arxiv:0810.3204v2 [nucl-ex] 16 dec 2008 · epj manuscript no. (will be inserted by the editor)...

EPJ manuscript No.(will be inserted by the editor)

Evidence for the production of thermal muon pairs with massesabove 1 GeV/c2 in 158A GeV Indium-Indium collisions

NA60 Collaboration

R. Arnaldi11, K. Banicz4,6, K. Borer1, J. Castor5, B. Chaurand9, W. Chen2, C. Cicalo3, A. Colla11, P. Cortese11,S. Damjanovic4,6, A. David4,7, A. de Falco3, A. Devaux5, L. Ducroux8, H. En’yo10, J. Fargeix5, A. Ferretti11,M. Floris3, A. Forster4, P. Force5, N. Guettet4,5, A. Guichard8, H. Gulkanian12, J.M. Heuser10, M. Keil4,7,L. Kluberg9, Z. Li2, C. Lourenco4, J. Lozano7, F. Manso5, P. Martins4,7, A. Masoni3, A. Neves7, H. Ohnishi10,C. Oppedisano11, P. Parracho4,7, P. Pillot8, T. Poghosyan12, G. Puddu3, E. Radermacher4, P. Ramalhete4,7,P. Rosinsky4, E. Scomparin11, J. Seixas7, S. Serci3, R. Shahoyan4,7 a, P. Sonderegger7, H.J. Specht6, R. Tieulent8,G. Usai3, R. Veenhof7, and H.K. Wohri3,7.1 Laboratory for High Energy Physics, Bern, Switzerland.2 BNL, Upton, New York, USA.3 Universita di Cagliari and INFN, Cagliari, Italy.4 CERN, Geneva, Switzerland.5 LPC, Universite Blaise Pascal and CNRS-IN2P3, Clermont-Ferrand, France.6 Physikalisches Institut der Universitat Heidelberg, Germany.7 IST-CFTP, Lisbon, Portugal.8 IPN-Lyon, Univ. Claude Bernard Lyon-I and CNRS-IN2P3, Lyon, France.9 LLR, Ecole Polytechnique and CNRS-IN2P3, Palaiseau, France.

10 RIKEN, Wako, Saitama, Japan.11 Universita di Torino and INFN, Italy.12 YerPhI, Yerevan, Armenia.

Date: 11/12/2008

Abstract. The yield of muon pairs in the invariant mass region 1<M<2.5 GeV/c2 produced in heavy-ioncollisions significantly exceeds the sum of the two expected contributions, Drell-Yan dimuons and muonpairs from the decays of D meson pairs. These sources properly account for the dimuons produced inproton-nucleus collisions. In this paper, we show that dimuons are also produced in excess in 158 A GeVIn-In collisions. We furthermore observe, by tagging the dimuon vertices, that this excess is not due toenhanced D meson production, but made of prompt muon pairs, as expected from a source of thermaldimuons specific to high-energy nucleus-nucleus collisions. The yield of this excess increases significantlyfrom peripheral to central collisions, both with respect to the Drell-Yan yield and to the number of nucleonsparticipating in the collisions. Furthermore, the transverse mass distributions of the excess dimuons arewell described by an exponential function, with inverse slope values around 190 MeV. The values areindependent of mass and significantly lower than those found at masses below 1 GeV/c2, rising there upto 250 MeV due to radial flow. This suggests the emission source of thermal dimuons above 1 GeV/c2 tobe of largely partonic origin, when radial flow has not yet built up.

PACS. 14.40.Lb – 25.75.Nq – 25.75.Cj

1 Introduction

The intermediate mass region (IMR) of the dimuon massspectrum, between the φ and the J/ψ resonances, is ex-pected to be well suited to search for thermal dimuonproduction [1], due to the favourable relative productionyield with respect to the other contributions (Drell-Yandimuons, meson decays, etc).

a Corresponding author: ruben.shahoyan@cern.ch

Intermediate mass dimuon production in proton-nucle-us and heavy-ion collisions was previously investigated byNA38 [2] and HELIOS-3 [3] in p-W and S-U(W) collisionsat 200 GeV, and by NA50 [4,5] in p-A (where A standsfor Al, Cu, Ag, W) and Pb-Pb collisions, respectively at450 and 158 GeV. All three experiments reported a veryreasonable description of the IMR opposite-sign dimuonmass continuum measured in the “elementary” proton-nucleus collisions. This continuum could be accounted for

2 NA60 Collaboration: Evidence for thermal-like IMR dimuon production in In-In collisions.

WallMWPCs

Vertextelescope

Beam tracker+ target

Triggerhodoscopes

Toroidalmagnet

Hadron absorber

hodoscopesTrigger

fielddipole2.5 T

Muon Spectrometer

Fig. 1. Schematic representation of the NA60 experimental layout.

by a superposition of the two expected “signal” processes,the Drell-Yan dimuons and the muon pairs resulting fromsimultaneous semi-muonic decays of (correlated) D andD mesons, on the top of a “background” contribution.The latter is due to uncorrelated decays of pions andkaons and can be estimated from the measured like-signmuon pairs. In contrast, all experiments observed that theopposite-sign dimuon samples collected in the heavy-ioncollision systems, taking into account the estimated back-ground contribution, significantly exceeded the level ex-pected from Drell-Yan and “open charm” sources, calcu-lated using the same procedures that successfully repro-duced the p-A data.

As discussed in [6], two prime interpretations were ableto describe the findings of NA38 and NA50 equally well:the long-sought thermal dimuons [7], and an increase inthe open charm production cross section per nucleon, fromp-A to A-A collisions [8]. Several other reasons whichcould increase the yield of IMR dimuons were also pro-posed. Alternatively to charm enhancement, the numberof muon pairs entering the phase space window of theexperiment could be increased, while the total charm pro-duction cross section remains unchanged. This could re-sult from, e.g., the smearing of the D/D pair correla-tion resulting from rescattering of the charmed quarksor mesons in the surrounding dense matter [9]. It wasalso suggested that the mass spectrum of the Drell-Yandimuons could be modified in heavy-ion collisions with re-spect to the proton-nucleus case, because of higher-twisteffects that increase the yield of low mass dimuons [10].Another source of dimuons that could be present in heavy-ion collisions, while being negligible in p-nucleus colli-sions, is secondary Drell-Yan production, where the quark-antiquark annihilation uses valence antiquarks from pro-duced pions [11].

A decisive step in understanding the origin of the ex-cess dimuons is to clarify the decade-long ambiguity be-tween prompt dimuons and off-vertex muon pairs. In thefirst case they can be thermal dimuons or extra Drell-Yandimuons; in the second case they result from decays of Dmesons, which have a relatively long lifetime: cτ = 312 µmfor the D+ and 123 µm for the D0. The clarification of the

physical origin of the IMR dimuon excess was one of themain motivations of the NA60 experiment. Thanks to itsability to measure the offset of the muons with respect tothe interaction vertex, NA60 can separate, on a statisticalbasis, the prompt dimuons from the off-vertex muon pairs.

In this paper we present a study of the intermediatemass dimuons produced in In-In collisions at 158 GeV/nuc-leon, based on data collected by the NA60 experimentin 2003. The paper is organized as follows: Section 2 de-scribes the NA60 experimental setup, the data reconstruc-tion procedure and the general performance of the appa-ratus; Section 3 explains in some detail the backgroundsubtraction procedure; Section 4 presents the results. Pre-liminary results were presented before [12].

2 The NA60 experimental setup and datareconstruction

Figure 1 shows a general view of the NA60 apparatus. Itsmain components are the muon spectrometer (MS), previ-ously used by the NA38 and NA50 experiments [13], and anovel radiation-hard silicon pixel vertex tracker (VT) withhigh granularity and high readout speed [14], placed insidea 2.5 T dipole magnet just downstream of the targets (seeFig. 2). The first spectrometer is separated from the sec-

dipole, 2.5 T

tracker

vertex

tgt.boxbeam tracker

muonfilter

Fig. 2. View of the target region. From the left: 2 stations ofthe beam tracker followed by 7 Indium targets and 16 planesof the vertex tracker.

ond by a hadron absorber with a total effective thicknessof ∼ 14 λint and ∼ 50 X0.

