If the scale of quantum gravity is near a TeV, the LHC will be producing one
black hole (BH) about every second. The BH decays into prompt, hard photons and
charged leptons is a clean signature with low background. The absence of
significant missing energy allows the reconstruction of the mass of the
decaying BH. The correlation between the BH mass and its temperature, deduced
from the energy spectrum of the decay products, can test experimentally the
higher dimensional Hawking evaporation law. It can also determine the number of
large new dimensions and the scale of quantum gravity.Comment: 5 pages, 3 figures, submitted to PRL. Results presented at the Les
  Houches Workshop "Physics at the TeV Colliders" (May 30, 2001) and the
  "Avatars of M-Theory" conference, ITP at Santa Barbara (June 7, 2001),
  http://online.itp.ucsb.edu/online/mtheory_c01/dimopoulo

E. Eichten

Greg Landsberg

I. Antoniadis

N. Arkani-Hamed

P. C. Argyres

R. C. Myers

R. Emparan

Savas Dimopoulos

T. Sjöstrand

English

arXiv

If the scale of quantum gravity is near a TeV, the LHC will be producing one black hole (BH) about every second. The BH decays into prompt, hard photons and charged leptons is a clean signature with low background. The absence of significant missing energy allows the reconstruction of the mass of the decaying BH. The correlation between the BH mass and its temperature, deduced from the energy spectrum of the decay products, can test experimentally the higher dimensional Hawking evaporation law. It can also determine the number of large new dimensions and the scale of quantum gravity

