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TeV String Theories, Mini Black Holes and Trans-GZK Cosmic Rays 5 0 G. Domokosa∗ and S. Kovesi-Domokosa† 0 2 aDepartment of Physics and Astronomy n The Johns Hopkins University, Baltimore, MD a J Wereviewtheproposalthattrans-GZKcosmicrayinteractionsarecausedbyneutrinoprimaries. Theprimaries 0 cause excitations of strings and give rise to extensive air showers (EAS) resembling EAS induced by nuclei. We 3 alsoshowthatin“lowscale” (M ≈70TeV)stringmodelstheexcitedstringandtheminiblackholepicturesare ∗ equivalent. 1 v 0 8 1. Introduction Sommers [1] for possible sources of trans- 2 GZK cosmic rays within the the so called 1 The existence of cosmic rays transcending the GZK sphere, astrophysicists have been 0 Greisen-Zatsepin-Kuzmin(GZK)cutoffappearto lookingatthesky,but,inessence,foundno 5 be a fact of life. While there is still some contro- goodcandidates. Theastrophysicsproblem 0 versyregardingtheobservationaldata,itappears / hasbeensomewhataggravatedbythe work h thatopinionsconvergetowardacknowledgingthe of Stanev et al. [2]. Those authors showed p existence of trans-GZK events. Clearly, the issue that random intergalactic magnetic fields - will be satisfactorily clarified once future detec- p cause the high energy protons to undergo e tors,such as OWL, EUSO,the PierreAuger Ob- a Brownian motion. As a consequence, the h servatory, various neutrino telescopes, etc. will distance along the line of sight of a can- : v begin to take data. In the meantime, one may didate source for emitting trans-GZK pro- i relyupontheexistingsetofobservationsandseek X tons has to be less than about 14Mpc as an understanding of the phenomenon. It is to be opposedto ≈50Mpc as previouslybelieved r a emphasized that if indeed trans-GZK cosmic ray on the basis of assuming propagationalong events exist, they pose a serious challenge either a straight line. to our current understanding of particle physics, or of astrophysics (or, perhaps, both). There has been no dearth of theoretical • Fromtheparticlephysicspointofview,itis schemes proposing to understand the existence tobenotedthatthewell-knownGZKcutoff of trans-GZK CR events. In fact, currently, the is a low energy effect: at the GZK energy number of theoretical papers on this subject is (of a few times 1019eV), the average CMS aboutanorderofmagnitudelargerthenthenum- energy in the interaction of a high energy berofsucheventsobserved. Thisisclearlyavery proton with a photon in the CMB is of the unhealthy situation; however,it will change once order of the mass of the ∆ resonance. This the new detectors start collecting data. energy region has been extensively studied Fortunately, a substantial number of the pro- for the pasthalfcentury or soandit is well posed explanations is dead: they are, by now, understood. excluded by accelerator based data, data on the CMB, etc. See the talk of S. Kovesi-Domokos[3] • From the astrophysics point of view, start- discussing this issue. ing with the famous search of Elbert and In this talk we mainly follow a recent paper of ours [4], where a more detailed discussion of the ∗Speaker. e-mail: [email protected] Invited talk issues and a more complete list of references can givenatXIIIISVHECRI,Pylos,Greece †e-mail: [email protected] be found. 1 2 2. The Survivors if the primaries are neutrinos, the new physicshastohavethepropertythatinthe In essence, there are two proposals which have new physics regime, neutrinos have a large notbeenexcludedbynewdataorconsistencyre- cross section, about the size of a hadronic quirements. Both of them assume that the pri- one. This is plausible: in string models, maries of trans-GZK cosmic rays are neutrinos3 once the string is excited, the interactions and both of them rely upon the notion that the are unified: all interactions have the same characteristic scale of the “new physics” beyond strength. the StandardModel canbe in the TeV range,in- stead of 1013 to 1016TeV [7]. The surprising fact is that the black hole and string pictures are, in essence, different facets of • The excited string picture[6] the same scheme, even though they seem to be based on very different physics. • The mini black hole picture as applied to How can this happen? cosmic rays[8] Let us briefly review the main problems any suc- 3. Strings and Black Holes: the Equiva- cessful model of trans-GZK cosmic rays should lence solve. Let us illustrate the situation on a simple ex- • The penetration problem. In the absence of ample. Supposethatwewanttoproduceahighly nearby sources, one has to make sure that excited string in a neutrino – quark interaction. the primary can penetrate the CMB over (Thisispossible,sincetheexcitedstringisunsta- large distances. For neutrinos, this require- ble and it will eventually decay: there is no con- ment is beautifully satisfied: in an inter- flictwiththeconservationofenergy-momentum.) action of a neutrino having an energy, say, Apart from trivial factors, the probability of this 1020eV, with a typical CMB photon, the process is given by: CMS energy is of the order of a few hun- dredMeV.Consequently,onedoesnoteven P ∝Xhi|O†|N,αihN,α|O|iiδ(E−NM∗)(1) have to now about the existence of the W α and Z bosons. This is low energy physics: Ineq.