NA60 Collaboration: Evidence for thermal-like IMR dimuon production in In-In collisions. 3

Before entering into more details, we list the key fea-tures of this somewhat unique setup:

– The vertex telescope tracks all charged particles up-stream of the hadron absorber and determines theirmomenta independently of the MS, free from multiplescattering effects and energy loss fluctuations in theabsorber. The matching of the muon tracks before andafter the absorber, both in coordinate and momentumspace, strongly improves the dimuon mass resolution inthe low-mass region (less so higher up), significantlyreduces the combinatorial background due to π andK decays and makes it possible to measure the muonoffset with respect to the primary interaction vertex.

– The additional bend by the dipole field in the targetregion deflects muons with lower momenta into theacceptance of the MS, thereby strongly enhancing theopposite-sign dimuon acceptance, in particular at lowmasses and low transverse momenta, with respect toall previous dimuon experiments. A complete accep-tance map in two-dimensional M-pT space is containedin [15].

– The selective dimuon trigger and the radiation-hardvertex tracker with its high read-out speed allow theexperiment to run at very high rates for extended peri-ods, maintaining the original high luminosity of dimuonexperiments despite the addition of an open spectrom-eter.

A detailed description of the muon spectrometer canbe found in [13]. Its magnet defines the rapidity windowwhere the dimuons are accepted, 3 < ylab < 4. The triggersystem is based on four hodoscopes along the beam di-rection. Each of them has hexagonal symmetry, with thesextants operating independently. The system provides ahighly selective dimuon trigger requiring that the four ho-doscope slabs hit by each muon match one of the prede-fined patterns. This ensures that the muon was producedin the target region. In addition, the trigger imposes thatthe two muons must be detected in different sextants.

A detailed description of the radiation-hard silicon pixelvertex tracker used by NA60 in 2003 can be found in [16].The readout pixel chips, developed for the ALICE andLHC-B experiments [17], operate with a 10 MHz clockfrequency. The VT can provide up to 12 space points pertrack, 9 of them from planes oriented such that the hori-zontal coordinate (in the bending plane) is measured withhigher precision.

The target system is composed of seven Indium sub-targets, 1.5 mm thick each and separated by an inter-distance of 8 mm, adding up to an interaction probabil-ity of 16 % for the incident Indium ions. An interactioncounter is located downstream of the VT. It is made of2 scintillator blades, appropriately holed to let the beampass through. They are independently read by 2 photo-multiplier tubes in coincidence and thus allow to tag theinteractions in the target region. A beam tracker [18],made of two tracking stations 20 cm apart, was placedupstream of the target system. The beam tracker allowsto measure the flight path of the incoming ions and to de-rive the transverse coordinates of the interaction point, in

the target, with an accuracy of 20 µm, independently ofthe collision centrality. A zero degree calorimeter, previ-ously used in NA50, is located in the beam line, inside themuon filter, just upstream of the Uranium beam dump. Itestimates the centrality of each nucleus-nucleus collisionthrough the measurement of the energy deposited by thebeam “spectator” nucleons.

Around 230 million dimuon triggers were recorded ontape during the 2003 run. In approximately half of theseevents a dimuon was reconstructed from the muon spec-trometer data. Two data samples were collected, with dif-ferent currents in the ACM toroidal magnet: 4000 A and6500 A. The higher field reduces the acceptance in thehighly populated region of low transverse mass (mT) muonpairs, thereby increasing the number of high mass dimuonevents collected per day, for a constant lifetime of the dataacquisition system. The details of the event selection canbe found in [16].

The reconstruction of the raw data proceeds in severalsteps. First, muon tracks are determined from the data ofthe eight MWPCs and validated by the hits recorded inthe trigger hodoscopes. If the event has two reconstructedmuon tracks which fulfil the trigger conditions, the tracksin the silicon planes of the vertex tracker are also recon-structed, and the interaction vertices are searched for. Thetrack reconstruction efficiency is ∼ 95 % for peripheral In-In collisions and ∼ 90 % for the most central ones. The keystep in the data reconstruction is the matching betweenthe muon track, extrapolated from the muon spectrome-ter to the target region, and the charged tracks found inthe vertex tracker. This is done by selecting those associa-tions between the MS tracks and the VT tracks which givethe smallest weighted squared distance (matching χ2) be-tween these two tracks, in the space of angles and inversemomenta, taking into account their error matrices. Thematching procedure combines the good MS momentumresolution (σp/p ∼ 2 %) with the excellent VT angularprecision (' 1 mrad) to obtain the kinematics of the muonbefore undergoing the multiple scattering and energy lossinduced by the hadron absorber. This procedure, as men-tioned before, improves the dimuon mass resolution, from70-80 MeV/c2 to 20-25 MeV/c2 in the ω and φ mass re-gion, and allows to correlate the muon’s trajectory withthe interaction vertex, the point of primary interest forthe present paper.

The resolution of the vertex determination, and its de-pendence on the number of tracks associated with the ver-tex, can be obtained from the dispersion between the mea-surements provided by the beam tracker and by the vertextracker. As shown in Fig. 3, it is better than 10 µm in xand 15 µm in y, except for the most peripheral collisions.

Figure 4 shows the distribution of the z coordinate ofthe reconstructed vertices, for the events with only onevertex found. We can clearly identify the seven In targets,placed between the two windows that keep the target boxin vacuum, downstream of the two beam tracker stations,also placed in vacuum.

The resolution of the offset distance measured betweenthe matched muon tracks and the collision vertex can be

TracksN50 100 150 200

µ (σ

Fig. 3. Dispersion between the transverse coordinates of theinteraction vertex given by backtracing the VT tracks and byextrapolating the beam tracker measurement (open symbols),as a function of the number of tracks attached to the vertex.Derived vertex resolution (solid symbols).

Z (cm)-50 -40 -30 -20 -10 0 10

In targets

BT sensors

Beam windows

Fig. 4. Distribution of the z coordinate of the interaction ver-tex for the events that only have one good vertex reconstructed.

evaluated by using the muons from J/ψ decays. Since theB → J/ψ contribution is negligible at SPS energies, all theJ/ψ mesons are promptly produced. Moreover, the pionand kaon decay background is negligible under the J/ψpeak. Therefore, the offset distribution made with thesemuons (shown in Fig. 5) directly reflects the resolution ofthe muon offset measurement: 37 µm in x (bending plane)and 45 µm in y. These values are the convolution of thetrack uncertainties with the accuracy of the transversecoordinates of the vertex.

Since the offset resolution of the matched tracks isaffected by multiple scattering in the silicon planes, theanalysis is performed using a weighted muon offset vari-able, essentially insensitive to the particle’s momentum.Its definition is

∆µ =√∆x2V −1

xx +∆y2V −1yy + 2∆x∆yV −1

xy , (1)

m)µOffset (-600 -400 -200 0 200 400 600

Fig. 5. Offset distribution for matched muons from J/ψ de-cays, in the x (circles) and y (triangles) coordinates, normalizedto unit area.

where V −1 is the inverse error matrix accounting for theuncertainties of the vertex fit and of the muon kinematicsfit. ∆x and ∆y are the differences between the coordinatesof the vertex and those of the extrapolated muon track, inthe transverse plane crossing the beam axis at z = zvertex.We then characterize the dimuon through the weighteddimuon offset, defined as

∆µµ =√

(∆2µ1 +∆2

µ2)/2 . (2)

3 Background subtraction

The sample of collected dimuons include a combinatorialbackground (CB) originating from decays of uncorrelatedhadrons, mostly π’s and K’s. Since the production and de-cay of the parent hadrons are independent processes, thiscombinatorial background (CB) contributes in the sameway to the opposite-sign and like-sign samples of muonpairs, increasing quadratically with the charged particlemultiplicity. It is important to emphasise that the NA60trigger treats in exactly the same way the opposite-signand the like-sign muon pairs.

