters in comparison with the experimental ble/expected from pQCD perspective, this prediction
data,thatisalltheparameterscorrespondtostandard canbe quite distinct in otherapproaches,ase.g. AdS-
literature values. CFT predicts a clear suppression mass hierarchy,even
for high momentum regions [42, 43].
TheexperimentaldatashowninFig. 1areinagood
NUMERICAL RESULTS agreement with the generated theoretical predictions.
Moreover,these data also confirm the predicted quali-
In this section, we will generate predictions which tativedistinctionbetweenthelight/charmandbottom
correspond to the probe suppression at both lower suppressionsatlowermomentumregion. Atthehigher
( 10GeV) andhigh( 100GeV)momentumranges. momentum range, such comparison between the light
∼ ∼
At high momentum ranges, we will also compare the and heavy flavor experimental data cannot be made,
single particle and jet measurements with each other, as the corresponding single particle data are currently
and with the generated theoretical predictions. The available only for charged hadrons. Therefore, the
predictions will be generated both as a function of overlap of the light and heavy flavor suppressions at
probe momentum and the number of participants and high momentum ranges, provides a clear prediction to
for both light and heavy flavor observables. be tested by the upcoming experiments.
We first show predictions for the suppression de- For understanding the difference between D me-
pendence on the number of participants at 2.76 TeV sonandnon-promptJ/Ψ suppressions,we studied the
Pb+Pb collision energy. In Fig. 1 (left) we compare importance of different contributions to this suppres-
predictionswiththedatainthelowermomentumrange sion difference. Regarding this, note that it has been
(p⊥ 10GeV),whileinFig.1(right)wecomparepre- considered that this difference may largely originate
∼
dictions with the data in the high momentum range fromthedifferencesintheinitialdistributionsbetween
(p⊥ 100 GeV). Note that the formalism is devel- charm and bottom quarks, rather than the difference
∼ 2 2
oped under the assumption that M /E 1, so, for in their energy losses [39]. We show in Fig. 2 (left)
≪
all types of quarks (both light and heavy), our predic- that this is not the case, i.e. the contribution to the
tions are valid for p⊥ & 10 GeV. The predictions in suppression difference from the initial distributions is
Fig. 1 (left) are generated for J/Ψ and D mesons, and small, while the contribution due to the different en-
compared with the corresponding CMS experimental ergylossissubstantiallylarger. Notehoweverthatthe
data [38] - D meson data from ALICE [10], not shown contributions shown in the Fig. 2 (left) are not pure
for figure representation, are consistent with CMS D effects of initial distribution and energy loss. This is
meson data. Also, the charged hadrons (light probes) sinceJ/Ψsuppressionisnotadirectprobeofbquarks,
are not shown in Fig. 1 (left) for clarity, as it was i.e. it includes a decay from B mesons to J/Ψ, i.e.
previously shown that both experimental data [9, 10] f(B J/Ψ). Consequently, to exclude the decay
→
and theoretical predictions [11] largely overlap with contribution from these two effects, in Fig. 2 (mid-
those for D mesons. Since charged hadrons are in- dle) we show the same contributions but with the B
direct/complex probes, composed of both light quarks mesons (clear b quark probe) instead of J/Ψ. We see
andgluonswithnontrivialeffectoffragmentationfunc- that, in the case of B mesons, the energy loss contri-
tions [11], for mass tomography it is clearly beneficial bution becomes even larger, while the initial distribu-
to, whenever possible, concentrate on D mesons (clear tionbecomesevensmaller. Therefore,the strongmass
charm quark probes [11]) instead of charged hadrons. dependence of the suppression, which is observed and
InFig.1(right),thetheoreticalpredictionsforcharged predicted at lower momentum ranges,is clearly a con-
hadrons,DandB mesonsaregeneratedandshownto- sequence of the differences in the energy loss, rather
gether with the ATLAS charged hadron experimental than the consequenceof the initial distributions orde-
4
FIG. 1: RAA vs. Npart for single particles at the 2.76 TeV Pb+Pb collisions at the LHC experiments. Left
panel: Theoretical predictions for RAA vs. Npart are compared with CMS experimental data for D mesons [38] (red
triangles)andnon-promptJ/Ψ[41](orangecircles)in,respectively,8<p⊥ <16GeVand6.5<p⊥ <30GeVmomentum
regions. Gray bands with dashed, and dot-dashed boundaries, respectively, correspond to predictions for D mesons and
non-prompt J/Ψ in corresponding momentum regions. Right panel: Theoretical predictions for h±, D and B meson RAA
vs. Npart in 60 < p⊥ < 95 GeV momentum region are, respectively, provided as white bands with full, dashed and dot-
dashedboundaries. Theh± predictionsarecomparedwithATLAS(greensquares)[40]h± experimentaldatainthesame
momentumregion. Oneachpanel,theupper(lower) boundaryofeachgray (orwhite) bandcorrespondstoµM/µE =0.6
(µM/µE =0.4).
