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Centauros And/Or Chirons As Evaporating Mini Black Holes

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Centauros And/Or Chirons As Evaporating Mini Black Holes Centauros and/or Chirons as evaporating mini black holes Theodore N. Tomarasa ∗ aDepartment of Physics and Institute of Plasma Physics, University of Crete, P.O.Box 2208, 71003 Heraklion, Crete, Hellas and Fo.R.T.H. It is argued that the signals expected from the evaporation of mini black holes - predicted in TeV-scale gravity models with large extra dimensions, and possibly produced in ultra high energy collisions in the atmosphere - have characteristics quite similar to the ones of the Centauro events, an old mystery of cosmic-ray physics. 1. Introduction the context of the above scenario [1]. After a quick review of the relevant scales and of the main The theoretical framework of this talk is the features of MBHs in TeV-gravity, as well as of TeV-scale gravity with large extra dimensions. the basic characteristics of the Centauro events, The basic assumption, easily accomodated in Su- I present in Section 5 the somewhat qualitative perstring Theory, is that our spacetime is a 4 di- arguments that support our interpretation. The mensional hypersurface (a D3-brane) embedded talk ends with a critical discussion. in a 10 dimensional world (the bulk), with the The first steps towards a more quantitative additional feature that all known matter (quarks, analytical/Monte Carlo investigation of the mini leptons, higgses), as well as the carriers of the fun- black hole picture are described in [2] and [3]. damental interactions of the Standard Model of Particle Physics (photon, W, Z, gluons) are con- 2. TeV-scale gravity models fined on our 4 dimensional subspace. Only grav- arXiv:hep-ph/0411081v1 5 Nov 2004 ity can propagate in the bulk. The fact that the Even though non-compact extra dimensions are only communication with the bulk is via the grav- not a priori excluded, the most straightforward itational force, allows for a fundamental gravita- realization of the above theoretical scenario is to tional scale to be of O(1TeV), while at the same neglect the tension on the brane, which would time the size of the extra spatial dimensions may modify the gravitational background, and to con- be as large as a fraction of a mm. sider the extra dimensions compact and forming Clearly, such a scenario, if true, leads to the ex- a higher dimensional torus T n, with equal radii citing prospect of observing string physics, large R. higher dimensions and quantum gravity effects, In the simplest case of n = 1, one is deal- within the next few years in the forthcoming ac- ing with a 4 dimensional Minkowski space with celerator (LHC), neutrino and cosmic-ray exper- one extra transverse dimension, a circle of radius iments. R. One may compute the gravitational poten- Even better, in this talk I will argue that the tial Φ(x,θ) (in the Newtonian approximation) of long known Centauro-like events (CLEs) may be a point mass M at the origin, by solving the cor- due to the formation and subsequent evapora- responding Poisson equation tion of mini black holes (MBHs), predicted in 2 2 1 ∂ Φ (4) δ(θ) ∇ Φ+ 2 2 = −G Mδ(x) (1) ∗This talk is mostly based on [1]. Research supported in R ∂θ 2πR part by the EU under the RTN contract HPRN-CT-2000- (4) 3 00122, and by a grant P.O. Education - Heraklitos from where G ≡ 1/M∗ is the 4 dimensional gravita- the Hellenic Ministry of Education. tional constant, with fundamental gravitational 1 2 scale equal to M∗. Its solution is long as their impact parameter is smaller than the Schwarzschild radius corresponding to their 2πMG(4) 1 − e−2r/R Φ(x,θ)= (2) center of mass energy. A black hole with mass Rr 1 − 2e−r/R cos θ + e−2r/R of the order of the ones discussed here can be where r = |x| and θ is the position in the com- produced in the collision of an ultra high energy pact transverse direction. Near the mass M, primary with atmospheric partons. The energy i.e. for r ≪ R and θ ≪ π it gives Φ ∼ of the primary should exceed 1000 TeV and the (4) 2 2 2 4πMG /(r + R θ ), the correct expression for cross section of the process is conjectured to be a 4 dimensional gravitational potential. At large 2 −37 2 weak σ ∼ πRS ∼ 10 cm ∼ σνN , comparable to distances (r ≫ R) from the mass M, on the the neutrino-nucleon weak interaction cross sec- (4) other hand, one obtains Φ ∼ 2πMG /Rr, the tion at these energies. correct 3 dimensional Newtonian potential with Once produced, black holes are believed to (4) 3 