While this kind of background was already present inprevious dimuon experiments, such as NA38 and NA50,a new type of background appears in the NA60 dimuonspectra due to the matching procedure. Indeed, any VTtrack having a small enough matching χ2 with respectto the muon track is considered a matching candidate.For high enough charged particle multiplicities, the muontrack will have several possible matches and, naturally, atmost one of them is correct. All the other associations arefake matches and, if selected, need to be subtracted. Pairswhere one muon match is fake and the other one is cor-rect are also part of the fake matches dimuon background(FB). Because the probability of having a fake match, foreach muon, is proportional to the track density, the yieldof matched muon pairs where only one muon is fake riseslinearly with the charged particle multiplicity, while theyield of doubly fake pairs rises quadratically.

Fig. 6 shows the single muon matching χ2 distributionsfor correct and fake matches, normalized to unit area. Thedistribution for fake matches is obtained from the realdata using the mixed-events technique (see section 3.2):each muon from the MS is matched with the VT tracksof another event with the same vertex position and mul-tiplicity. Since the probability of having a fake match isdetermined only by the density of the non-muon tracksin the phase space of the matching parameters, the ob-tained distribution of the fake matches is automaticallyobtained with correct normalization. By subtracting itfrom all matches, the distribution for the correct ones isobtained. One can see that the distribution for the fakematches is much flatter than the corresponding distribu-tion for the correct matches. Selecting exclusively matcheswith a matching χ2 below a certain threshold value, thesignal-to-background ratio can be improved at the expenseof losing some fraction of the signal.

2χMatching 0 0.5 1 1.5 2 2.5 3

Correct Matches

Fake Matches

Fig. 6. Matching χ2 distributions for correct and fake matches,normalized to unit area.

Despite generating the fake matches background, themuon matching procedure leads to a very significant re-duction of the combinatorial background due to muonsfrom pion and kaon decays. This happens for two rea-sons. First, when the pions or kaons decay within the ver-tex tracker, the kink at the decay point prevents mostof the muon tracks from being reconstructed by the sil-icon tracker, thereby removing these decay muons fromthe matched muons sample. Second, if the pions or kaonsdecay downstream of the vertex tracker, the matching be-tween the meson track and the muon track usually resultsin rather large matching χ2 values due to the kink be-tween the parent meson and decay muon. By only select-ing matches of relatively low χ2 values, we suppress theyield of correctly matched muons from π,K decays.

3.1 Combinatorial background

The combinatorial background contribution to the oppo-site-sign dimuon distributions can be evaluated from the

measured like-sign muon pair samples, using an event mix-ing technique. Two muons from different events with simi-lar characteristics are randomly picked and paired to buildthe “mixed CB” sample. Only muon pairs respecting thedimuon trigger conditions are kept (in particular, the mu-ons must be in different sextants). Additionally, a sextant-dependent weight is applied to the measured muons to cor-rect the bias introduced by the “different-sextants” triggerrequirement. The mixing is done separately in 40 narrowbins in centrality in order to avoid the bias due to thevariation of the single muon kinematics and the µ+/µ−ratio within the bin width. The technical details are givenin Appendix A. It is important to notice that this mixed-event procedure reproduces not only the shape of the CBspectra but also their absolute normalization.

An important issue to consider in the CB generationconcerns the selection of the muons used for the mixingand for the computation of the sextant-dependent weights:they must share the same target, the same field polar-ities, the same charged track multiplicity bin, and thesame configuration of the silicon pixel planes (same ac-ceptances, efficiencies, etc). Since we are interested in de-termining the background contributions to the matchedopposite-sign dimuon spectra, it could seem natural toonly use for the event mixing single muons which have atleast one match. This would ensure that the normaliza-tions, given by Eq. (A-7), would be correctly computedfor the matched dimuons spectra. Unfortunately, in thecase of the analysis presented in this paper, the eventmixing must be made using all muons (including non-matched muons), for reasons explained in the next sec-tion. Therefore, the computed normalizations correspondto all the dimuons reconstructed in the muon spectrome-ter, matched and non-matched.

The accuracy of the mixed-event method can be evalu-ated by comparing the mixed and measured distributionsof like-sign muon pairs, as shown in Figs. 7 and 8, respec-tively for the mass and weighted offset (see also section 3.4below).

3.2 Fake matches background

The most direct way to evaluate the fake matches back-ground is to use the overlay Monte Carlo method: the VThits of generated dimuons are superimposed on the VThits of measured data, in order to ensure realistic occu-pancy conditions. By definition, every matched track builtwithout the sufficient number of the Monte Carlo muonhits is a fake match (conventionally we define the match asfake if the track has more than two non-muon hits). Thismethod works well for studies that do not use the muonoffset information. However, while the kinematic variablesof the dimuons are quite robust with respect to the un-avoidable differences between the measured and simulateddata (in particular the residual misalignment of the geo-metrical setup), the offset distribution is much more sen-sitive. Therefore, for studies which require the muon offsetinformation, such as the study reported in this paper, wehad to develop a fake subtraction procedure which only

410Like-Sign dimuons

/ ndf 2χ 15.8 / 14p0 0.005± 1.001 p1 0.0058± 0.0003

)2Mass (GeV/c1 2 3

Fig. 7. Measured (squares) and mixed (circles) like-signdimuon mass spectra (top) and their ratio (bottom).

uses measured data and provides reliable spectra in anydimuon parameter.

This is again achieved by an event mixing technique,matching the muons of a given event with the VT tracksof other events (with the same production target, chargedmultiplicity, running conditions, etc.), for the real dataand for the artificial CB sample. Since the real data samplealso contains dimuons where only one of the two muonswas incorrectly matched, we added to our simulated FBsample a certain proportion of muon pairs where one ofthe muons retains its own match (see Appendix B).

In principle, there could be two alternative approachesfor reproducing the matched dimuons. If the two muontracks from the MS have m1 and m2 matches, then thereare m1×m2 matched dimuons. Given the different shapesof the χ2 distributions for correct and fake matches (Fig. 6),the pair composed by the two best matches (those withthe smallest χ2) has the highest probability of being thecorrect one. However, this probability decreases with theincrease of the number of matching candidates, leadingto a degradation of the correct matching efficiency fromperipheral to central collisions. Also, as explained in Ap-pendix B, since it appears impossible to estimate analyti-cally the amount of FB in such best matches spectra, oneshould rely on the overlay Monte Carlo method. Alterna-tively, one can consider all m1 ×m2 matches for a givenMS dimuon. Although this will increase the amount of FBto subtract – hence increasing the statistical error – such

DataMixed

/ ndf 2χ 23.6 / 14p0 0.003± 1.003 p1 0.0016± -0.0016

Dimuon weighted offset0 2 4 6 8 10

Fig. 8. Same as previous figure but for the dimuon weightedoffset.

“all matches dimuon spectra” offer a better control of thesystematic errors, and allow us to cross-check the MonteCarlo based subtraction method. The results presented inthis paper are obtained using this “all matches” proce-dure. Finally, to reproduce the offsets of the fake matchesat the interaction vertex, we apply the same algorithm asused for the CB (see Appendix B).

The top panel of Fig. 9 shows the mass distribution ofMonte Carlo ω dimuons (with “all matches”) and thoseof the fake contributions, both as estimated by MonteCarlo tagging and by event mixing. The bottom panelshows the ratio between the mixed and the MC-taggedfake backgrounds. Both methods are seen to agree in themass range having meaningful statistics.

3.3 Extraction of the correctly matched signal

The CB and FB contributions obtained via event mixingare not independent from each other. As explained above,the combinatorial pairs can be correct or fake matches,CB = CBcorr + CBfake. Clearly, the latter is also presentin the total sample of “fake” pairs, due to signal or tocombinatorial dimuons, FB = FBsig + FBcb, with FBcb

≡ CBfake. Therefore, if we subtract the total fake back-ground and the total combinatorial background from thedata, we do not obtain the correctly matched signal, be-cause the “fake combinatorial” pairs are subtracted twice:Data − FB − CB = Data − FBsig − CBcorr − 2CBfake =

Monte-Carloω

All Matches

FB "Mixed"

FB "MCTagged"

/ ndf 2χ 11.86 / 15p0 0.0067± 0.9992

)2Mass (GeV/c0.4 0.6 0.8 1 1.2 1.4

Fig. 9. Top: Dimuon mass distributions for the ω simulation,using “all matches” (points), and for the FB, obtained withthe event mixing technique (filled squares) or by Monte Carlotagging (open squares). Bottom: Ratio between “mixed” and“MC-tagged” fake distributions.

