EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2012-037 2012/02/20 CMS-EXO-11-087 Search for large extra dimensions in dimuon and dielectron √ events in pp collisions at s = 7TeV 2 1 The CMS Collaboration∗ 0 2 b e F 7 1 ] Abstract x e - p Resultsarepresentedfromasearchforlarge,extraspatialdimensionsineventswith e h eithertwoisolat√edmuonsortwoisolatedelectrons. Thedataarefromproton-proton [ interactions at s = 7TeV collected with the CMS detector at the LHC. The size 1 of the data sample corresponds to an integrated luminosity of approximately 2fb−1. v The observed dimuon and dielectron mass spectra are found to be consistent with 7 standard-model expectations. Depending on the number of extra dimensions, the 2 8 limits at 95% confidence level are in the range 2.5TeV < Ms < 3.8TeV, where Ms 3 characterizesthescalefortheonsetofquantumgravity. . 2 0 2 SubmittedtoPhysicsLettersB 1 : v i X r a ∗SeeAppendixAforthelistofcollaborationmembers 1 Models that extend the structure of space-time predict new phenomena beyond the standard model(SM)ofparticlephysics. Additionalspatialdimensions,essentialforformulatingquan- tumgravityinthecontextofstringtheory,havebeenproposedasasolutiontotheSMhierar- chy problem [1–3]. In this letter, we present a search for events at large dimuon or dielectron invariantmassduetocontributionsfromvirtualgravitonprocessesintheArkani-Hamed,Di- mopoulos,Dvali(ADD)model[1,2]. TheADDmodelpostulatestheexistenceofcompactifiedextradimensions. Gravityisassumed to propagate in the entire higher-dimensional space, while particles of the SM are confined to a3-dimensionalsliceofthemultidimensionalspace. TheresultingfundamentalPlanckenergy scale M in the ADD model can be reduced to significantly lower values than suggested by D theapparentPlanckmass M ≈ 1.2·1019GeVdeducedfor3spatialdimensions. M mustbe Pl D of the order of the scale of electroweak symmetry breaking to provide an explanation of the hierarchyproblem. Thisscenariopredictsphenomenologicaleffectsthatmightbeobservedin proton-protoncollisionsattheLHC.Inthispaper,weadopttheassumption[4,5]thatallextra dimensions are compactified on a torus of size r. In this case, M is related to M through D Pl Mn+2 = M2 (cid:14)(8πrn),wherenisthenumberofextradimensions. D Pl Thegravitoninthis(3+n)-dimensionalformulationcanbeequivalentlyexpressedasasetof 3-dimensional Kaluza–Klein (KK) modes [6] with different graviton masses. The coupling of the KK modes to the SM energy–momentum tensor leads to an effective theory with virtual- graviton exchange at leading order (LO) in perturbation theory. An ultraviolet (UV) cutoff Λ must be introduced to avoid divergences in the summed contributions from all modes. A phenomenologicalconsequenceofthesmallmassseparationbetweenadjacentKKmodesisan enhancement in the expected rate of dilepton events at large invariant masses that appears to be non-resonant. Depending on the details of the model, virtual-graviton effects can provide thedominantexperimentalADDsignatureathigh-energycolliders[4,5]. Several ways of parameterizing the LO differential cross sections are provided in the litera- ture, including the Han, Lykken, Zhang (HLZ) [4] and the Giudice, Rattazzi, Wells (GRW) [5] conventions. In t√he GRW convention, the leading-order phenomenology for partonic cent√re- of-massenergies sˆ (cid:28) ΛisdescribedbyasingleparameterΛ ,whichdoesnotdependon sˆ T for n ≥ 3. The HLZ convention describes the phenomenology in terms of n and a mass scale M ,whereM isrelatedtotheselectedUVcutoffandreflectsthescalefortheonsetofquantum s s gravity. Typically, M is expected to be of order M . The parameter Λ can be related to the s D T parametersintheHLZconvention[7]. Theeffectivetheorybreaksdownatenergyscalesatwhichtheunderlyingtheoryofquantum gravity starts to affect the phenomenology. We assume that the range of validity is character- √ izedbyavalue sˆ ,roughlycorrespondingtothemass M oftheleptonpairsemittedin max √ max thedecayofthegraviton. Asnoclearpredictionfor