1 1 1
HaL HbL HcL
initialdistributioneffect initialdistributioneffect initialdistributioneffect
0.8 energylosseffect 0.8 energylosseffect 0.8 energylosseffect
J(cid:144)Ψ B
0.6 0.6 0.6
A A
A A B
R R
0.4 0.4 0.4
D D
0.2 0.2 0.2
D
p¦~10GeV 8<p¦<16GeV 0-10%
0 0
0 100 200 300 0 100 200 300 0 10 20 30 40 50
Npart Npart p¦HGeVL
FIG. 2: Suppression contributions. Left panel (a): Theoretical predictions for RAA vs. Npart are compared for D
mesons (dashed curve, 8 < p⊥ < 16 GeV momentum region) and non-prompt J/Ψ (dot-dashed curve, 6.5 < p⊥ < 30
GeV momentum region). Gray curve shows the analogous non-prompt J/Ψ predictions, if the originating bottom quark
wouldhavethesameenergylossascharmquarkinQGP.Middlepanel (b): Theoretical predictionsforRAA vs. Npart are
comparedforDandBmesonsin8<p⊥ <16GeVmomentumregion. Comparingtheleftandthemiddlepanelsshowsthe
effect of decay functions to the contributions analyzed in the left panel. Right panel (c): Theoretical predictions for RAA
vs. p⊥ are compared for D and B mesons. In the middle and the right panels, the curve legend is the same as in the left
panel. Oneach panel, thefullarrow pointstothecontribution ofthedifferentinitial distributionstothedifferenceinthe
suppressionbetweenDmesonandnon-promptJ/Ψ(orBmeson),whilethedashedarrowpointstothecontributionofthe
different energy losses to the difference between D meson and the non-prompt J/Ψ (or B meson) suppression. Magnetic
to electric mass ratio is set to µM/µE =0.4.
5
cay. Furthermore,we show in Fig. 2 (right) that there is a consequence of fragmentation function effect on
is no momentum region in which initial distribution the light partons that compose the charged hadrons.
makes a significanteffect onthe suppressiondifference That is, the effect of fragmentation functions on the
between different types of probes. Therefore, study- light quarks is to decrease their suppression (noted by
ing the difference betweenD andB mesonsuppression the vertical arrow in the right panel of Fig. 3); the
patterns in lower momentum region is not influenced gluon contribution (partially) compensate this effect
by the production, fragmentation and the decay, and (asdiscussedin[11]),butforp⊥ >100GeV,thegluon
thereforeallowsdirectlyassessinghowdifferentprobes contribution,andthereforethegluoncompensationef-
interact with QGP. fect, is small. Due to this, we conclude that, if our
While there are currently only limited data for sin- predicted larger RAA for h± compared to heavy flavor
gle particles at high momentum, these type of mea- (D and B) in the high p⊥ region is indeed experimen-
surements are expected to become increasingly avail- tallyobserved,thisincreasewillbeapureconsequence
able at 5.02 TeV Pb+Pb collisions at the LHC. At of the fragmentationfunction effect, and therefore not