Signal−CBfake. To avoid this double subtraction, we mustestimate the “fake combinatorials” contribution. This isdone by applying the CB estimation algorithm describedin Appendix A to the generated FB sample, using its like-sign pairs for the event mixing.

Figure 10 shows the mass spectra (integrated over allcollision centralities) for the measured opposite-sign dimu-ons, full combinatorial and fake signal background sources,and the extracted correctly matched signal.

Figure 11 shows the dimuon weighted offsets distribu-tions. It is worth noticing that the region 2 < ∆µµ < 6, de-

)2Mass (GeV/c1 2 3 4 5

510 Data

Signal

Fake Signal

Fig. 10. The measured opposite-sign dimuon mass spectrum(points), the signal (bullets: correctly matched; solid line: in-correctly matched), and the combinatorial background (bothcorrectly and incorrectly matched: dashed line) for the 4000 Adata with matching χ2 <1.5.

cisive to disentangle the open charm contribution from theprompt one, has a significant level of incorrectly matchedsignal.

3.4 Systematic errors from the background subtraction

The yield of like-sign dimuons remaining after the subtrac-tion of the mixed-event spectra constitutes a very good es-timate of the residual combinatorial background contribu-tion left in the opposite-sign spectra. Based on the ratiosshown in Fig. 7, 8, the accuracy of the generated back-ground is estimated to be ∼ 1%. The resulting system-atic uncertainty of the extracted signal is defined by thesignal-to-background ratio which strongly depends on thekinematic bin and the cut imposed on the matching χ2.Being comparable to the statistical error, it changes from∼ 25% for pT <0.25 GeV/c at masses around 1.2 GeV/c2to ∼ 1% near 2.5 GeV/c2 with a lose cut χ2=3, and itimproves by more than a factor 2 for a χ2=1.5 cut.

To account for these systematic errors in the severalfits mentioned in the next section, whenever necessary, thestatistical errors of the estimated background were glob-ally scaled up to ensure that the residuals of the like-signspectra are compatible with zero within three standarddeviations. Even in the worst case (when fitting a pT dis-tribution in a narrow dimuon mass range), the errors werenot increased by more than ∼ 10 %.

The results presented in the next section were checkedby repeating the fits with both cuts on the χ2 and bothlow and high magnetic field data and were found to bealways compatible within the quoted errors.

4 Results

4.1 Expected sources of IMR dimuons

The analysis was separately performed for the 4000 A and6500 A event samples. Dimuons were selected in the kine-

Dimuon weighted offset0 5 10 15 20

4102Data, 1.16<M<2.56 GeV/c

Fake Signal

Signal

Fig. 11. Data, signal and background spectra for weighteddimuon offset distributions (defined in Eq. 2) in IMR for 4000 Adata with matching χ2 <1.5.

matical domain defined by 0 < ycms < 1 and | cos θCS| <0.5, where θCS is the Collins-Soper decay angle. Only eventswith a single reconstructed vertex in one of the seven In-dium targets were kept for the analysis. Since the signal-to-background ratio strongly depends on the matching χ2

cut (see Fig. 6), the data were analyzed with two differentcuts (χ2 < 1.5 and χ2 < 3) to evaluate possible systematiceffects related to the background subtraction.

The shapes of the Drell-Yan and open charm con-tributions were obtained with the Pythia Monte Carloevent generator [19] version 6.325, using the CTEQ6Lset of parton distribution functions [20] including nucleareffects through the EKS98 model [21]. The primordialkT was generated from a Gaussian distribution, of width0.8 GeV/c for Drell-Yan (to describe the pT distributionof dimuons heavier than the J/ψ) and 1.0 GeV/c for theopen charm [22]. The charm quark mass was kept at thedefault value of 1.5 GeV/c2 and the PV parameter (proba-bility that the c-quark hadronizes in vector states) was setto 0.6 [23], resulting in an effective cc→ µ+µ− branchingratio 0.84 %.

The Pythia events were generated at the vertices ofreal events and propagated through the experimental setupusing the Geant 3.2 transport code [24]. The resulting hitswere added to those of the real event used to set the in-teraction vertex and the resulting overlay Monte Carloevents were then reconstructed, with the codes used toprocess the measured data. We only kept the events sur-viving the selection cuts also applied to the real data. Itis worth noticing that the | cos θCS| < 0.5 window signifi-cantly cuts the open charm contribution, because Pythia’sstrong D/D pair correlations give a cos θCS distributionpeaked at −1 and +1. This means that the fraction ofaccepted dimuons from D pair decays is small and verysensitive to the kinematic distributions and correlationsused in Pythia. Figure 12 shows the cos θCS distributionof the cc→ µ+µ− dimuons, with mass in the range 1.16–2.56 GeV/c2, before and after the reconstruction step.

CSθcos -1 -0.5 0 0.5 1

-µ +µ → cc

Pythia 6.325

21.16<M<2.56 GeV/c

Fig. 12. cos θCS distribution of cc → µ+µ− dimuons in the1.16–2.56 GeV/c2 range, as generated by Pythia, before (upperline, normalized to unit area) and after (lower line) applyingthe muon reconstruction algorithm.

The basic goal of the analysis is to compare the mea-sured yield of signal IMR dimuons to the expected yield,from the Drell-Yan and open charm contributions. Sincethis comparison is to be done as a function of collision cen-trality, the events are distributed in 12 sub-samples, usingthe number of tracks reconstructed in the VT as centralityestimator. The corresponding average number of nucleonsparticipating in the In-In collision, Npart, can be derivedwithin the Wounded Nucleon Model Nch ≈ qNpart, whereNch is the number of charged particles produced in theVT angular window, corrected for acceptances and effi-ciencies [25]. The proportionality constant q is found bymatching the observed dN/dNch to dN/dNpart generatedfrom the Glauber model.

To judge if the sum of the expected contributions re-produces or not, in amplitude and shape, the measuredmass and weighted offset IMR dimuon signal distribu-tions, we must determine the normalizations of the Drell-Yan and open charm spectra. We start by fixing the rel-ative normalization of the open charm contribution withrespect to the Drell-Yan contribution, by calculating theratio of their production cross sections. In order to cal-culate this ratio, we use the high-mass Drell-Yan crosssections measured by NA3 [26] and by NA50 [27], whichshow that Pythia’s Drell-Yan spectrum needs to be up-scaled by a K-factor of 1.9, and we use a charm crosssection of σcc = 8.6 µb. The latter number corresponds tothe value required to reproduce the dimuon mass distribu-tions measured by NA50 in p-A collisions at 450 GeV [4,5], 36± 3.5 µb, scaled down in energy (to 158 GeV) usingPythia. It is worth noting that this value is around 1.8times higher than what would be obtained from a “worldaverage” estimate [22] based on measurements of D mesonproduction from fully reconstructed hadronic decays. Oneshould stress that neither NA50 nor NA60 are suited tomeasure the full phase space cc cross section: as can beseen from Fig. 12, the acceptance window | cos θCS| < 0.5defined by the muon spectrometer contains less than 20 %of all dimuons from DD decays, and the extrapolation ofthe measurement to full phase space strongly depends onhow well the correlations between the two decay muons aredescribed by Pythia. The obtained open charm to Drell-Yan cross-section ratio is then kept the same for all cen-trality bins, since both processes are expected to scale withcentrality in exactly the same way (proportionally to thenumber of binary nucleon-nucleon collisions).