sˆ canbemadewithintheADDmodel, √ max andtotakeintoaccounttherequirement sˆ (cid:28) Λ,mostresultsinthispaperarepresented max bothfor M = M andforarangeofdifferentvaluesof M . max s max Constraints on virtual-graviton signatures in the ADD model of extra dimensions have been obtained at HERA [8, 9], LEP [10–15], and the Tevatron [16, 17]. At the LHC, limits have been presentedbasedonmeasurementsofdiphotonevents[18–20]. CMS uses a right-handed coordinate system with axes labeled x, y, and z, and the origin at the center of the detector. The z-axis points along the direction of the anticlockwise beam. The azimuthal and polar angles are φ and θ, with θ measured from the positive z-axis. The pseudorapidityη isdefinedbyη = −lntan(θ/2). 2 A main feature of the CMS apparatus is a superconducting solenoid of 6m internal diameter, providingamagneticfieldof3.8T. Locatedwithinthefieldvolumearesiliconpixelandstrip inner trackers, an electromagnetic calorimeter (ECAL), and a hadronic calorimeter (HCAL). The ECAL consists of lead-tungstate crystals covering pseudorapidities of |η| < 1.5 (barrel) and 1.5 < |η| < 3.0 (endcaps). The CMS muon detectors are embedded in the return yoke of the magnet. Muons are measured with detection planes using three different technologies: DriftTubes,CathodeStripChambers,andResistivePlateChambers. ThefirststageoftheCMS triggersystememployscustomhardwareandprocessesinformationfromthecalorimetersand themuonsystem. Theeventrateisfurtherreducedbyacomputerfarmusingtheeventinfor- mationfromalldetectorsystems. AdetaileddescriptionofCMScanbefoundinRef.[21]. This analysis uses data samples collected with the CMS detector in 2011, corresponding to an integrated luminosity [22] L of 2.3±0.1fb−1 (dimuons) or 2.1±0.1fb−1 (dielectrons). The integrated luminosity for the dimuon channel is larger because the muon selection has less stringent requirements on the performance of the calorimeters during data-taking. The event selectionfollowscloselythecriteriausedinasearchforZ(cid:48) bosons[23]. Themuondatasample was collected using a single-muon trigger with a transverse momentum (p ) threshold which T was varied between 15 and 40GeV over the course of data-taking to allow for changes in in- stantaneous luminosity. The selection of electron events is based on a trigger requiring the presence of 2 electrons or photons with energy depositions > 33GeV. Candidate events are required to have a reconstructed interaction vertex with |z| < 24cm, and a radial distance (cid:112) x2+y2 < 2cm. Foreventspassingthecompleteselectionrequirements,thetriggerefficien- cies for signal and SM Drell–Yan (DY) events with large mass are > 99%, with an uncertainty of< 1%. Muonswith|η| < 2.1and p > 45GeVareselected. Thecandidatesarerequiredtobeidenti- T,µ fiedbothintheoutermuonsystemandtheinnertracker,andtheinnertrackmustcontainre- constructedenergydepositsinatleast1pixellayerandmorethan10strip-trackerlayers. Muon candidatesarerequiredtohavesignalsfromatleasttwomuondetectorlayersincludedinthe reconstructedmuontrack. Muoncandidatessatisfytheisolationrequirement∑pi /p < 0.1, T T,µ wherethesumextendsoverthemomenta pi ofallchargedparticletracks(excludingthemuon T (cid:113) track) within a cone of size ∆R = (∆η)2+(∆φ)2 = 0.3 around the muon direction of flight. To reject backgrounds from cosmic-ray muons, we require a transverse impact parameter rel- ative to the primary vertex of < 0.2cm, and an opening angle of α < π−0.02 between the µµ 2 muon momentum vectors. No charge requirement is applied to the muon pairs. However, all selected muon pairs of mass > 450GeV are found to have opposite charges. Events with 2 muonspassingtheselectioncriteriaareacceptedforanalysis. Electron candidates are reconstructed from energy depositions in the ECAL (superclusters) matched to a track in the silicon tracker. ECAL superclusters are constructed from 1 or more clustersofenergydepositionssurroundingthecrystalwiththehighestlocalenergydeposition. Anassociatedtrackisrequiredtocontainsignalsfromatleast5trackerlayers. Thetrackmust