Dimopoulos, Savas K

Landsberg, G L

CERN Document Server

arXiv:hep-ph/0106295   27 Jun 2001BlackHolesattheLHCSavasDimopoulosayandGregLandsbergbaPhysicsDepartment,StanfordUniversity,Stanford,CA94305-4060,USAbDepartmentofPhysics,BrownUniversity,Providence,RI02912,USAIfthescaleofquantumgravityisnearaTeV,theLHCwillbeproducingoneblackhole(BH)abouteverysecond.TheBHdecaysintoprompt,hardphotonsandchargedleptonsisacleansignaturewithlowbackground.TheabsenceofsignicantmissingenergyallowsthereconstructionofthemassofthedecayingBH.ThecorrelationbetweentheBHmassanditstemperature,deducedfromtheenergyspectrumofthedecayproducts,cantestexperimentallythehigherdimensionalHawkingevaporationlaw.Itcanalsodeterminethenumberoflargenewdimensionsandthescaleofquantumgravity.PACSnumbers:04.70,04.50,14.80.-jIntroduction:AnexcitingconsequenceofTeV-scalequantumgravity[1]isthepossibilityofproductionofblackholes(BHs)[2,3,4]attheLHCandbeyond.TheobjectiveofthispaperistopointouttheexperimentalsignaturesofBHproduction.Blackholesarewellunder-stoodgeneral-relativisticobjectswhentheirmassMBHfarexceedsthefundamental(higherdimensional)PlanckmassMPTeV.AsMBHapproachesMP,theBHsbe-come\stringy"andtheirpropertiescomplex.ThisraisesanobstacletocalculatingtheproductionanddecayoflightBHs,thosemostdirectlyaccessibletotheLHC,wherethecenter-of-mass(c.o.m.)energyofcollidingbeamsiscomparabletothePlanckmass.Inwhatfollows,wewillignorethisobstacleandestimatethepropertiesoflightBHsbysimplesemiclassicalarguments,strictlyvalidforMBHMP.Weexpectthatthiswillbeanadequateapproximation,sincetheimportantexperimen-talsignaturesrelyontwosimplequalitativeproperties:(i)theabsenceofsmallcouplingsand(ii)the\demo-cratic"(avorindependent)natureofBHdecays,bothofwhichmaysurviveasaveragepropertiesofthelightdescendantsofblackholes.Nevertheless,becauseoftheunknownstringycorrections,ourresultsareapproximateestimates.Forthisreason,wewillnotattemptselectivepartialimprovements{suchastimedependence,angularmomentum,charge,hair,andotherhigher-ordergeneralrelativisticrenements{which,forlightBHs,maybemaskedbylargerunknownstringyeects.WewillfocusontheproductionandsuddendecayofSchwarzschildblackholes.Production:TheSchwarzschildradiusRSofan(4+n)-dimensionalblackholeisgivenby[5]:RS=1pMP"MBHMP 8  n+32n+2!#1n+1;(1)assumingthatextradimensionsarelarge(RS).Considertwopartonswiththec.o.m.energyps^=MBHmovinginoppositedirections.Semiclassicalrea-soningsuggeststhatiftheimpactparameterislessthanthe(higherdimensional)Schwarzschildradius,aBHwiththemassMBHforms.Thereforethetotalcrosssectioncanbeestimatedfromgeometricalarguments[6],andisoforder(MBH)R2S=1M2P"MBHMP 8  n+32n+2!#2n+1(2)(seeFig.1a).Thisexpressioncontainsnosmallcouplingconstants;ifthepartonc.o.m.energyps^reachesthefundamentalPlanckscaleMPTeVthenthecrosssectionifofor-derTeV 2400pb.AttheLHC,withthetotalc.o.m.energyps=14TeV,BHswillbeproducedcopiously.Tocalculatetotalproductioncrosssection,weneedtotakeintoaccountthatonlyafractionofthetotalc.o.m.energyinappcollisionisachievedinaparton-partonscattering.Wecomputethefullparticlelevelcrosssec-tionusingthepartonluminosityapproach(afterRef.[7]):d(pp!BH+X)dMBH=dLdMBH^(ab!BH)s^=M2BH;wherethepartonluminositydL=dMBHisdenedasthesumoveralltheinitialpartontypes:dLdMBH=2MBHsXa;bZ1M2BH=sdxaxafa(xa)fb(M2BHsxa);andfi(xi)arethepartondistributionfunctions(PDFs).WeusedtheMRSD 0[8]PDFsetwiththeQ2scaletakentobeequaltoMBH,whichiswithintheallowedrangeforthisPDFset,uptotheLHCkinematiclimit.ThedependenceofthecrosssectiononthechoiceofPDFis10%,i.e.satisfactoryforthepurposeofthisesti-mate.Thedierentialcrosssectiond=dMBHfortheBHproducedattheLHCisshowninFig.1bforseveralchoicesofMP.ThetotalproductioncrosssectionattheLHCforBHmassesaboveMPrangesfrom0.5nbforMP=2TeV,n=7to120fbforMP=6TeVandn=3.IfthefundamentalPlanckscaleis1TeV,LHC,withthepeakluminosityof30fb 1/yearwillproduceover107blackholesperyear.ThisiscomparabletothetotalnumberofZ'sproducedatLEP,andsuggeststhatwemaydohighprecisionstudiesofTeVBHphysics,aslongasthebackgroundsarekeptsmall.Decay:ThedecayoftheBHisgovernedbyitsHawk-ingtemperatureTH,whichisproportionaltotheinverse2050001000005000100001010 210 310 410 5                        a)MBH, GeVMP , GeVParton σ, pb10-910-710-510-310-1100 5000 10000                  b)MBH, GeVdσ/dMBH, pb/GeVMS = 1 TeVMS = 3 TeVMP = 5 TeVMP = 7 TeV0 500010000050001000010 210 310 4                        c)MBH, GeVMP , GeV      T H, GeV01020300 5 10                  d)MBH/MPÆNæn=2n=4n=6FIG. 1: a) Parton-level production cross section, b) dieren-tial cross section d=dMBHat the LHC, c) Hawking temper-ature, and d) average decay multiplicity for a