5.02 TeV collision energy, the R measurements for related with the mass tomography in the QGP.
AA
charged hadrons are expected to become available up Moreover, the predictions presented in Fig. 3 show
to p⊥ 400 GeV, for D mesons the RAA measure- that the mass tomography effects can be clearly ob-
∼
ments might be available up to p⊥ 200 GeV, while served below 50 GeV. In particular, we see that be-
∼
for bottom mesons the measurements are expected up low 50 GeV, bottom suppression significantly differs
to p⊥ 100 GeV [44] and possibly even higher. It is, compared to charm and light probes. On the other
∼
therefore, useful providing single particle R predic- hand,suchadistinctiondoesnotappearforhighprobe
AA
tions in the high momentum region, and studying the momentum (above 50 GeV) where all the suppression
effects of high p⊥ mass tomography. predictions nearly overlap (apart from fragmentation
With this goal, in Fig. 3, we provide predictions for functionseffectdiscussedabove). Furthermore,wealso
charged hadrons, D and B mesons R at 5.02 TeV showed that indirect bottom probes (i.e. non-prompt
AA
0-10%centralPb+Pbcollisions at the LHC. From the J/Ψ) lower the dead-cone [8] effect compared to the
right panel, we see that at p⊥ 100 GeV, all types clear B meson probes. Consequently, we propose that
∼
of probes show similar suppressions, as supported by one should concentrate on the lower momentum range
the right panel of Fig. 1. However,for p⊥ >100 GeV, andonthedifferencebetweentheBmesonsuppression
we also observe that, while D and B (i.e. heavy) me- onone side, andD meson/chargedhadronsuppression
son R s become almost identical, the h± (i.e. light ontheotherside,forobservingsignificantmasstomog-
AA
hardon) R shows a surprising tendency for a lower raphy effects.
AA
suppression compared to heavy mesons. Moreover,we Furthermore, in [24], we have shown that, for heavy
see that the difference between light and heavy me- flavor,the R predictionsfor 5.02TeV and2.76TeV
AA
sonsuppressionincreasewithincreasingp⊥,leadingto overlap with each other, due to interplay between en-
more than 10%higher R for h± comparedto heavy ergy loss and initial distributions. In Fig. 4, we show
AA
mesons at p⊥ > 150 GeV. That is our observation is that the same conclusion is valid for charged hadrons
that, contrary to the 2.76 TeV collision energy where as well. We therefore conclude that all the predic-
overlap between h± and D meson R was observed tions/observationspresentedinthispaperarevalidfor
AA
for the entire momentum region where both data are both 2.76 TeV and 5.02 TeV collision energies.
available(p⊥ <50GeV), we here predictthat increas- With regard to this, we note that, while high p⊥
ing momentum (abovep⊥ of 100GeV) will leadto the data are not available for single particles at the cur-
separationin the RAA of these two observables,but in rently available 2.76 TeV collisions, high p⊥ data are
a different direction than intuitively expected. abundant for jets. As our theoretical predictions for
A naive conclusion from this prediction would be single particle R data at 5.02 TeV are also appli-
AA
that, for highly energetic partons, the light partons cable for 2.76 TeV collision energy, it is tempting to
start to lose notably less energy compared to heavy compare these predictions with the available jet data
partons,whichisnotinaccordancewithpQCD,asdis- at 2.76 TeV collision energy. Before comparing sin-
cussedjustafterthe Fig. 1. Tofurtherinvestigatethis gle particle predictions with the jet data, we address
issue, in the middle panel of Fig. 3, we compare R the same comparison with the experimental data, i.e.