be matched geometrically to the supercluster, and the spatial distribution of energy must be consistent with that expected for an electron. Only electron candidates with a ratio of energy depositionsintheHCALandECALbelow0.05areconsidered. Tominimizethecontamination fromjets,electroncandidatesarerequiredtobeisolated. Candidateswithasumoftransverse track momenta ≥ 5GeV within 0.04 < ∆R < 0.3 around the candidate track are rejected. In the ECAL and inner HCAL layer, the deposited transverse energy E in a cone ∆R = 0.3 T around the electron candidate (excluding the transverse energy E of the electron) must be T,e < 2GeV+0.03×E for the barrel, or < 2.5GeV(<2.5GeV+0.03×(E −50GeV)) for the T,e T,e 3 endcaps if E < 50GeV(E ≥ 50GeV). Additionally, the E deposition in the outer HCAL T,e T,e T layerwithin0.15 < ∆R < 0.3aroundtheelectronpositionisrestrictedto< 0.05GeV. Selected events must contain 2 electrons of opposite charge, each with transverse energy E > 35GeV T (inthebarrelregion),orwith E > 40GeV(intheendcaps). Theexplicitchargerequirementis T foundtohavenegligibleinfluenceonthepresentedresults. Eventsinwhichbothelectronsare reconstructedintheendcapsarenotusedintheanalysis,sinceelectronsfromtheADDsignal wouldonaveragebeproducedatsmallervaluesofη thantheSMbackgrounds. Thesearchisperformedwithasetofeventsthatcontainseitherelectronormuonpairsabove a mass value M . The lower bound of the signal region is chosen to maximize the expected min Λ upper limits of the ADD model parameter in each lepton channel. The optimum value of T M isfoundtobe1.1TeVforboththedimuonandthedielectronchannel,basedonsimulation min studies. In both search channels, the PYTHIA 8.142 [24, 25] event generator with the MSTW08 [26] par- ton distribution function (PDF) set is used to simulate the expected signal. Interference terms betweenthestandardmodelDYprocessandthevirtualgravitonaretakenintoaccountinthe evaluation of the signal cross sections. Simulated events for both signal and SM backgrounds arepassedthroughadetaileddetectorsimulationbasedonGEANT4[27],usingarealisticCMS alignmentscenario,andthesamereconstructionchainasdata. In this analysis, The SM DY process is the dominant background. In the dimuon channel, we use the MC@NLO [28, 29] event generator with the CTEQ6.6 [30] PDF set to simulate the DY background. The parton level events from MC@NLO are passed to HERWIG 6 [31] for the sim- ulation of the QCD parton shower and hadronization, PHOTOS [32] for the simulation of the electroweak(EW)partonshower,andJIMMY[33]forthesimulationofmultiplepartoninterac- tions. The simulated reconstruction efficiencies in the chosen region of acceptance, including allselectioncriteria,arefoundtobe90%±3%forthehigh-massDYdimuonbackgroundand 90%±4%fortheADDdimuonsignal. Mass-dependentcorrections[34]beyondtheQCDnext-to-leadingorder(NLO)predictionsim- plementedinMC@NLOarestudiedtoimprovetheSMDYestimateinthedimuonchannel. EW NLOeffectsareevaluatedbycomparingHORACE[35]NLOpredictionsinterfacedtoHERWIG6 with HORACE LOpredictionsinterfacedto HERWIG 6and PHOTOS. Inthisprocedure, PHOTOS corrections are applied to the LO results to account for radiation effects as these corrections are also included in the DY simulation based on MC@NLO. The effect of electroweak NLO corrections is found to be smaller than the QCD NLO contribution and of opposite sign. The estimated correction factor for the DY background beyond 1.1TeV is ≈ 0.90±0.06. Next-to- next-to-leading order (NNLO) QCD corrections are obtained using higher-order calculations from FEWZ [36]. The corresponding multiplicative correction factor for the DY background in the signal region is estimated to be 1.03±0.03. For the purpose of setting limits, both the EW NLOandQCDNNLOcorrectionsareappliedtotheDYbackgroundpredictionobtainedfrom MC@NLO. TheDYbackgroundinthedielectronchannelissimulatedwith PYTHIA 6[37]andnormalized according to the observed data in the range 60–120GeV around the Z resonance. As in the dimuon channel, electroweak NLO corrections at large mass are studied with HORACE. The estimated correction factor for the DY background beyond 1.1TeV is found to be 0.92±0.06. The simulated reconstruction efficiency for the high-mass DY dielectron background and the ADDdielectronsignalintheselectedacceptancerange,includingallselectioncriteria,isfound tobe84%±3%. 