The next step is to determine the Drell-Yan normaliza-tion from the yield of high-mass dimuons. Given the rela-tively small statistics, especially when the events are sub-divided in several centrality bins, we calculate the Drell-Yan yield from the much larger number of J/ψ eventsand expected J/ψ/DY ratio. The latter is measured inproton-nucleus collisions [28] by NA50 (at 400–450 GeVand scaled to 158 GeV) and is corrected for the J/ψ “anoma-lous suppression” measured in In-In collisions [29]. A 10 %relative systematic error is applied to the resulting normal-izations, to account for uncertainties in the J/ψ anomaloussuppression and normal absorption patterns.

410 0.13±Prompt: 1.19

0.27±Charm : 2.77

/NDF: 1.12χFit

Fit range

4000 A

)2Mass (GeV/c1.5 2 2.5 3 3.5 4 4.5 5 5.5

410 0.12±Prompt: 1.36

0.29±Charm : 2.45

/NDF: 2.22χFit

6500 A

Fig. 13. Signal dimuon mass distribution measured from the4000 A (top) and 6500 A (bottom) data samples, comparedto the superposition of Drell-Yan dimuons (dashed line) andmuon pairs from open charm decays (dotted line), scaled upwith respect to the expected yields.

4.2 Data versus expectations in dimuon mass andoffset

Figure 13 compares the signal dimuon mass distributionsobtained from the 4000 A and 6500 A data samples, inte-grated over collision centrality, with the sum of the Drell-Yan and open charm contributions. With respect to theexpected normalizations, described in the previous para-graphs, these contributions must be scaled up (by the val-ues quoted in the figure) so as to provide the best descrip-tion of the measured signal spectrum in the dimuon masswindow 1.16 < M < 2.56 GeV/c2. Within errors, the twodata samples give perfectly compatible results. A globalfit gives scaling factors of 1.26 ± 0.09 for Drell-Yan and2.61± 0.20 for open charm, with χ2/ndf = 1.02. Further-more, essentially the same numerical values are obtained ifthe analysis is redone only selecting events with a match-ing χ2 below 1.5 (instead of 3). As previously observedby NA38 [2] and NA50 [4], a significant excess of IMRmuon pairs is observed, which can be well accounted forby increasing the charm normalization.

The big advantage of NA60, with respect to the dimuonmeasurements made by all other heavy-ion experiments,is the availability of the dimuon weighted offset variable,

0.13±Prompt: 2.39

0.25±Charm : 1.23

/NDF: 0.52χFit

4000 A

Dimuon weighted offset0 1 2 3 4 5

0.09±Prompt: 2.26

0.22±Charm : 1.06

/NDF: 1.52χFit

6500 A

Fig. 14. Same as previous figure but for the dimuonweighted offset distributions of the dimuons in the mass range1.16–2.56 GeV/c2.

which provides complementary information ideally suitedto distinguish prompt dimuons from muon pairs stemmingfrom displaced decay vertices. Figure 14 shows the dimuonweighted offset distribution for the signal dimuons in themass range 1.16–2.56 GeV/c2, for the 4000 A and 6500 Adata samples, compared to the sum of the two contribu-tions: prompt dimuons and open charm decays, scaled toprovide the best fit to data.

The shape of the prompt dimuon distribution was builtusing the measured dimuons in the J/ψ and φ peaks,where the non-prompt signal contributions are less than1 %. The shape of the open charm distribution was de-fined using the muon pairs from the overlay Monte Carlosimulation, including the additional smearing needed toreproduce the measured J/ψ and φ distributions (see [16],section 8.4.1 for details).

The excess dimuons are clearly concentrated in theregion of small dimuon offsets, excluding the possibilitythat they are due to open charm decays. The best de-scription of the measured distribution is obtained whenthe prompts contribution is scaled up by more than a fac-tor of two with respect to the expected Drell-Yan yield,while the open charm contribution is compatible with theyield assumed by NA50 to reproduce the IMR spectra inp-A collisions [4]). Fig. 14 underlines the fact that the

dimuon weighted offset is a really efficient discriminatorbetween prompt and charm dimuons. On the other hand,due to the extreme similarity of the mass distributions ofthe excess and charm dimuons (see Fig. 16), it is clearthat mass alone is completely unable to separate themand, therefore, perfectly accommodates the assumptionthat the excess is due to open charm, from the purelystatistical point of view (see Fig. 13).

A global fit of both data sets provides scaling factorsof 2.29 ± 0.08 and 1.16 ± 0.16, for the prompt and opencharm contributions, respectively (with χ2/ndf = 1.52). Ifthe analysis is redone only using events with matching χ2

below 1.5, instead of 3, the results remain the same withinthe statistical errors. If the open charm yield is restrictedto be within 10% of the nominal value rather than leftfree in the fit, the scaling factors become 2.43± 0.09 and1.10 ± 0.10, respectively, i.e. again the same within thestatistical errors.

Since the tail of the offset distribution lacks the statis-tics needed to define the open charm normalization dif-ferentially in bins of mass, pT and centrality, its scale iskept fixed to the value determined from the integratedsample, corresponding to a full phase space cross sectionσcc = 9.5 µb/nucleon with 14% statistical and 15% sys-tematic errors accounting for the uncertainty of the ex-pected Drell-Yan contribution. This is the value neededto describe the measured data and does not depend onthe assumed reference cross section. However, the extrap-olation of the cross section to full phase space dependson the kinematical distributions of the simulated c and c.The associated uncertainty is not accounted in the quotedsystematic error. For instance, we would obtain a value19 % smaller if we would use the conditions of the NA50analysis: Pythia 5.7, different parton densities and with-out nuclear modifications, effective cc→ µ+µ− branchingratio of 0.97 % instead of 0.84 %, etc.

4.3 Kinematic properties of the excess dimuons

The excess dimuons are defined as the statistical differencebetween the total yield and the sum of fitted charm andnominal Drell-Yan. Unbiased physics insight requires cor-recting the measured excess for reconstruction efficienciesand detection acceptances. The acceptances were calcu-lated by Monte Carlo simulations, in dimuon mass and pT

bins, for each of the two data samples, assuming a uniformcos θCS distribution and the same rapidity distribution asthat of the Drell-Yan dimuons (approximately Gaussianwith σ ∼ 1). Assuming a Gaussian rapidity distributionof width 1.5 gives 20 % less excess dimuons, while a 0.5width leads to 40 % more excess dimuons. After check-ing that the 4000 A and 6500 A data sets give statisti-cally compatible results, they were analyzed together. Inthis way we obtain a two-dimensional distribution of theacceptance-corrected excess as a function of mass and pT.

Figure 15 shows the ratio between the excess dimuonyield (corrected for acceptance with the assumptions justmentioned) and the expected Drell-Yan yield (directly tak-en from the generator), in the mass range 1.16–2.56 GeV/c2

participantsN0 50 100 150 200

Excess/DY

(a.u.)participants 2Excess/N

Fig. 15. Ratio between the excess and the Drell-Yan dimuonyields, after acceptance correction, versus centrality (open cir-cles). The excess per squared number of participants is alsoshown, in arbitrary units (filled circles).

as a function of Npart. The smaller error bars represent thestatistical errors while the larger ones represent the sum,in quadrature, of statistical and systematic uncertaintiesof the fitted Drell-Yan and open charm normalizations. Weobserve that the yield of excess dimuons, per Drell-Yandimuon, increases from peripheral to central In-In colli-sions. Furthermore, we see that even the most peripheralevent sample has a considerable yield of excess dimuons(essentially identical to the yield of expected Drell-Yandimuons).

To gain further insight into the properties of these ex-cess dimuons, we have calculated the ratio between theiryield andN2

part. The excess/DY was scaled by the ratio be-tween the number of binary nucleon-nucleon collisions andthe squared number of participant nucleons, Ncoll/N

2part,

calculated for each In-In centrality bin using the Glaubermodel. The resulting excess/N2

part ratio, also plotted inFig. 15, shows a slight decrease with Npart. This impliesthat the increase of the excess with centrality is some-where in between of linear and quadratic in Npart.