AA
predictionsforbarequarks,i.e. forup,charmandbot- we start by asking how the single particle data and
tom quarks. We here observe that for p⊥ > 100 GeV, the jet measurements correspondto each other, in the
andinaccordancewithpQCD,finitemasseffectsforall momentum range where both are available. Conse-
types of quarksbecome negligible,leading to the same quently, in Fig. 5, we compare the available experi-
suppressions for both light and heavy flavor partons. mental data for charged hadrons (the green squares
However,fromtherightpanelofFig.3,weseethatthe and circles) and inclusive jets (the blue squares and
nonintuitive result observed in the left panel of Fig. 3, circles). In the left panel, we show the comparison of
6
1 1 0.7
HaL HbL HcL
0.8 h± 0.8 h±
u 0.6
0.6 0.6
A B A A u
RA RA b RA
0.4 0.4 0.5
D c
0.2 0.2
0.4
0 0
0 100 200 300 400 0 100 200 300 400 100 200 300 400
p¦HGeVL p¦HGeVL p¦HGeVL
FIG.3: RAA vs. p⊥ forsingleparticlesat the5.02TeVPb+Pb 0-10% central collisionsat theLHC.Leftpanel
(a): Theoretical predictions for h±, D and B meson RAA vs. p⊥ are, respectively, given as white bands with full, dashed
and dot-dashed boundaries. The upper (lower) boundary of each band corresponds to µM/µE = 0.6 (µM/µE = 0.4).
Middlepanel(b): TheoreticalpredictionsforbarequarkRAA vs. p⊥ areshownforu(dottedcurve),c(dashedcurve)and
b(dot-dashedcurve). µM/µE ratioissetto0.4. Right panel (c): Theoretical predictionsforRAA vs. p⊥ arecomparedfor
u (dotted curve) with h± (full curve). µM/µE ratio is set to 0.4.
suppression predictions, done with the dynamical en-
ergyloss,agreewiththejetsuppressionmeasurements.
Tothatend,inFig.6,weshowourpredictionsofR
AA
vs. p⊥ for the light (full curve), charm (dashed curve)
and bottom (dot-dashed curve) probes. These leading
particle predictions are shown together with inclusive
jets fromthe ATLAS experiments [14] (left panel)and
with both inclusive jets [13] and b-jets [12] from CMS
(rightpanel). Thepredictionsforbothlightandheavy
probes are in a good agreement with the available jet
measurements. This,togetherwiththe nearoverlapof
the single particle and the jet suppression data shown
in Fig. 5, therefore suggests that the leading particle
predictionsagreewellwiththejetR measurements.
AA
FIG. 4: Comparison of RAA predictions for charge Thereare few other importantconclusions: i) above
hadrons at 2.76 and 5.02 TeV. Charged hadron sup-
50 GeV, we predict almost the same suppressions for
pression predictions, as a function of transverse momen-
the light, charm and bottom quarks (see also the mid-
tum, are shown. RAA predictions at 5.02 TeV (2.76 TeV)
dle panel of Fig. 3); ii) this prediction, extrapolated
0-10% central Pb+Pb collisions at the LHC. are presented
as white bands with full (dashed) boundaries. The upper from the single particle predictions to the light and b-
(lower)boundaryofeachbandcorrespondstoµM/µE =0.6 jets, is in agreement with the measured experimental
(µM/µE =0.4). data. Sincecharmjetsuppressionisnotyetmeasured,
our result that the charm suppression overlaps with
the lightandbottomsuppressions,likelysuggeststhat
the measured suppression dependencies on the probe c-jetR willoverlapwithbothunidentifiedandb-jet
AA
momentum (for the similar, fixed centrality region), R s.