Schwarzschildblack hole. The number of extra spatial dimensions n = 4 isused for a)-c). The dependence of the cross section and Hawk-ing temperature on n is weak and would be hardly noticableon the logarithmic scale.radius, and given by [5]:TH= MP MPMBHn+ 28  n+32!1n+1n+ 14p(3)(see Fig. 1b). As the parton collision energy increases,the resulting black hole gets heavier and its decay prod-ucts get colder.Note that the wavelength  =2THcorresponding tothe Hawking temperature is larger than the size of theblack hole. Therefore, the BH is, to rst approxima-tion, a point-radiator and therefore emits mostly s-waves.This indicates that it decays equally to a particle on thebrane and in the bulk, since it is only sensitive to theradial coordinate and does not make use of the extra an-gular modes available in the bulk. Since there are manymore particles on our brane than in the bulk, this has thecrucial consequence that the black hole decays visibly tostandard model (SM) particles [4, 9].The average multiplicity of particles produced in theprocess of BH evaporation is given by: hN i =DMBHEE,where E is the energy spectrum of the decay products.In order to nd hN i, we note that the BH evaporationis a blackbody radiation process, with the energy uxper unit of time given by Planck's formula:dfdxx3exc,where x  E=TH, and c is a constant, which depends onthe quantum statistics of the decay products (c =  1 forbosons, +1 for fermions, and 0 for Boltzmann statistics).The spectrum of the BH decay products in the masslessparticle approximation is given by:dNdE1EdfdEx2exc.In order to calculate the average multiplicity of the par-ticles produced in the BH decay, we use the average ofthe distribution in the inverse particle energy:1E=1THR10dx1xx2excR10dxx2exc= a=TH; (4)where a is a dimensionless constant that depends on thetype of produced particles and numerically equals 0.68 forbosons, 0.46 for fermions, and12for Boltzmann statistics.Since a mixture of fermions and bosons is produced inthe BH decay, we can approximate the average by usingBoltzmann statistics, which gives the following formulafor the average multiplicity: hN i MBH2TH. Using Eq. (3)for Hawking temperature, we obtain:hN i =2pn+ 1MBHMPn+2n+1 8  n+32n + 2!1n+1: (5)Eq. (5) is reliable when the mass of the BH is muchlarger than the Hawking temperature, i.e. hN i  1; oth-erwise, the Planck spectrum is truncated at E MBH=2by the decay kinematics [10]. The average number ofparticles produced in the process of BH evaporation isshown in Fig. 1d, as a function of MBH=MP, for severalvalues of n.We emphasize that, throughout this paper, we ignoretime evolution: as the BH decays, it gets lighter and hot-ter and its decay accelerates. We adopt the \sudden ap-proximation" in which the BH decays, at its original tem-perature, into its decay products. This approximationshould be reliable as the BH spends most of its time nearits original mass and temperature, because that is whenit evolves the slowest; furthermore, that is also when itemits the most particles. Later, when we test the Hawk-ing mass-temperature relation by reconstructing Wien'sdispacement law, we will minimize the sensitivity to thelate and hot stages of the BHs life by looking at onlythe soft part of the decay spectrum. Proper treatmentof time evolution, for MBH MP, is diÆcult, since itimmediately takes us to the stringy regime.Branching Fractions: The decay of a BH is ther-mal: it obeys all local conservation laws, but otherwisedoes not discriminate between particle species (of thesame mass and spin). Theories with quantum gravitynear a TeV must have additional symmetries, beyondthe standard SU (3)  SU (2)  U (1), to guarantee pro-ton longevity, approximate lepton number(s) and avorconservation [11]. There are many possibilities: discreteor continuous symmetries, four dimensional or higher di-mensional \bulk" symmetries [12]. Each of these possi-ble symmetries constrains the decays of the black holes.Since the typical decay involves a large number of par-ticles, we will ignore the constraints imposed by the fewconservation laws and assume that the BH decays withroughly equal probability to all o  60 particles of