4 The parton distribution functions have a strong impact on the SM DY background in both searchchannels. ThePDFuncertaintiesfortheDYprocessareevaluatedbycomparingresults from the CTEQ6.6 [30], MSTW08 [26], and NNPDF21 [38] PDF groups. This procedure follows the recommendations of the PDF4LHC working group [39]. The uncertainties are defined by constructinganenvelopethatembracesthethreeseparatePDFsetsfromtherespectivegroups, together with their individual associated uncertainties. Within each group, PDF reweighting [40] is used to evaluate the respective uncertainties. Additional uncertainties from the depen- dence on the strong coupling constant αs are estimated with MSTW08 PDF sets. The resulting uncertaintyontheintegratedSMDYdistributionformassesabove1.1TeV,fromalluncertain- tiesrelatedtothechoiceofPDF,isestimatedtobe13%. 2.3fb 2.1fb V V e e G G 0 γ 0 γ 2 2 s / ADD, s / nt nt e e ADD, v v E E [GeV] Figure 1: Dimuon (left) and dielectron (right) invariant mass spectra compared with the SM predictionsandasimulatedADDsignalwith Λ = 2.8TeV(ADDK-factor1.0,nosignaltrun- T cation). The highest-mass bins contain all contributions above 2.3TeV. The error bars reflect thestatisticaluncertainty. Contributionsfromtt,tW,andEWvectorbosonpairproductiontothedimuonanddielectron mass spectrum are estimated by using simulations with MADGRAPH [41] and PYTHIA 6. The background contributions are cross-checked with a control sample dominated by these pro- cesses, including events with an electron and a muon passing requirements similar to those used for the signal leptons. Taking into account the differences in the acceptance and efficien- ciesbetweenmuonsandelectrons,theratiosbetweentheexpectedee,µµ,andeµbackgrounds fromthett, tW, anddibosoncontributionsintheSMarewellunderstoodfromleptonuniver- sality. The measured eµ mass spectrum is found to be well reproduced by the simulations. The agreement has been confirmed up to masses of ≈ 500GeV, above which the statistical uncertaintiesontheeµspectrumbecomelarge. Backgroundcontributionsatlargedimuonmassfrommultijetprocessesandcosmic-raymuons arenegligibleforoureventselectionrequirements. In addition to those backgrounds that are common with the dimuon channel, the dielectron channel receives background contributions from multijet events with 2 jets that pass the elec- tron selection and W+jets events with 1 jet passing electron selection. Events of the type γ+jets,wherethephotonconvertstoe+e− andboththephotonandajetarereconstructedas electrons that pass selection, are also considered. The rate for jets to be reconstructed as elec- tronsisdeterminedfromacontrolsampleofeventsselectedbyasingle-electromagnetic-cluster 5 trigger with a lower threshold. The electron selection criteria, including the isolation require- ments, are relaxed to define electron candidates in this sample. Events are required to have no more than 1 such reconstructed electron to suppress the contribution from the DY process. Residual contributions from W+jets and γ+jets events in the control sample are estimated fromsimulation. Theestimatedprobabilityforanelectroncandidatetopassthefullsetofelec- tronselectioncriteriaisthenusedtoweighttheeventsthathave2suchcandidatespassingthe double-electromagnetic-clustertrigger. Both for dimuon and dielectron events, the contributions from non-DY processes sum up to lessthan10%oftheexpectedbackgoundinthesignalregion. Using Z-candidate events, detailed studies are performed of possible differences in the elec- tron and muon reconstruction efficiencies of simulated events and data [42]. No statistically significant