(1)αstandsforthecollectionoflabelsnec- the mean free path of the neutrino is com- essary for the full specification of states at level parable with the horizon size. By contrast, N: one has to sum over (most of) those, since in an interaction with a nucleus in the at- the quantum numbers carried by |ii and O do mosphere, the CMS energy is in the range not fully specify the substate at level N. (We re- ofhundreds of TeV. Thus,if indeed the on- member that, apart from a constant – the Regge setofthe “newphysics”isaroundaTeVto intercept – the mass of string levels is given by a few tens of a TeV, one is well in the new M2 ∼ M2N, where N is a positive integer. Ev- ∗ physics regime there. erywhere,M∗ is the characteristicenergyscaleof the string model.) • The interaction problem. All observed We recognize that the quantity in eq. (1), trans-GZK events are “hadron-like”: it ap- pearsthatthattheobservedshowershavea ρM =X|N,αihN,α|δ(E−NM∗) (2) normal development, with an Xmax (where α known) as in a hadronic shower. Hence, is just the microcanonical density matrix of the 3Itisinterestingtorememberthatneutrinoprimariesfor finalstate. (Instatisticalmechanics,asmoothing the extreme energy cosmic rays were first proposed by of the delta function is necessary in order to de- G.CocconiatoneoftheearlyTexasSymposia(1967)and fine aleveldensity;inthe presentcontext,sucha soon thereafter by Berezinsky and Zatsepin [5], based on smoothing is automatic if the finite width of res- the Fermi theory of weak interactions. Unfortunately, it appears thatCocconi’sconjecturehasnotbeenrecorded. onances is taken into account.) The summation 3 over α leads to the information loss discussed by the Hagedorn temperature. It is necessary to Amati [9]characteristic of a black hole. takeKaluza-Klein(KK)excitationsintoaccount: Now, it is intuitively clear that a large micro- otherwise, the Hagedorn temperature is not the canonical ensemble is like a canonical one: a suf- maximal, but a minimal temperature, which is ficiently large system acts like its own thermal clearly unphysical. The contribution of the KK reservoir. (In ref. [4] we gave a formal proof of excitations to the level density is proportionalto this statement, using a saddle point expansion.) (E/M )n,nbeingthenumberofcompactifieddi- ∗ In fact, the temperature of the large ensemble is mensions. The expression of the Hagedorn tem- given by the usual formula all of us learned in perature in terms of M is somewhat model de- ∗ an undergraduate course on statistical mechan- pendent: inthecalculationscitedabove,onehas, ics, viz. T = M /a, with a ranging, approximately, be- H ∗ tween2and4forvariousstringmodels. For pur- 1 ∂S = , (3) poses of numerical estimates, we take a=3. T ∂E Anestimateofthesingleparticleinclusivecross where S (the entropy) is just the logarithm of sectionwasgiveninref.[4]andwereferthereader the level density as a function of the energy of to that article for details. The basis of the esti- excitation. mate is thatinthe restframe ofthe excitedreso- Thus,forahighlyexcitedstring,wemayassign nance (a leptoquark in our case) the distribution a temperature to it. Also, since the level density of the observed particle is given by a Fermi or grows as the exponential of the energy of excita- Bose distribution, respectively. tion,thereis alimiting temperaturetowhichthe Here we summarize the salient features of the system converges in the limit of very high (“infi- inclusive distribution as measured in the labora- nite”)excitations. Thus,atveryhighexcitations, tory frame. strings∼= black holes. One might say that this is a neat theoreti- • Thedistributionsarestronglypeakedinthe calconstruction,perhapssatisfyingtothepurists forward direction; they are exponentially who do not like two solutions to the same prob- decreasingwiththeemissionangleoftheob- lem, but does it have observable consequences? served particle. Remarkably, the answer is “yes”. We now turn In the early days of dual resonance models to explore the consequences of the equivalence of (ca. 1968), Gabriele Veneziano pointed out the string and black hole pictures. thatthefixedangleelasticscatteringampli- tudewasexponentiallysmallawayfromthe 4. Observable Consequences forwarddirection. We now see that this re- Considerleveldensitiesoftheasymptoticform: sult is much more general and it is, in fact, independent of the tree approximationto a −γ d(E)=expS(E)∼C(E/M ) exp(α(E/M ).(4) ∗ ∗ dual amplitude. The quantities C,γ,α,δ depend onthe specific • The total particle multiplicities can be model considered. This asymptotic form of the estimated by creating a model for the level density comprises all known string models. hadronization of quarks and gluons, for in- We now evaluate the microcanonical density stance,asitwasdoneinref.[4]. Onearrives matrix , eq. (2) by means of the saddle point attheconclusionthattotalmultiplicitiesre- method. semble hadron multiplicities created by an The inverse temperature turns out to be: incomingheavynucleus,e.g. Fe. Ofcourse, ∂S γ+3/2 β = ∼− +αM−1 (5) since at high string excitations the excited ∂E E ∗ string behaves as a system in a heat bath The temperature is asymptotically constantand, at the Hagedorn temperature, the relative hence,its limit asE →∞maybe identified with multiplicity of any particle species is pro- 4 portional to its statistical weight. Hence, showersinthestring/blackholepicture,we a number of prompt leptons is also cre- canintroducean“effectiveatomicnumber”: ated,withasmaller(byaboutafactorof3, multiplicity in the string picture because of the absence of color) statistical Aeff = (6) weight. However, once one begins a real- extrapolated multiplicity istic simulation of ν induced air showers in thispicture,theremaybeanoticeable(and, (Of course, this estimate of Aeff assumes a simple superposition picture of air showers perhaps, observable) difference in shower inducedbynuclei. Inanycase,thesuperpo- development. At this meeting, Claudio Co- sition picture is qualitatively correct.) The riano presented the results of a simulation result is displayed in the next Table. ofshowersusingthesemiclassicalblackhole picture [11]. It is likely that an adaptation ofthesimulationtotheschemepresentedin this talk will yield interesting and testable n 6 7 8 results. Aeff 69 16 4 • In order to assess the importance of the Table 2 multiplicity question, let us adopt the ap- Comparison of proton and black hole induced proximations made in ref. [4] and list the showers at EL = 3 × 1011GeV in terms of an hadronic multiplicities as a function of n, “effective atomic number”. the number of compactified dimensions. (Recall that for superstrings, n = 6.) The result is summarized below. It is noteworthy that A.A. Watson has empha- sizedoverthe yearsthatthe masscompositionof the extreme energy cosmic rays is uncertain and n 6 7 8 that, in fact, the data may favor a heavy com- N 1.76×104 4.16×103 1.12×103 had position, see [12] and references quoted in that paper. Table 1 Hadron multiplicity for various numbers of extra 5. Discussion: Can we tell the difference? dimensions We presented a scheme of understanding the events induced by extreme energy (trans-GZK) cosmic rays, based on a scenario involving “new We used a value of the characteristicstring physics”asabstractedfromaclassofstringmod- scale M ≈ 80TeV, as estimated in [10]. els. It is to be emphasized that the scheme ∗ This result is to be compared with an ex- presented here is more general than any specific trapolation of hadronic multiplicities as- stringmodelknowntoday. Itisessentialthatone suming that there is no new physics be- relyupontheparadigmofstronglycoupledstring tween present day accelerator energies and models: the features discussedhere, as far asone theenergiesoftrans-GZKcosmicrays. This knows, can be realized in strongly coupled string is relatively easy: most data listed in the models (and their future generalizations to a yet particle data group can be fitted by means better theory) only. of a quadratic polynomial in logs. In this Itis pleasingthatonecancandiscernsomees- way, one obtains a baseline: multiplicities sential differences between the string/black hole in hadronic interactions assuming no “new scheme advocated here and the heavy nucleus physics”. Comparing that to what we ob- scheme as advocated by Alan Watson, loc. cit. tainedinourestimatesforneutrinoinduced Both schemes favor “heavy nucleus” primaries of 5 the trans-GZK cosmic ray interactions, see our 94 (1996) N. Arkani-Hamed, S. Dimopoulos Table of effective atomic numbers. andG.R.Dvali,Phys.Lett.B429,263(1998). However, if the primaries are, indeed, nuclei, I.Antoniadis,N.Arkani-Hamed,S.Dimopou- they should undergo photo disintegration in sun- los and G.R. Dvali, Phys. Lett. B4336, 257 light: this is the celebrated Zatsepin effect [13]. (1998). (Briefly, heavy nuclei entering the neighborhood 8. J.L.FengandA.D.Shapere,Phys.Rev.Lett. ofoursolarsysteminteractwithsunlightandun- 88 021303 (2002). dergo photo disintegration. In the process, one 9. D. Amati, in Proceedings of The Abdus or a few nucleons are broken off and get sepa- Salam Memorial Meeting, edited by J. El- rated from the incoming nucleus. Thus, one can lis, F. Hussain, T. Kibble, G. Thompson and observe practically simultaneous air showers at M. Virasoro. World Scientific Publishing Co. detectors separated by distances of the order of Singapore (1997). 103km or so.) Clearly, no Zatsepin effect can be 10. W.S. Burgett, G. Domokos and S. Kovesi- observediftheprimaryofatrans-GZKairshower Domokos, hep-ph/0209162 (Expanded ver- isastronglyinteractingneutrino. Thus,thepres- sion of a paper presented at ICHEP 2002, ence or absence of the Zatsepin effect will differ- Amsterdam, The Netherlands. entiate between the (conservative) heavy nucleus 11. A. Cafarella, C. Coriano and T.N. Tomaras, and the (radical?) strongly interacting neutrino these Proceedings. schemes, once new detectors, such as both sites 12. A.A. Watson, these Proceedings. of the Pierre Auger observatory, will become op- 13. G.T. Zatsepin, Dokl. Akad. Nauk (USSR), erational. 80, 577 (1951) N.M. Gerasimova and G.T. Acknowledgment. We thank the organizers Zatsepin, Soviet Phys. 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