the3SM.Sincetherearesixchargedleptonsandonephoton,weexpect10%oftheparticlestobehard,primarylep-tonsand2%oftheparticlestobehardphotons,eachcarryinghundredsofGeVofenergy.Thisisaverycleansignal,withnegligiblebackground,astheproductionofSMleptonsorphotonsinhigh-multiplicityeventsattheLHCoccursatamuchsmallerratethantheBHproduc-tion(seeFig.2).Theseeventsarealsoeasytotriggeron,sincetheycontainatleastonepromptleptonorphotonwiththeenergyabove100GeV,aswellasenergeticjets.TestoftheHawking'sradiation:Furthermore,sincetherearethreeneutrinos,weexpectonly5%averagemissingtransverseenergy(E/T)perevent,whichallowsustopreciselyestimatetheBHmassfromthevisibledecayproducts.WecanalsoreconstructtheBHtemperaturebyttingtheenergyspectrumofthedecayproductstothePlanck'sformula.Simultaneousknowl-edgeoftheBHmassanditstemperatureallowsforatestoftheHawking'sradiationandcanprovideanevidencethattheobservedeventscomefromtheproductionofBH,andnotfromsomeothernewphysics.Thereareafewimportantexperimentaltechniquesthatwewillusetocarryoutthenumericaltest.Firstofall,toimproveprecisionoftheBHmassreconstruc-tionwewilluseonlytheeventswithE/Tconsistentwithzero.GiventhesmallprobabilityforaBHtoemitaneutrinooragraviton,totalstatisticswon'tsuerap-preciablyfromthisrequirement.SinceBHdecayshavelargejetactivity,theMBHresolutionwillbedominatedbythejetenergyresolutionandtheinitialstateradiationeects,andisexpectedtobe100GeVforamassiveBH.Second,wewilluseonlyphotonsandelectronsinthenalstatetoreconstructtheHawkingtemperature.Thereasonistwofold:nalstateswithenergeticelectronsandphotonshaveverylowbackgroundathighps^,andtheenergyresolutionforelectronsandphotonsremainsexcellentevenatthehighestenergiesachievedinthepro-cessofBHevaparation.Wedonotusemuons,astheirmomentaaredeterminedbythetrackcurvatureinthemagneticeld,andthustheresolutiondeterioratesfastwiththemuonmomentumgrowth.Wealsoignorethe-leptondecaymodes,asthenalstateswith'shavemuchhigherbackgroundthaninclusiveelectronorpho-tonnalstates,andalsobecausetheirenergiescannotbereconstructedaswellasthosefortheelectromagneticobjects.Fractionofelectronsandphotonsamongthe-nalstateparticlesisonly5%,butthevastamountofBHsproducedattheLHCallowsustosacricetherestofthestatisticstoallowforahigh-precisionmeasurement.(Also,thelargenumberofdecayparticlesenhancestheprobabilitytohaveaphotonoranelectronintheevent.)Finally,iftheenergyofadecayparticleapproachesthekinematiclimitforpairproduction,MBH=2,theshapeoftheenergyspectrumdependsonthedetailsoftheBHdecaymodel.Inordertoeliminatethisunwantedmodeldependence,weuseonlythelowpartoftheenergyspec-1 10 102103104105106107108010002000300040005000600070008000900010000MBH, GeVdN/dMBH × 500 GeVMP = 1 TeVMP = 3 TeVMP = 5 TeVMP = 7 TeVFIG.2:NumberofBHsproducedattheLHCintheelectronorphotondecaychannels,with100fb 1ofintegratedlumi-nosity,asafunctionoftheBHmass.Theshadedregionscorrespondtothevariationinthenumberofeventsfornbe-tween2and7.ThedashedlineshowstotalSMbackground(frominclusiveZ(ee)anddirectphotonproduction).ThedottedlinecorrespondstotheZ(ee)+Xbackgroundalone.trumwithE<MBH=2.Theexperimentalprocedureisstraightforward:wese-lecttheBHsamplebyrequiringeventswithhighmass(>1TeV)andmutiplicityofthenalstate(N4),whichcontainelectronsorphotonswithenergy>100GeV.Wesmeartheenergiesofthedecayproductswiththereso-lutionstypicaloftheLHCdetectors.Webintheeventsintheinvariantmasswiththebinsize(500GeV)muchwiderthanthemassresolution.ThemassspectrumoftheBHsproducedattheLHCwith100fb 1ofinte-gratedluminosityisshowninFig.2forseveralvaluesofMPandn.BackgroundsfromtheSMZ(ee)+jetsand+jetsproduction,asestimatedwithPYTHIA[13],aresmall(seegure).TodeterminetheHawkingtemperatureineachMBHbin,weperformamaximumlikelihoodtoftheenergyspectrumofelectronsandphotonsintheBHeventstothePlanckformula(withthecoeÆcientcdeterminedbytheparticlespin),belowthekinematiccuto(MBH/2).WethenusethemeasuredMBHvs.THdependenceandEq.(3)todeterminethefundamentalPlanckscaleMPandthedimensionalityofspacen.NotethattodeterminenwecanalsotakethelogarithmofbothsidesofEq.(3):log(TH)= 1n+1log(MBH)+const;(6)wheretheconstantdoesnotdependontheBHmass,butonlyonMPandondetailedpropertiesofthebulkspace,suchasshapeofextradimensions.Therefore,theslopeofastraight-linettothelog(TH)vs.log(MBH)dataoersadirectwayofdeterminingthedimensionalityofspace.ThisisamultidimensionalanalogofWien'sdisplacementlaw.NotethatEq.