deviations between data and simulations are found, indicating that the simulated leptonreconstructionefficienciesarereliable. Inbothchannels,uncertaintiesonthesimulated acceptance and reconstruction efficiencies at large dilepton mass are included in the statisti- cal evaluation of the result. Uncertainties related to momentum reconstruction of muons and energyestimationofelectronsarealsotakenintoaccount. Thesystematicuncertaintiesfortheintegrateddimuonanddielectronbackgroundsinthesig- nal region are summarized in Table 1. With the exception of the uncertainty on the integrated luminosity,whichistreatedasfullycorrelatedbetweenthe2channels,theyareassumedtobe independent. Figure 1 shows the observed and expected mass distributions in the 2 search channels as a function of dilepton mass. Measurements and SM predictions are found to be in agreement withinstatisticalandsystematicuncertainties. Inbothchannels,nosignificantexcessofevents is observed in the high-mass region, and no events are found in the signal region. The cor- responding SM background expectation for dilepton mass above M = 1.1TeV is 1.0±0.2 min events in the dielectron channel and 1.3±0.2 events in the dimuon channel. The observed number of events N and the SM expectation are in agreement in several control regions, as obs shownininTable2. Table1: Summaryofsystematicuncertaintiesfortheintegrateddimuonanddielectroninvari- antmassspectrainthesignalregions. Systematicuncertainty Uncertainty Uncertainty onsignal(%) onbackground(%) Integratedluminosity 4.5 4.5 Triggerandreconstructionefficiency 4(µµ),3(ee) 3(µµ),3(ee) Muonmomentumresolution 1 5 Electronenergyscale 1−3 1−3 Drell–YanPDFuncertainties — 13 Drell–Yanhigherordercorrections — 10 For the statistical evaluation of the measurements, we count the observed events above M . min For each channel, the probability of observing N events in the signal region is given by a obs Poissondistribution. ThestatisticalmodelforthePoissonmeansincludesparametersthatare used to describe the influence of the systematic uncertainties listed in Table 1 on the expected signalandbackgroundevents. Limitsonthecrosssectionsforsignalsintheregionsofaccep- tance are calculated with a CLs approach [43]. The applied test statistic is a one-sided profile likelihood ratio [44] corresponding to the selected models. The systematic uncertainties are included in the statistical evaluation by extending the likelihood with additional probability 6 Table 2: Comparison of the observed and expected number of events in control and signal regions for the dimuon and dielectron mass distributions. Expected signal contributions are shownforΛ = 2.8TeV(ADDK-factor1.0,signaltruncationat M = Λ ). T max T µµ,L =2.3fb−1 ee,L =2.1fb−1 Mass N Background Signalexp. Mass N Background Signalexp. obs obs region[TeV] expectation ΛT=2.8TeV region[TeV] expectation ΛT=2.8TeV Controlregions Controlregions 0.14–0.20 3723 3690±300 - 0.12–0.20 6592 6598±530 - 0.20–0.40 1674 1605±160 - 0.20–0.40 1413 1301±120 - 0.40–0.60 131 122±13 - 0.40–0.60 88 103±11 - 0.60–0.80 16 21±3 - 0.60–0.80 21 18±3 - 0.80–1.10 8 5±1 0.8 0.80–1.10 7 6±1 0.6 Signalregion Signalregion >1.10 0 1.0±0.2 3.2 >1.10 0 1.3±0.2 2.7 densityfunctionsthatparameterizetherespectiveuncertainties. Theexclusionthresholdisset toCLs = 0.05(> 95%confidence). The RooStats [45] software for statistical data analysis is used for the numerical evaluation of the CL limits. At 95% confidence level (CL), we exclude signal cross sections σ above 1.2fb s s (1.8fb expected) in the dimuon channel and 1.6fb (2.3fb expected) in the dielectron channel. The combined upper limit at 95% CL on the signal cross section in both channels σs,µµ+ee is foundtobe1.4fb,whiletheexpectedlimitis2.2fb. The observed limits on σ are translated into exclusion limits on the ADD parameters. To ac- s countforinterferenceeffects,theexpectedsignalcontributionforaparticularchoiceofmodel parameters is evaluated by subtracting the SM DY cross section at LO from the cross