Black Holes at Accelerators: Problems and Perspectives Savina - PowerPoint PPT Presentation

Black Holes at Accelerators: Problems and Perspectives Savina Maria, JINR, Dubna International Workshop "Bogoliubov readings", Dubna, 22 September 2010 1 1

Black Hole formation in TeV- Black Hole formation in TeV -scale gravity scale gravity In large extra dimension models • Gravity stronger at small distances • Horizon radius larger • For M ~ TeV it increases from 10 -38 fm to 10 -4 fm For these BH R h << R and they have approximately higher dimensional spherical symmetry Pictures by Sabine Hossenfelder At the LHC partons can come closer than their Schwarzschild horizon black hole production 2 2

Evolution stages for BH I. Balding phase Asymmetric production, but “No hair” theorem: BH sheds its high multipole moments for fields (graviton and GB emitting classically), as electric charge and color. Characteristic time is about t ~ R S Result: BH are classically stable objects II-III. Hawking radiation phases (short spindown + more longer Schwarzschild) Quantum-mechanical decay trough tunneling, transition from Kerr spinning BH to stationary Schwarzschild one. angular momentum shedding (up to ~ 50% mass loss). Corrections with Gray Body Factors After this – thermal decay to all SM particles with black body energy spectra. Accelerating decay with a varying growing temperature. No flavor dependence, only number of D.o.f.– “democratic” decay IV. Planck phase: final explosion (subj for QGr) BH remnant (non-detectable energy losses), N-body 3 3 decay, Q, B, color are conserved or not conserved

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BH production in pp collisions: some well- -known formulas known formulas BH production in pp collisions: some well 1 ⎡ ⎤ ⎛ ⎞ + + n 3 n 1 Γ Schwarzschild raduis of a ⎜ ⎟ 8 ( ⎢ ