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Randall-Sundrum Black Holes at the LHC

Randall-Sundrum Black Holes at the LHC. Greg Landsberg Brown University DPF 2006, Honolulu October 30, 2006. Outline. Black holes in General Relativity Randall-Sundrum Model Production of Black Holes at Accelerators Basic Idea Production and Decay Wien’s Law

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Randall-Sundrum Black Holes at the LHC

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  1. Randall-Sundrum Black Holes at the LHC Greg Landsberg Brown University DPF 2006, Honolulu October 30, 2006

  2. Outline • Black holes in General Relativity • Randall-Sundrum Model • Production of Black Holes at Accelerators • Basic Idea • Production and Decay • Wien’s Law • Randall-Sundrum vs. large-ED black holes • Conclusions Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  3. Black holes (BH) are direct prediction of Einstein’s General Relativity (GR) It’s somewhat ironical that Einstein himself never believed in BH! Karl Schwarzschild showed (1916) that the space-time metric for a massive body has a singularity at r = RS 2MGN/c2 r and t essentially swap places for r < RS Hence, if the mass M is enclosed within its Schwarzschild radius RS, a “black hole” is formed The term “black hole” was coined much later by John Wheeler ~1967 Naїvely, a black hole would only grow once it’s formed In 1975 Steven Hawking showed that this is not true [Commun. Math. Phys. 43, 199 (1975)], as the black hole can evaporate by emitting virtual pairs at the event horizon, with one particle of the pair escaping the BH These particles have a black-body spectrum at the Hawking temperature: In natural units ( = c = k = 1), one has: RSTH = (4p)-1 If TH is high enough,massive particles can be also producedin the process of evaporation Black Holes in General Relativity Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  4. Randall-Sundrum Model x5 SM brane Rc AdS5 f k – AdS curvature SM brane(f = p) Planck brane (f = 0) • Randall-Sundrum (RS) model[PRL 83, 3370 (1999); ibid., 4690 (1999)] • + brane – no low energy effects • +–branes – TeV Kaluza-Klein modes of graviton • Low energy effects on SM brane are given by Lp; for kRC ~ 10, Lp ~ 1 TeVandthe hierarchy problem is solvednaturally G AdS Planck brane Anti-deSitter space-time metric: Reduced Planck mass: Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  5. Randall-Sundrum Model Observables • Need only two parameters to define the model:k and RC • Equivalent set of parameters: • The mass of the first KK mode, M1 • Dimensionless coupling • To avoid fine-tuning and non-perturbative regime, coupling can’t be too large or too small • 0.01 ≤ ≤ 0.10 is theexpected range • Gravitons are narrow Expected Run II sensitivity in DY Drell-Yan at the LHC M1 Davoudiasl, Hewett, Rizzo [PRD 63,075004 (2001)] Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  6. Current Limits on RS Gravitons [PRL 95, 091801 (2005)] Assume fixed K-factor of 1.34 for the signal M1 > 250-870 GeV Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  7. Based on the work done with Savas Dimopoulos a few years ago [PRL 87, 161602 (2001)] Related study by Giddings, Thomas[PRD 65, 056010(2002)] Extends previous theoretical studies by Argyres, Dimopoulos, March-Russell[PLB 441, 96 (1998)],Banks, Fischler[JHEP, 9906, 014 (1999)],Emparan, Horowitz,Myers[PRL 85, 499 (2000)] to collider phenomenology Big surprise: BH production is not an exotic remote possibility, but the dominant effect! Main idea:when the c.o.m. energy reaches the fundamental Planck scale, a BH is formed; cross section is given by the black disk approximation: This is an enormous cross section! For a 400 TeV machine, RS ~ 1 fm, so nothing, including diffraction, will be seen except for the BH production! Theoretical Framework s ~ pRS2 ~ 1 TeV -2 ~ 10-38 m2 ~ 100 pb ^ parton M2 = s RS parton Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  8. Assumptions and Approximations • Fundamental limitation: our lack of knowledge of quantum gravity effects close to the Planck scale • Consequently, no attempts for partial improvement of the results, e.g.: • Grey body factors • BH spin, charge, color hair • Relativistic effects and time-dependence • The underlying assumptions rely on two simple qualitative properties: • The absence of small couplings; • The “democratic” nature of BH decays • We expect these features to survive for light BH • Use semi-classical approach strictly valid only for MBH» MP; only consider MBH > MP • Clearly, these are important limitations, but there is no way around them without the knowledge of QG Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  9. Schwarzschild radius is given by Argyres et al.[hep-th/9808138], after Myers, Perry[Ann. Phys. 172 (1986) 304]; it leads to: Hadron colliders: use parton luminosity w/ MRSD-’ PDF (valid up to the VLHC energies) Note: at c.o.m. energies ~1 TeV the dominant contribution is from qq’ interactions Black Hole Production Dimopoulos, GL,[PRL 87, 161602 (2001)] stot = 0.5 nb (MP = 2 TeV, n=7) LHC n=4 stot = 120 fb (MP = 6 TeV, n=3) Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  10. Black Hole Decay Dimopoulos, GL,[PRL 87, 161602 (2001)] Note that the formula for N is strictly valid only for N » 1 due to the kinematic cutoff E < MBH/2; If taken into account, it increasesmultiplicity at low N • Hawking temperature:RSTH = (n+1)/4p • BH radiates mainly on the braneEmparan, Horowitz, Myers,[hep-th/0003118] • l ~ 2p/TH > RS;hence, the BH is a point radiator, producing s-waves, which depends only on the radial component • The decay into a particle on the brane and in the bulk is thus the same • Since there are much more particles on the brane, than in the bulk, decay into gravitons is largely suppressed • Democratic couplings to ~120 SM d.o.f. yield probability of Hawking evaporation into g,l±, and n ~2%, 10%, and 5% respectively • Averaging over the BB spectrum givesaverage multiplicity of decay products: • Stefan’s law:t ~ 10-26 s Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  11. Black Hole Factory Dimopoulos, GL,[PRL 87, 161602 (2001)] Black-Hole Factory n=2 n=7 g+X Drell-Yan Spectrum of BH produced at the LHC with subsequent decay into final states tagged with an electron or a photon Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  12. Relationship between logTH and logMBH allows to find the number of ED, This result is independent of their shape! This approach drastically differs from analyzing other collider signatures and would