AA
while in the right panel, we show the comparison of Finally, the similarconclusionis also obtainedif the
themeasuredsuppressiondependenciesonthenumber suppression is analyzed as a function of the number
of participants (for the similar, fixed momentum re- of participants (Fig. 7). In particular, we also see
gion). Therefore,onecanseethatsimilarsuppressions that R vs. N single particle predictions for all
AA part
are observed for single particles and jets, i.e. while three types of probes nearly overlap with each other
the inclusive jets show a somewhat higher suppression and explain well the inclusive and b-jets data, which
comparedtochargedhadrons,theyarethesamewithin are also shown in the figure. Finally, the overlap of
the error bars. the suppression predictions is also consistent with the
The results presented above then motivate us to in- overlapin the data - similarly, as shown in Fig. 4, the
vestigate how our bare quark (i.e. leading particle) case of the charm jets is a new prediction to be tested
7
FIG. 5: Comparison of single particle and jet suppression data at the LHC experiments. Left panel: RAA
vs. p⊥ experimental data are compared for inclusive jets from ATLAS [14] (blue squares) and CMS [13] (blue circles)
and charged hadrons [40] from ATLAS (green squares) and CMS [45] (green circles). ATLAS jet data correspond to
0-10% centrality, while the other data correspond to 0-5% centrality. Right panel: RAA vs. Npart ATLAS experimental
data are compared for inclusive jets [14] (blue squares, 63 < p⊥ < 80 GeV) and charged hadrons [40] (green squares,
65<p⊥ <90 GeV).
FIG. 6: Single particle suppression predictions vs. jet data. Left panel: Theoretical RAA vs. p⊥ predictions for
single particles are compared with 0-10% centrality ATLASexperimentaldata for inclusivejets [14](bluesquares). Right
panel: RAAvs. p⊥ singleparticlepredictionsarecomparedwithCMSexperimentaldataforinclusivejets[13](bluecircles,
0-5% centrality) andb-jets[12](orangetriangles, 0-10% centrality). Oneach panel,whitebandswith dashed,dot-dashed
andfullboundaries,respectively,correspondtocharm,bottomandlightflavorpredictions,andtheupper(lower)boundary
of each band corresponds to µM/µE =0.6 (µM/µE =0.4).
by the future measurements. CONCLUSION
In this paper, we systematically explored the mass
tomographyeffects,whichcanbeobservedfordifferent
probes and in the wide momentum range correspond-
ingtothespanoftheavailableexperimentaldata. The
8
suppression [47–54]), but includes an advanced dy-
namicalenergy loss description for the leading parton.
Therefore, the agreement between the single particle
and jet R measurements, both with respect to the
AA
experimental data and the theoretical predictions is
currentlyunclear,andevenifthisagreementturnsout
to be accidental, understanding it may provide an im-
portant outlook for the future research.
Finally, we here provide clear predictions for the
upcoming experimental data at 5.02 TeV collision en-
ergy: for the single particle data, we predict that, at
the high momentum range p⊥ > 100 GeV, B and D
meson (and likely c and b-jet) R data will nearly
AA
overlap with each other. On the other hand, our pre-
±
dictions for h R unintuitively suggests a tendency
AA
for lower suppression compared to heavy mesons. We,
however, show that this lower suppression is a pure
consequence of fragmentation function effect on h±,
FIG. 7: Single particle suppression predictions vs.
while finite mass effect is negligible in this region. Fi-
jet data. Single particle predictions for RAA vs. Npart nally,wepredictedsignificantmasstomographyeffects
arecomparedwithATLASdataforinclusivejets[14](blue
related with B meson suppression below 50 GeV. As
squares, 80<p⊥ <100 GeV momentum region) and CMS
data for b-jets [12] (orange triangles, 80 < p⊥ < 90 GeV discussed above, these predictions also provide spe-
momentum region). Whitebandswith dashed,dot-dashed cific guidelines on where future experimental efforts
andfullboundaries,respectively,correspondtocharm,bot- related to this goal should be concentrated. For ex-
tom and light flavor predictions for 80 < p⊥ < 100 GeV. ample, given these results, we think that it is clearly
The upper (lower) boundary of each band corresponds to
beneficial to concentrate further efforts on improving
µM/µE =0.6 (µM/µE =0.4). b probe data in the relevant momentum region; this
can include both directly measuring B mesons instead
ofnon-promptJ/Ψ,reducingtheuncertainties,aswell
predictions of the suppression dependence from both
increasing the number of available measurements for
the momentum and the number of participants were
this important probe. With regards to this, note that
generated and compared with the available single par-
the CMS experiment already published their measure-
ticle and jet measurements. As a result, we obtained
mentofthe nuclearmodificationfactorforfully recon-
both the agreement of the theoretical results with the
structed B mesons in p+Pb collisions [55], while such
available data, and generated new predictions to be
measurementsinPb+Pbcollisionsareexpectedto be-
testedintheupcomingexperiments,aswebrieflysum-
come available soon from ALICE.
marized below.