The mass distribution of the excess dimuons, after ap-plying the corrections for acceptance and reconstructionefficiencies, is shown in Fig. 16. The mass spectra of opencharm and Drell-Yan pairs are plotted for comparison.The shapes of these spectra are directly taken from thegenerator. The yields reflect the fit values discussed be-fore; the bands correspond to the associated systematicerrors. Clearly, the mass spectrum of the excess drops offmuch more steeply with mass than that of the Drell-Yanpairs. In contrast, the slopes are nearly the same for theexcess and open charm. This explains why the excess, al-ready seen by the NA38/NA50 experiment, was found tobe quite fairly described by any source, be it prompt ordelayed, with a similar mass distribution as open charm,when using the mass spectrum only as a discriminator [6].

Fig. 17 summarizes the different aspects of the trans-verse momentum distributions of the excess dimuons. Thetop plot shows the excess/DY ratio as a function of thedimuon pT, clearly indicating that the process responsible

)2Mass (GeV/c1.2 1.4 1.6 1.8 2 2.2 2.4

Drell-YanOpen charmExcess

Fig. 16. Mass distribution of all three contributions to theIMR spectrum, corrected for acceptances and efficiencies asdescribed in the text. From top to bottom at the highest massbin: Drell-Yan (as expected from the measured number of J/ψdimuons), excess (the difference between all prompt and Drell-Yan pairs) and open charm (with scaling factor of 1.16).

for the production of the excess dimuons is significantlysofter than the Drell-Yan dimuons. While in the lowest pT

bin there are around 3.5 times more excess dimuons thanexpected Drell-Yan dimuons, this ratio drops to 0.5 athigh pT. The pT spectra themselves are shown in Fig. 17-middle, in 3 consecutive dimuon mass windows: 1.16–1.4,1.4–2.0 and 2.0–2.56 GeV/c2. Again, a significant devia-tion from the behaviour of Drell-Yan pairs is observed.The three pT spectra are all different from each other,while the pT spectra and the mass spectra of Drell-Yanfactorize: the primordial kT=0.8 GeV/c characterizing theGaussian distribution is independent of mass in the regionmeasured, i.e. from 3 to >10 GeV/c2 [30].

Finally, Fig. 17-bottom shows the same data in termsof dimuon transverse mass (mT =

√p2T +m2) spectra, for

the same three dimuon mass windows defined before. Allspectra are essentially exponential. However, a steepeningis observed at very low mT in the lowest mass window,which finds its counterpart in all mT spectra observed inthe low mass region below 1 GeV/c2 [31], but seems tobe switched-off in the upper two mass windows as seenhere. The phenomenon is outside any systematic errorsas discussed in [31], but has so far not found a convinc-ing physical interpretation. Ignoring the low-mT rise, thedata can be fit with simple exponentials 1/pT dN/dpT =1/mT dN/dmT ∼ exp(−mT /T ) over the complete pT -range (lines in Fig. 17-middle and bottom), resulting in thefollowing respective Teff values: 189±15 (stat)±4 (syst),197±13±2, and 166±17±4 MeV. The systematic errorsare dominated by the uncertainties of the Drell-Yan andopen charm contributions. If the fit is instead restricted topT ≥ 0.5 GeV/c, consistent with [31] to exclude the rise atlow-mT , the Teff values slightly (but hardly significantly)

(GeV/c)Tp0 0.5 1 1.5 2 2.5

510 1.16 - 1.401.40 - 2.02.0 - 2.56

2M (GeV/c )

(GeV/c)0 - MTM0 0.2 0.4 0.6 0.8 1 1.2 1.4

Fig. 17. Ratio between the excess and the Drell-Yan dimuonyields, after acceptance correction, versus dimuon transversemomentum (top). Transverse momentum (middle) and trans-verse mass (bottom) spectra of the excess dimuons, in threedimuon mass windows: 1.16–1.4, 1.4–2.0 and 2.0–2.56 GeV/c2.

rise to 199± 21± 3, 193± 16± 2 and 171± 21± 3 MeV,respectively.

5 Discussion

The central results of the present paper are connected totwo essentially independent physics issues:

– The observed yield of muon pairs from D meson decaysleads to σcc = 9.5± 1.3(stat)± 1.4(syst) µb (the sys-tematic error does not reflect the uncertainty relatedto the kinematic distribution of the c and c quarks)

and is compatible with the charm production cross sec-tion deduced from the IMR dimuon data measured byNA50 in p-A collisions. Charm production in A-A col-lisions is not enhanced relative to expectations, and ittherefore cannot be made responsible for the dimuonenhancement seen by NA38 and NA50.

– The dimuon enhancement in the IMR as observed be-fore in Pb-Pb collisions also exists in In-In collisions.It is now experimentally proven to be solely due tothe prompt component. The dimuon excess has beenstatistically isolated by subtracting the Drell-Yan andopen charm contributions from the total. It is on aboutthe same level as Drell-Yan (and charm) and increasessignificantly from peripheral to central collisions rel-ative to Drell-Yan and Npart. Both its mass and pTspectra show a much steeper fall-off than Drell-Yan.Moreover, the pT spectra depend on mass and do notshow the factorization between mass and pT charac-teristic for Drell-Yan. Conversely, fits to the essentiallyexponential mT -spectra lead to inverse slope parame-ters Teff , of about 190 MeV, which do not depend onmass, within the (relatively large) errors.

The prime contender for the interpretation of the ex-cess is thermal radiation. The remainder of this sectionplaces the results reported in this paper into a wider con-text, relating them to other experimental results fromNA60 and to the latest theoretical predictions on thermalradiation in the IMR.

NA60 has also studied dimuon mass and pT spectra inthe low mass region (LMR) M<1 GeV/c2 [31,32,33]. Thetotal mass spectrum, unifying the results from the LMRanalysis and from the IMR data in Fig. 16, is shown inFig. 18-top. The LMR results correspond to the integralof the pT -differential acceptance-corrected mass spectrapublished previously [32,33]; a cut pT > 0.2 GeV/c is ap-plied to avoid the very large errors in the region of lowacceptance [32,33]. The mass spectrum is absolutely nor-malized in the LMR region as described in [32]; the IMRdata from Fig. 16 have independently been normalized fol-lowing an analogous procedure. Recent theoretical resultson thermal radiation from two major groups working inthe field are included for comparison [34,35], calculatedabsolutely (not normalized relative to the data); a furtherresult [36] exists, but is left out here due to the lack of finalnormalization. The general agreement between data andmodel results both as to spectral shapes and to absoluteyields is most remarkable, supporting the term ”thermal”used throughout this paper. The strong rise towards lowmasses reflects the Boltzmann factor, i.e. the Planck-likeradiation associated with a very broad, nearly flat spec-tral function. Even this part is well described by [34], dueto the particularly large contribution from baryonic inter-actions to the low-mass tail of the ρ spectral function inthis model. Higher up in mass, the ρ pole remains visible,followed by a broad bump in the region of the φ. This isdescribed in [34] as in-medium broadening of a small frac-tion of the φ (caution should, however, be presently takenon that, since corrections for the resolution function of theNA60 apparatus are still under investigation). In the IMR

/d µµN2

-610excess dimuons

Renk/RuppertHees/Rapp

LMRIMR (this analysis)

)2Mass (GeV/c0 0.5 1 1.5 2 2.5

400 )φ, ω, ρ, ηhadrons ( dimuonsLMRLMR, w/o DYIMR

In-In>30η/dchdN

(this analysis)

-µ+µ → DD

Fig. 18. Top: Acceptance-corrected mass spectra of theexcess dimuons for the combined LMR/IMR. Errors in theLMR part are statistical; the systematic errors are mostlysmaller than that. Errors in the IMR part are total er-rors. The theoretical model results are labeled according tothe authors Hees/Rapp [34] (EoS-B+ option is used) andRenk/Ruppert [35]. Bottom: Inverse slope parameter Teff ofthe excess mT -spectra vs. dimuon mass [31,32]. For the LMRdata M<1 GeV/c2 (triangles), Drell-Yan is not subtracted(would decrease the values only within the error bars [31]).The IMR data (closed circles) correspond to the present work.Open charm is subtracted throughout. The bands show the in-verse slopes for the Drell-Yan and open charm contributionsas provided by Pythia.

region above 1 GeV/c2, the description is good for bothscenarios (only available up to 1.5 GeV/c2 for [34]).