constitute a “smoking cannon” signature for a TeV Planck scale Shape of Gravity at the LHC Dimopoulos, GL,[PRL 87, 161602 (2001)] Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  13. First Detailed LHC Studies • First studies already initiated by ATLAS and CMS • ATLAS –CHARYBDIS HERWIG-based generator with more elaborated decay model Harris/Richardson/Webber • CMS – TRUENOIR,GL • Also:CATFISH – see R.Godang’s talk Simulated black hole event in the CMS detector, A. de Roeck & S. Wynhoff Simulated black hole event in the ATLAS detector, from ATLAS-Japan Group Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  14. Randall-Sundrum Black Holes • Not nearly as studied as BH in large ED • Originally suggested in Anchordoqui, Goldberg, Shapere,[PRD 66, 024033 (2002)] • A few authors extended work to various cases:Rizzo,[JHEP 0501, 28 (2005); hep-ph/0510420; hep-ph/0603242];Stojkovic,[PRL 94, 011603 (2005)] • The event horizon has a pancake-like shape (squashed in the 5th dimension by e-kpRc) • Nevertheless, the comparison with the ADD BH is trivial, GL,[hep-ph/0607297] • If RSe-kpRc<< pRC the BH is still “small” and can be treated as a 5D BH in flat space (ignoring the AdS curvature at the SM brane ~k2 << 1) • For BH production,Lp in the RS model plays the same role as the fundamental Planck scale MD in the ADD model Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  15. RS to ADD Mapping • Unlike the ADD, the 5D Planck scale, M, is of order of MPl: • The Schwarzschild radius: • Given M3 kMPl2 = Lp2ke2pkRc, • Compare with: • Then if one sets Lp = MD and k = 1/8p  0.04, the RS formula turns into the ADD one! Thus, the two cases are equivalent within the approximations we used! • TH = 1/(2pRS) (ADD formula in 5D) Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  16. More generally, the mapping between the ADD and RS parameters is as follows: n = 1, MD = Lp(8pk)1/3 Note that generally, the BH production cutoff, if chosen equal to Lp, won’t be equal to MD However, this parameter set is usable in the BH eventgenerators to study arbitrary coupling values Cross section is somewhat higher for RS BH and they are colder than their ADD counterparts Consequently, the RS BH decay results in higher number of final state particles, making it easier to establish the signal Results for RS Black Holes ~ unphysical ~ k = 1/8p unphysical ~ Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  17. RS BH: Samples & Wien’s Law ~ k = 1/8p Lp = MD 100 fb-1 @ the LHC Impressive precisionin proving n=1! Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  18. In terms of probing k vs. M1, RS black holes would offer the entire allowed range to be probed with ~1 year at a nominal LHC luminosity Significant fraction of the allowed parameter space can be probed with just 1 fb-1 (up to M1 ~ 3 TeV for k = 0.1) The reach is fairly competitive with direct searches for RS gravitons in the dilepton/diphoton mode Probing Randall-Sundrum Model w/ BH  Lp = 10 TeV ~ ~ CMS Sensitivity Single-eventlevel Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  19. Conclusions • Black hole production at future colliders is likely to be the first signature for quantum gravity at a TeV • Large production cross section, low backgrounds, and little missing energy would make BH production and decay a perfect laboratory to study strings and quantum gravity • Precision tests of Hawking radiation may allow to determine the shape of extra dimensions • Properties of black holes in the Randall-Sundrum model are similar to those in models with large extra dimensions, but the former are somewhat easier to find and measure • A possibility of studying black holes at future colliders is an exciting prospect of ultimate ‘unification’ of astro-particle physics and cosmology Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  20. BH at Accelerators: Basic Idea NYT, 9/11/01 Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  21. SM fields are localized on the (3+1)-brane; gravity is the only force that “feels” the bulk space What about Newton’s law? Ruled out for infinite extra dimensions, but does not apply for sufficiently small compact ones The ADD Model (Large Extra Dimensions) Gravity is fundamentally strong force, bit we do not feel that as it is diluted by the volume of the bulk G’N = 1/MD2; MD  1 TeV More precisely, from Gauss’s law: Amazing as it is, but no one has tested Newton’s law to distances less than  1mm (as of 1998) Current limits: n = 2 nearly ruled out; for n > 2 limits are: MD > 1.4 TeV ~ Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  22. Dimopoulos/Emparan,[PL B526, 393 (2002)] – an attempt to account for stringy behavior for MBH ~ MS GR is applicable only for MBH > Mmin ~ MS/gS2, where gS is the string coupling; MP is typically less than Mmin They show that for MS < M < Mmin, a string ball, which is a long jagged string, is formed Properties of a string-ball are similar to that of a BH: it evaporates at a Hagedorn temperature:in a similar mix of particles, with perhaps a larger bulk component Cross section of the string ball production is numerically similar to that of BH, due to the absence of a small coupling parameter: It might be possible to distinguish between the two cases by looking at the missing energy in the events, as well as at the production cross section dependence on the total mass of the object Very interesting idea; more studies of that kind to come! String Balls at the LHC Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  23. Geometrical cross section approximation was argued in early follow-up work by Voloshin [PL B518, 137 (2001), PL B524,376 (2002)] More detailed studies showed that the criticism does not hold: Dimopoulos/Emparan – string theory calculations [PLB 526, 393 (2002)] Eardley/Giddings – full GR calculations for high-energy collisions with an impact parameter [PRD 66, 044011 (2002)]; extends earlier d’Eath and Payne work Yoshino/Nambu - further generalization of the above work [PRD 66, 065004 (2002); PRD 67, 024009 (2003)] Further improved byYoshino/Rychkov[hep-th/0503171] Hsu – path integral approach w/ quantum corrections [PL B555, 29 (2003)] Jevicki/Thaler – Gibbons-Hawking action used in Voloshin’s paper is incorrect, as the black hole is not formed yet! Correct Hamiltonian was derived: H = p(r2 – M)  ~ p(r2 – H), which leads to a logarithmic, and not a power-law divergence in the action integral. Hence, there is no exponential suppression [PRD 66, 024041 (2002)] Geometrical Cross Section Suppression? Greg Landsberg - Randall-Sundrum Black Holes at the LHC