(6)isfundamentallydierentfromotherwaysofdeterminingthedimensionalityofspace-time,e.g.bystudyingamonojetsignatureoravirtualgravitonexchangeprocesses,alsopredictedbytheories477.27.47.67.886.5 7 7.5 8 8.5 9log(MBH/1 GeV)log(TH/1 GeV)(MP=2 TeV, n=7) - Fit: n=6.69 ± 0.40(MP=3 TeV, n=4) - Fit: n=3.86 ± 0.34(MP =5 TeV, n=2) - Fit: n=1.95 ± 0.46FIG. 3: Determination of the dimensionality of space viaWien's displacement law at the LHC with 100 fb 1of data.TABLE I: Determination of MPand n from Hawking's radi-ation. The two numbers in each column correspond to frac-tional uncertainty in MPand absolute uncertainty in n, re-spectively.MP1 TeV 2 TeV 3 TeV 4 TeV 5 TeVn = 2 1%/0.01 1%/0.02 3.3%/0.10 16%/0.35 40%/0.46n = 3 1%/0.01 1.4%/0.06 7.5%/0.22 30%/1.0 48%/1.2n = 4 1%/0.01 2.3%/0.13 9.5%/0.34 35%/1.5 54%/2.0n = 5 1%/0.02 3.2%/0.23 17%/1.1n = 6 1%/0.03 4.2%/0.34 23%/2.5 Fit failsn = 7 1%/0.07 4.5%/0.40 24%/3.8with large extra dimensions.Test of the Wien's law at the LHC would provide aconrmation that the observed e + X and  + X eventexcess is due to the BH production. It would also bethe rst experimental test of the Hawking's radiation hy-pothesis. Figure 3 shows typical ts to the simulatedBH data at the LHC, corresponding to 100 fb 1of in-tegrated luminosity, for the highest fundamental Planckscales that still allow for determination of the dimension-ality of space with reasonable precision. The reach of theLHC for the fundamental Planck scale and the numberof extra dimensions via Hawking's radiation extends toMP 5 TeV and is summarized in Table [14].Note, that the BH discovery potential at the LHC ismaximized in the e=+X channels, where background ismuch smaller than that in the +X channel (see Fig. 2).The reach of a simple counting experiment extends up toMP 9 TeV (n = 2{7), where one would expect to seea handful of BH events with negligible background.Summary: Black hole production at the LHC may beone of the early signatures of TeV-scale quantum gravity.It has three advantages:Large Cross Section. Because no small dimension-less coupling constants, analogous to , suppress the pro-duction of BHs. This leads to enormous rates.Hard, Prompt, Charged Leptons and Photons.Because thermal decays are avor-blind. This signaturehas practically vanishing SM background.Little Missing Energy. This facilitates the deter-mination of the mass and the temperature of the blackhole, and may lead to a test of Hawking's radiation.It is desirable to improve our primitive estimates, es-pecially for the light black holes (MBH MP); this willinvolve string theory. Nevertheless, the most telling sig-natures of BH production { large and growing cross sec-tions; hard leptons, photons, and jets { emerge from qual-itative features that are expected to be reliably estimatedfrom the semiclassical arguments of this paper.Perhaps black holes will be the rst signal of TeV-scalequantum gravity. This depends on, among other factors,the relative magnitude of MPand the (smaller) stringscale MS. For MS MP, the vibrational modes of thestring may be the rst indication of the new physics.Note added: After the completion of this work, a re-lated paper [15] has appeared in the LANL archives.Acknowledgments: We would like to thank GiaDvali, Veronika Hubeny, Nemanja Kaloper, Elias Kir-itsis, Konstantin Matchev, and Lenny Susskind for valu-able conversations, and many of the participants of the\Physics at TeV Colliders" and \Avatars of M-Theory"workshops for their interest.5Results presented at the Les Houches Work-shop \Physics at the TeV Colliders" (May 30,2001) and the \Avatars of M-Theory" confer-ence, ITP at Santa Barbara (June 7, 2001),http://online.itp.ucsb.edu/online/mtheory c01/dimopoulos.[1] N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys.Lett. B 429, 263 (1998); I. Antoniadis, N. Arkani-Hamed,S. Dimopoulos, and G. Dvali, Phys. Lett. B 436, 257(1998); N. Arkani-Hamed, S. Dimopoulos, and G. Dvali,Phys. Rev. D 59, 086004 (1999).[2] P.C. Argyres, S. Dimopoulos, and J. March-Russell,Phys. Lett. B441, 96 (1998).[3] T. Banks and W. Fischler, hep-th/9906038.[4] R. Emparan, G.T. Horowitz, and R.C. Myers, Phys. Rev.Lett. 85, 499 (2000) [hep-th/0003118].[5] R.C. Myers and M.J. Perry, Ann. Phys. 172, 304 (1986).[6] In fact the cross section is somewhat enhanced by initial-state attraction [4].[7] V.D. Barger and R.J.N. Phillips, \Collider Physics, Up-dated Edition," Addison-Wesley, 1997, p. 157.[8] A.D. Martin, R.G. Roberts, and W.J. Stirling, preprintRAL-92-078 (1992).[9] L. Susskind, private communication.[10] To avoid this limitation when performing numerical testsof Wien's law, we truncate the integrals in Eq. (4) at thekinematic limit (MBH/2).[11] Any form of new physics at a TeV requires such newsymmetries. An example, for TeV-scale supersymmetry,is R-parity.[12] N. Arkani-Hamed and S. Dimopoulos, hep-ph/9811353.[13] T. Sjostrand, Comp. Phys. Comm. 82, 74 (1994).[14] We checked the eect of introducing an additional cut-o at E < MS, where string dynamics is expectedto aect the shape of the Planck spectrum, by takingMS=MP=2. As a result, the uncertainties in MPand nincreased by about a factor of 2.[15] S.B. Giddings and S. Thomas, hep-ph/0106219, v2.

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