Newton’s constant GN =2πG /R =2π/RM∗ . evaporate. Even though noone has worked out These formulas generalize trivially to n toroidal the details of the evaporation process for such transverse dimensions, in which case Newton’s light black holes, we shall assume the semiclas- constant is given by sical formulas of the standard treatment. So, n+2 n+3 n+3 1 1 within τBH ∼ M∗ (4πRS) /(n + 1) ∼ GN ∼ 2 n (3) −27 M∗ (RM∗) 10 seconds the black hole decays ”democrat- ically” into all kinds of quarks, leptons, gauge Assume that the fundamental scale M of grav- ∗ bosons, gravitons, higgses. It is a fireball of tem- ity is of the order of the weak interaction scale perature T = (n+1)/4πR ∼ 1TeV. The num- M ∼ O(1TeV). Then, (3) leads to the correct BH S ∗ ber of initial particles emitted by the black hole value G ≃ 10−38GeV−2 for a value of R given N is determined by its entropy N ∼ S = by R ≃ 1/(M (M 2G )1/n). The value n = 1 is initial BH n ∗ ∗ N πM R /2. For the case of black holes with excluded, since it leads to R of the order of the BH S mass of order 1-2 TeV of interest here and n = 4, size of the solar system. For n = 2 one obtains this number is of the order of O(10). R2 ∼ 2mm. Accelerator and astrophysical con- straints lead to a prefered value of n ≥ 4 with a corresponding value for R, much larger than the 4. The Centauro-like events (CLEs) usual value 10−33cm. A normal high energy cosmic ray event is 3. Mini black holes created by the collision of a primary particle with a particle in the atmosphere. Typically a couple As described, the world contains black holes, of leading partons emerge from the interaction generalizations to D = 4+ n spacetime di- region with high transverse momenta, leaving be- mensions of the well known Schwarzschild met- hind a number of soft fragments, mainly pions ric. They are characterized by their mass with relative abundance 1:1:1. The neutral pions MBH , and can exist as long as MBH is subsequently decay to photons and the shower at least a few times the fundamental grav- ends up consisting of low pT < 1 GeV/c parti- ity scale. Lighter black holes cannot exist. cles with Nhadron/Nem ∼ 1 or even less, if one Thus, it is reasonable to expect that for M∗ takes into account the extra photons that will be a fraction of a TeV, the black hole masses produced as the shower develops even further. are MBH ≥ 2TeV. If, in addition, MBH ≪ In contrast to the above picture, several events 2 −(n+1)/n M∗(GN M∗ ) , the black hole is essentially have been observed since 1972 with the following 4+n-dimensional, since its Schwarzschild radius main characteristics [4]: (a) They were claimed −1 (1/n+1) RS ∼ M∗(M∗/MBH ) ∼ M∗ is much to have taken place at distances smaller that 500 smaller than the radius of the large extra di- m above the detectors at Pamir and Chacaltaya. mensions. Black holes are expected to be pro- It should be pointed out, however, that the alti- duced in the collision of any two particles, as tude was measured directly only for one of these 3 events, and even that has been questioned re- ing the evaporation of the MBH. cently [5]. (b) They are hadron rich, with typ- • Production rate. Assuming that the black ically Nhadron/Nem ≫ 1, (c) have fragments with holes are produced by primary neutrinos, one may high pT ≫ 1 GeV/c, (d) have in many cases obtain a rough estimate of the number of CLEs a heavy central core with tiny angular opening based on current figures for the neutrino flux Φν . (halo) and finally, (e) have all been observed with Since we are interested in neutrino energies of or- energies above a threshold around 500 TeV in the der 106 − 107GeV in the lab frame, one may use lab frame. the estimates for the gamma-ray burst muon neu- It should be pointed out that there are severe trino flux given in [6,7]. Their analysis leads to uncertainties in the observational data. One of ∼20 neutrino-induced muon events in a km3 wa- the speakers in this meeting presented a reanaly- ter or ice per year. Since the cross section of sis of the Centauro I and raised serious doubts MBH production by neutrinos is of the same or- about the altitudes reported in general for all der of magnitude as that of muon production, we these events [5]. Others express doubts about the would expect approximately the above number existence of these events altogether, worrying, for of black holes for each kind of neutrino. Multi- instance, about the fact that no such events have plying by 10-20 (the number of initial jets) and been observed yet in Kanbala and Fuji.
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