section with the ADD LO contributions. Limits are based either on the leading-order ADD scenario withouthigher-ordercorrectionsoronanassumedhigher-ordercorrectionfactor(K-factor)of 1.3 for the ADD signal contributions. Based on studies of QCD NLO corrections to dilepton processes in the ADD model [46, 47], the K-factor of 1.3 corresponds to a conservative choice. Figure2showsthelimitsfortheHLZconventionfordifferentrangesofvalidityofthemodel, assumingaK-factorof1.3andnosignalcontributionbeyondthecutoff M . Table3summa- max rizesthelimitsontheGRWandHLZparametersfortruncationofthesignalat M = Λ or max T M = M . Resultsarealsogivenforanevaluationoflimitsseparatelyfordimuonordielec- max s tron measurements. Including our recently published results on diphoton events [19], which havecomparablesensitivity,improvestheobservedcombinedlimitson M presentedinTable s 3 by 0.1 (0.3)TeV for n = 2 and 0.1 (0.1)TeV for n ≥ 3 without (with) K-factors for the signal contributions. Insummary,asearchfortheeffectsoflargeextradimensionsindimuonanddielectroninvari- antmassspectrausingtheCMSdetectorattheLHChasbeenpresented. Theresultsarefound tobeinagreementwithSMpredictions,andnosignificantexcessofeventsisobservedatlarge valuesofdimuonordielectronmass. Intheregionofdileptonmassesabove1.1TeV,noevents arefound. OurresultsextendthelimitsonADDmodelsbasedontheanalysisofdileptonsig- natures. Thecombinationwithdiphotonresultsprovidesthemoststringentlimitsongraviton decayintheADDframeworktodate. We thank M.C. Kumar, P. Mathews, and V. Ravindran for useful discussions on QCD NLO corrections in the ADD model. We wish to congratulate our colleagues in the CERN acceler- ator departments for the excellent performance of the LHC machine. We thank the technical 7 {2.3fb , μμ 2.1fb , ee V] e T [ n = 3 nn == 34 n = 5 n = 6 n = 7 ADD K-factor: 1.3 observed expected 2 sd expected (n=3) [TeV] Figure 2: Observed and expected 95% CL lower limits on M , obtained by combining the µµ s ee results, for different numbers of extra dimensions n, applying a signal K-factor of 1.3. A confidenceintervalfortheexpectedlimitcorrespondingto2standarddeviations(sd)isshown forthecasen = 3. Table 3: Observed lower limits in TeV at 95% CL within GRW and HLZ conventions for trun- cationat M = Λ (GRW)or M = M (HLZ). max T max s ADDK-factor Λ [TeV](GRW) M [TeV](HLZ) T s n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 µµ,σ < 1.2fb(1.8fbexpected)at95%CL s,µµ 1.0 2.8 3.0 3.4 2.8 2.5 2.3 2.2 1.3 3.0 3.2 3.5 3.0 2.7 2.4 2.3 ee,σ < 1.6fb(2.3fbexpected)at95%CL s,ee 1.0 2.8 2.9 3.3 2.8 2.5 2.3 2.2 1.3 2.9 3.1 3.4 2.9 2.5 2.4 2.2 µµandee,σs,µµ+ee< 1.4fb(2.2fbexpected)at95%CL 1.0 3.1 3.7 3.7 3.1 2.8 2.5 2.4 1.3 3.2 3.8 3.8 3.2 2.9 2.7 2.5 8 and administrative staff at CERN and other CMS institutes, and acknowledge support from: FMSR(Austria);FNRSandFWO(Belgium);CNPq,CAPES,FAPERJ,andFAPESP(Brazil);MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croa- tia); RPF (Cyprus); Academy of Sciences and NICPB (Estonia); Academy of Finland, MEC, and HIP(Finland); CEAand CNRS/IN2P3(France); BMBF, DFG,and HGF(Germany); GSRT (Greece);OTKAandNKTH(Hungary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP- FAI(Mexico);MSI(NewZealand);PAEC(Pakistan);MSHEandNSC(Poland);FCT(Portugal); JINR(Armenia,Belarus,Georgia,Ukraine,Uzbekistan);MON,RosAtom,RASandRFBR(Rus- sia);MSTD(Serbia);MICINNandCPAN(Spain);SwissFundingAgencies(Switzerland);NSC (Taipei); TUBITAK and TAEK (Turkey); STFC (United Kingdom); DOE and NSF (USA). Indi- viduals have received support from the Marie-Curie programme and the European Research Council(EuropeanUnion);theLeventisFoundation;theA.P.SloanFoundation;theAlexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la For- mation a` la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voorInnovatiedoorWetenschapenTechnologie(IWT-Belgium);theCouncilofScienceandIn- dustrialResearch,India;andtheHOMINGPLUSprogrammeofFoundationforPolishScience, cofinancedfromEuropeanUnion,RegionalDevelopmentFund.