  24. Phenomenology of mini-BH became a popular subject (~400 citations of the original papers) There have been a lot of studies of various second-order effects in BH formation and decay Many of the estimates suffer from the intrinsic lack of knowledge of the quantum gravity effects, which will affect these fine features tremendously Grey-body factor calculation has been attempted by many authors, e.g., Kanti, March-Russell, [PRD 66, 024023 (2002); PRD 67, 104019 (2003)] Kerr black holes have been considered extensively, e.g., Ida, Oda, Park,[PRD 67, 064025 (2003), erratum PRD 69, 049901 (2004)] Accounting for recoil effectse.g.,Frolov, Stojkovic,[PRD 66, 084002 (2002), PRL 89, 151302 (2002)] Number of people discussed the effect of Gauss-Bonnet terms, which arise naturally in perturbative expansion of string theory e.g.,Torii, Maeda,[hep-ph/0504127 and hep-ph/0504141] Randall-Sundrum BH studies Anchordoqui, Goldberg, Shapere,[PRD 66, 024033 (2002)] Exploring AdS/QFT duality to relate formation of black holes in AdS to QCD colorless scattering and Froissart unitarity bound saturation Giddings,[PRD 67, 126001 (2003)];Kang, Nastase, [hep-th/0409099, hep-th/0410173] RHIC fireball/BH duality Nastase,[hep-th/0501068] Other Recent Developments Greg Landsberg - Randall-Sundrum Black Holes at the LHC

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