Both for the LMR and IMR, the mT -spectra are pureexponentials (at least for pT >0.4 GeV/c), consistent withthe thermal interpretation [35,36]. Apart from the abso-lute scale, they can therefore be described by one single pa-rameter, the inverse slope Teff extracted from exponentialfits to the data. The combined results for Teff in the LMRand those reported in this paper are shown in Fig. 18-bottom [31]. For M < 1 GeV/c2 (triangles), a correctionfor Drell-Yan pairs is not done, due to their small contri-bution [31], the intrinsic uncertainties at low masses [34]as well as the inability of Pythia to generate Drell-Yan inthis region. The square points correspond to the exten-

sion of the LMR analysis up to M = 1.4 GeV/c2 whichdid not account for the systematic errors of the Drell-Yanand open charm contributions. One should note that thesquare points and circles are not statistically independent,since the two analyses were performed on overlapping datasamples. The inverse slopes for the Drell-Yan and opencharm contributions are shown for comparison. The dif-ference to the excess data is most remarkable.

Below 1 GeV/c2, the inverse slope parameters Teff arenot at all independent of dimuon mass, but monotonicallyrise with mass from the dimuon threshold, where Teff is∼180 MeV, up to the nominal pole of the ρ meson, whereTeff is ∼250 MeV. This is followed by a sudden decline tothe level of Teff ∼190 MeV reported here. That decline be-comes even more steep, jump-like, if the slope parametersTeff are corrected for the contribution of the freeze-outρ [33]. The initial rise is consistent with the expectationsfor radial flow of a hadronic source (here π+π− → ρ) de-caying into lepton pairs. However, extrapolating the lower-mass trend to beyond 1 GeV/c2, a jump of about 50 MeVdown to a low-flow situation is extremely hard to reconcilewith emission sources which continue to be of dominantlyhadronic origin in this region. Rather, the sudden loss offlow is most naturally explained as a transition to a qual-itatively different source, implying dominantly early, i.e.partonic processes like qq → µ+µ− for which flow has notyet built up, at least at SPS energies, due to the ”softpoint” in the equation-of-state. This may well representthe first direct, i.e. data-based evidence for thermal ra-diation of partonic origin, overcoming parton-hadron du-ality for the yield description in the mass domain (seebelow). The observed slope parameters Teff ∼190 MeVare then perfectly reasonable, with a purely thermal in-terpretation without much flow, reflecting the averagingin the space-time evolution of the fireball between the ini-tial temperature Ti ∼220-250 MeV (at the SPS) and thecritical temperature Tc ∼170 MeV.

Theoretically, the NA50 IMR dimuon enhancement [6]was successfully described as thermal radiation based onparton-hadron duality, without specifying the individualsources [7]. However, the same approach is not any longerappropriate for the NA60 data. The extension of the uni-fied LMR and IMR results over the complete M-pT planeplaces severe constraints on the dynamical trajectories ofthe fireball evolution, allowing for more detailed insightinto the origin of the different dilepton sources on the ba-sis of radial flow, sensitive to the time ordering of thesources. Indeed, all present scenarios [34,35,36] explicitlydifferentiate between hadronic (mostly 4π) and partoniccontributions in the IMR. The partonic fraction rangesfrom 0.65 for [34] (option EoS-B+ as used in Fig. 18-top)to ”dominant” in [35,36]. However, due to remaining un-certainties in the equation-of-state, in the fireball evolu-tion and in the role of hard processes [34], a quantitativedescription of the very sensitive inverse slope parameterTeff in Fig. 18-bottom is only slowly emerging. In partic-ular, the more recent results from the authors of [35,36],while very encouraging, are still preliminary and have notyet been formally published in their final form. A system-

atic comparison of several model results to the data inFig. 18-bottom is therefore presently not possible.

6 Conclusions

The dimuon excess in the mass region M>1 GeV/c2 seenin high-energy nuclear collisions before has now been pro-ven to be of prompt origin. Its properties, differing fromthose of Drell-Yan pairs in many ways, suggest an inter-pretation as thermal radiation. If linked to supplementaryinformation on dimuon excess production in the mass re-gion <1 GeV/c2, all indications favor an early, i.e. a domi-nantly partonic emission source. Present theoretical mod-elling, though still under development, supports our inter-pretation.

7 Acknowledgments

This work was partially supported by the Fundacao para aCiencia e a Tecnologia (Portugal), under the SFRH/BPD/5656/2001 and POCTI/FP/FNU/50173/2003 contracts,by the Gulbenkian Foundation (Portugal) and by the FundKidagan (Switzerland).

Appendix A : Combinatorial background

Our aim is to pick pairs of muons from different events insuch a way that after applying the trigger conditions theyreproduce the observed like-sign spectra, both in shapeand in absolute normalization. The problem arises fromthe fact that the data used as pool for the single muonsample is already affected by the trigger conditions whichinduces correlations between the registered muons. Wewill now describe the procedure used to account for thesecorrelations and to obtain the “unbiased” single muonpools.

We will denote by P+ and P− the average numbersof triggerable muons of positive and negative charge, re-spectively, in a single interaction (the numerical valuesof these probabilities are always � 1 since the probabil-ity for pion to produce a triggerable muon is ∼ 10−3). Ifwe neglect the correlation induced by charge conservationbetween the numbers of positive and negative hadrons (avery reasonable assumption in the case of high multiplicityheavy-ion collisions), the number of muon pairs of differ-ent charge combinations observed in N collisions will be

N++ = NP++ = NP+P+/2N−− = NP−− = NP−P−/2 (A-1)N+− = NP+− = NP+P− .

To account for the rejection of the same-sextant muonpairs by the trigger, we decompose P+ (and P−) in thecontributions from the different sextants, P+ =

∑6i=1 p

and rewrite Eqs. (A-1) excluding the rejected combina-tion:

P++ =6∑i<j

(P+P+ −

P−− =6∑i<j

p−i p−j =

(P−P− −

p−i2

)/2 (A-2)

P+− =6∑i 6=j

p+i p−j = P+P− −

p+i p−i .

It is worth noting that Eqs. (A-2) imply:(P+−

− 4P++P−− =6∑i

(P+p−i − P

−p+i

)2 −6∑i 6=j

p+i p−j (p+

i p−j − p

+j p−i ) .(A-3)

The well-known equation N+− = 2√N++N−− is a par-

ticular case of Eq. (A-3) when its right-hand side vanishes.Rewriting the latter as

p+j p−i

(1− p+

p−i/p+j

−6∑i 6=j

2p−j

p−j/p+i

), (A-4)

we see that it vanishes when the p+i /p

−i ratios are the same

for all sextants (in more general terms, this ratio should beconstant over the whole phase space). This is not the casein NA60 because the dipole magnet breaks the symmetryof the azimuthal distribution of the produced particles, ina charge dependent way. Therefore, in order to evaluatethe CB in NA60, we need to compute the single muonprobabilities and explicitly account for the exclusion ofthe same-sextant dimuons. Since the number of same-signpairs with muons in the sextants i and j is, for the positivecase, N+

ij = ρ+i ρ

+j /2, with ρ+

i =√Np+

i , we can extractρ+i as

(ρ+i )2 =

and then average over all possible {j, k} combinations.Once the values of ρ+

i and ρ−i are known, we can determinethe fractions of positive and of negative muons, no longerbeing biased by the trigger condition:

R+ =∑ρ+i∑

ρ+i +

∑ρ−i

, R− = 1−R+ . (A-6)

We can, then, build the artificial CB spectra according tothe following procedure:

i. Select randomly the charges of the two muons, accord-ing to the probabilities given by Eqs. (A-6).

ii. Select randomly the sextant of each muon, accordingto the weights ρ+

i and ρ−i , restarting from step 1 if thetwo selected sextants happen to be the same.

iii. Randomly pick two muons, of charges and sextantsas previously selected, from the single muon samplesbuilt out of the measured like-sign dimuon events. Ifthe two selected muons have more than one match toVT tracks (m1 and m2 matches, say), then we buildall possible (m1×m2) matched dimuons and apply toeach of them the selection cuts applied to the measuredevents.