Acknowledgments: We thank Yen-Jie Lee for use-
For the single particle predictions, we obtained that
ful discussions. This work is supported by Marie
significantmasstomographyeffects canbe noticedbe-
Curie IRG within the 7th EC Framework Programme
low 50 GeV, related with the difference between the
(PIRG08-GA-2010-276913)andbytheMinistryofSci-
bottom and the charm/light suppressions. While this
ence of the Republic of Serbia under project numbers
difference is sometimes attributed to different initial
ON173052and ON171004.
distributions for the charm and bottom quarks, we
here showed that this effect is almost entirely a conse-
quenceofthedifferencesintherespectiveenergylosses
(i.e. thedead-coneeffect),whiletheinitialdistribution
contribution to the difference is almost negligible.
[1] J. C. Collins and M. J. Perry, Phys. Rev. Lett. 34,
Furthermore, at the existing 2.76 TeV collision en- 1353 (1975).
ergy, we showed that the leading particle predictions [2] G.BaymandS.A.Chin,Phys.Lett.B62,241(1976).
agree well with the jet measurements. Moreover, the [3] M. Gyulassy and L.McLerran, Nucl.Phys.A750, 30
experimental results show that there is a reasonable (2005).
[4] E. V.Shuryak,Nucl. Phys.A 750, 64 (2005).
overlapbetweenthe single particleandjet suppression
[5] B.JacakandP.Steinberg,Phys.Today63,39(2010).
experimentaldata. Thesefindingsareinteresting,par-
[6] J. D. Bjorken: FERMILAB-PUB-82-059-THY (1982)
ticularly since our suppression approach does not in-
287, 292
cludethefeaturessuchasjetreconstruction[46](which [7] M. Djordjevic, M. Gyulassy and S. Wicks, Phys.Rev.
areconsideredcrucialforaccuratedescriptionof(di)jet Lett. 94, 112301 (2005).
9
[8] Yu.L.DokshitzerandD.Kharzeev,Phys.Lett.B519, [32] M. Djordjevic and M. Gyulassy, Phys. Rev. C 68,
199 (2001). 034914 (2003).
[9] ALICE collaboration, B. Abelev et al, Phys. Lett. B [33] Yu. Maezawa et al. [WHOT-QCD Collaboration],
720, 52 (2013). Phys. Rev.D 81 091501 (2010);
[10] J. Otwinowski (for the ALICE Collaboration), PoS [34] A.Nakamura,T.SaitoandS.Sakai,Phys.Rev.D69,
ConfinementX170 (2012). 014506 (2004).
[11] M. Djordjevic, Phys.Rev.Lett. 734, 286 (2014). [35] A. Hart, M. Laine and O. Philipsen, Nucl. Phys. B
[12] CMS Collaboration, S. Chatrchyan et al., Phys. Rev. 586, 443 (2000).
Lett.113, 132301 (2014). [36] D.Bak,A.Karch,L.G.Yaffe,JHEP0708,049(2007).
[13] G.I.Veres(fortheCMSCollaboration) Nucl.Phys.A [37] A. Dainese, Eur. Phys. J. C 33, 495 (2004).
904−905, 146c (2013). [38] CMSCollaboration (talkbyB.HongatQuarkMatter
[14] ATLASCollaboration, G.Aadet al.,Phys.Rev.Lett. 2015)
114 072302 (2015). [39] ALICE Collaboration, J. Adam et. all, JHEP 1511
[15] M. Djordjevic, Phys.Rev.C 80, 064909 (2009). 205 (2015)
[16] M. Djordjevic and U. Heinz, Phys. Rev. Lett. 101, [40] ATLASCollaboration, G.Aadetal.,JHEP1509,050
022302 (2008). (2015).
[17] M. Djordjevic, Phys.Rev.C 74, 064907 (2006). [41] CMSCollaboration,S.Chatrchyanetal.,JHEP1205,
[18] B.BlagojevicandM.Djordjevic,J.Phys.G42,075105 063 (2012).
(2015). [42] W. A. Horowitz, Phys.Rev.D 91, 085019 (2015).
[19] M. Djordjevic, Phys.Lett. B 709, 229 (2012). [43] W. A. Horowitz, Nucl. Phys. A 904-905, 186c-193c
[20] M. Djordjevic and M. Djordjevic, Phys. Lett. B 734, (2013).
286 (2014). [44] Private communication with Yen-JieLee.
[21] S. Wicks, W. Horowitz, M. Djordjevic and M. Gyu- [45] CMS Collaboration, S. Chatrchyan et al., Eur. Phys.
lassy, Nucl. Phys.A 784, 426 (2007). J. C 72, 1945 (2012).
[22] M.Gyulassy,P.LevaiandI.Vitev,Phys.Lett.B538, [46] M. Cacciari, G.P.Salam, and G.Soyez,Eur.Phys.J.
282 (2002). C bf 72, 1896 (2012).
[23] M.Djordjevic,M.DjordjevicandB.Blagojevic, Phys. [47] J.Casalderrey-Solana,J.G.MilhanoandU.A.Wiede-
Lett.B 737, 298 (2014). mann, J. Phys. G 38, 035006 (2011)
[24] M. Djordjevic and M. Djordjevic, Phys. Rev. C 92, [48] C.Young,B.Schenke,S.JeonandC.Gale,Phys.Rev.
024918 (2015). C 84, 024907 (2011)
[25] Z. B. Kang, I. Vitev and H. Xing, Phys. Lett. B 718, [49] Y. He, I. Vitev and B. W. Zhang, Phys. Lett. B 713,
482(2012),R.Sharma,I.VitevandB.W.Zhang,Phys. 224 (2012)
Rev.C 80, 054902 (2009) [50] F.Senzel,O.Fochler,J.Uphoff,Z.XuandC.Greiner,
[26] M.Cacciari,S.Frixione,N.Houdeau,M.L.Mangano, J. Phys.G 42, no. 11, 115104 (2015)
P.Nason and G. Ridolfi, JHEP 1210, 137 (2012) [51] X. N. Wang and Y. Zhu, Phys. Rev. Lett. 111, no. 6,
[27] D.deFlorian,R.SassotandM.Stratmann,Phys.Rev. 062301 (2013)
D 75, 114010 (2007). [52] G.Y.QinandB.Muller,Phys.Rev.Lett.106,162302
[28] M. Cacciari, P. Nason, JHEP 0309, 006 (2003), E. (2011) [Phys. Rev.Lett. 108, 189904 (2012)]
Braaten, K.-M. Cheung, S. Fleming and T. C. Yuan, [53] G. L.Ma, Phys. Rev.C 87, no. 6, 064901 (2013)
Phys.Rev.D 51, 4819 (1995) [54] K. C. Zapp, F. Krauss and U. A. Wiedemann, JHEP
[29] V. G. Kartvelishvili, A.K. Likhoded, V.A. Petrov, 1303, 080 (2013)
Phys.Lett. B 78, 615 (1978). [55] CMSCollaboration,V.Khachatryanetal.,Phys.Rev.
[30] M. Wilde (for the ALICE Collaboration) Nucl. Phys. Lett. 116, 032301 (2016).
A 904-905 573c (2013)
[31] A.Peshier, hep-ph/0601119 (2006).