The normalizations of these artificial CB samples are fixedby

N+− =∑i 6=j

ρ+i ρ−j , N++(−−) =

∑i6=j

ρ+(−)i ρ

+(−)j ,

(A-7)so that the generated like-sign dimuon spectra reproducethe corresponding measured spectra.

Special care must be taken in what concerns the off-sets of the muons in the “mixed” pairs. In order to repro-duce the offset distribution of the measured combinatorialmuons, we first randomly assign the vertex of one of thetwo events participating in the mixing to be the vertex ofthe generated event. Then, we modify the intercept pa-rameters of the muon from the other event so that withrespect to this vertex it retains the same offset as it had inits own event, with respect to its vertex. The accuracy ofthe method schematically depicted in Fig. 19 can be ap-preciated in Fig. 8, which compares the dimuon weightedoffset distributions of the generated and measured like-sign muon pairs.

Event 1

Event 2

Mixed event

Fig. 19. Schematic explanation of the method used to buildthe muon offsets for mixed events.

Appendix B : Fake matches background

Our aim is to estimate the probability for a given muonfrom the MS to be wrongly matched with the tracks in theVT and to use it in building the artificial fake dimuons

sample which reproduces both in spectral shape and innormalization the FB contributing to data.

Let ε be the probability that the correct match ispresent in the set of all found matches for a muon withgiven kinematics (regardless on the number of fake matchesand their matching χ2’s). Notice that the correct matchmay be missing not only due to track reconstruction inef-ficiency or the choice of the χ2 cut value, but also becausethe muon was produced in a decay or interaction down-stream of the VT, in which case its track is simply absent.Let us denote by φn (n ≥ 0) the probability for a givenmuon to have n fake matches in events with given char-acteristics such as interaction sub-target, multiplicity, etc.If we designate ν as the average number of fake matches,then φn is Poisson distributed with mean ν. Our deriva-tions do not require, however, any assumption about itsdistribution.

These quantities can be extracted for each muon witharbitrary precision using a event mixing technique in thefollowing way: one applies the usual matching procedurebut tries to associate the MS muon of one event with theVT tracks of many different events with same character-istics (i.e. multiplicity, interaction sub-target, etc.). Fromeach such event one gets a set of a priori fake matcheswith the same φn and χ2 distributions as for the fakes inthe real data. The latter distribution, B(χ2) (scaled downby the number of tried events per muon), after being sub-tracted from the χ2 distribution of the real data, providesthe spectrum for the correct matches, S(χ2) (both B(χ2)and S(χ2) are shown in Fig. 6). Then, the probability fora given muon to have n matches (either one correct andn− 1 fakes or all n fakes) can be written as:

P (n) = εφn−1 + (1− ε)φn (B-1)

and the probability that the correct match is present inthis n-plet is

Ppr(n) = εφn−1/P (n) . (B-2)

Provided that the correct match is present in this setof n matches, Bayes’ theorem states that the fraction oftimes Wb(n|pr) in which it will have the smallest (best)χ2 is equal to the ratio of the probability for configura-tion {χ2

1,corr., ...} to the sum of probabilities for all con-figurations with given χ2 values (i.e. {χ2

1,fake, χ22,corr., ...},

etc.). Expressing the probability of given arrangement ofχ2 values of n matches as the product of the probabilitiesfor each χ2, we can write:

Wb(n|pr) =S(χ2

1)∏nj=2B(χ2

j )∑ni=1 S(χ2

i )∏nj 6=iB(χ2

R1∑ni=1Ri

with Ri = S(χ2i )/B(χ2

i ). From Eqs. (B-1–B-3) we get theprobability for the best one of n matches being the correctone:

Wb(n) = Ppr(n)Wb(n|pr) =εR1(

1 + 1−εε

φn−1

)∑ni=1Ri

It is the presence of the ε in Eq. (B-4) which makes itdifficult to estimate the FB in the best matches spectrausing the data only: the probability of the correct matchbeing present in the set of the matches strongly dependson the kinematics of the muon. Even for muons with sim-ilar kinematics it differs for those coming from the inter-action point and those originating in π or K decays.

Consider now a pair of muons, each with its own εiand φ

(i)n , i = 1, 2. For the sake of generality consider two

extreme possibilities: the case in which the probability offinding the correct match for the first muon is not corre-lated with that of the second muon and the case in whichthe correct matches are present or absent always together,with common probability ε. In the first case the probabil-ity of finding n and k matches respectively, similarly toEq. (B-1), can be written as:

P (n, k) =[ε1φ

(1)n−1 + (1− ε1)φ(1)

] [ε2φ

(2)n−1 + (1− ε2)φ(2)

(B-5)while in the second, full correlation, case we have

P (n, k) = εφ(1)n−1φ

(2)k−1 + (1− ε)φ(1)

n φ(2)k . (B-6)

Taking into account the identities∑∞

1 nφn−1 = ν+ 1,∑∞0 nφn = ν and

∑∞0 φn = 1, the average number of

matched dimuons for given pair, W =∑∞n,k=1 nkP (n, k),

is equal to

W = ε1ε2 + [ε1ν2 + ε2ν1 + ν1ν2] (B-7)

for the case of absence of the correlation between the cor-rect matches and

W = ε+ [ε(ν1 + ν2) + ν1ν2] (B-8)

for the correlated case. Note that in Eqs. (B-7–B-8) theexpression in square brackets (involving the average num-ber of fake matches per muon, ν) gives the average numberof fake dimuons which is what we want to reproduce bythe event mixing technique.

We thus arrive at the following procedure for a givenpair of muons from the MS (including those which haveno matches)i. For each muon of the pair we generate the “mixed

fakes” by selecting matches from the same number oftracks as in the event where the pair comes from, butpicking the tracks from other events with similar char-acteristics.

ii. Combine all mixed fakes of the first muon with all orig-inal matches (if any) of the second one and vice-versa.The probability of obtaining this way n× k (includingthe cases of n or k = 0) a priori fake dimuons is

F (n, k) = φ(1)n

∞∑l=0

P (l, k) + φ(2)k

∞∑l=0

P (n, l) (B-9)

which, after substitution of Eq. (B-6), leads to

F (n, k) = φ(1)n

(2)k−1 + (1− ε)φ(2)

]+φ(2)

(1)n−1 + (1− ε)φ(1)

](B-10)

in the uncorrelated scenario and

F (n, k) = ε[φ(1)n φ

(2)k−1 + φ

(1)n−1φ

](B-11)

for the correlated one. Averaging over all possible {n, k}combinations (i.e. performing these two steps manytimes with different events using the same muon pair)we get for the average number of “mixed fake dimuons”,W1, defined as

∑∞n,k=1 nkF (n, k),

W1 = ε1ν2 + ε2ν1 + 2ν1ν2 , (B-12)W1 = ε(ν1 + ν2) + 2ν1ν2 , (B-13)

for the uncorrelated and correlated cases, respectively.

Note that these numbers reproduce the fake dimuonscontribution (in [ ]) of Eqs. (B-7) and (B-8), respectively,except for an extra factor 2 in the term correspondingto both matches being fake. This double counting can beeasily removed by combining the mixed fake matches ofthe first muon with those of the second one and countingthese dimuons with a negative sign, thus obtaining theneeded W2 = −ν1ν2 contribution.

This algorithm does not require any explicit determi-nation of ε’s of φn’s. For each pair of muons large amountsof “mixed” fake dimuons are generated with small weights(W1 −W2)/N , where N is the number of different eventsmatched to the same muon pair, thus smoothing the binto bin fluctuations.

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arxiv:0810.3204v2 [nucl-ex] 16 dec 2008 · epj manuscript no. (will be inserted by the editor)...

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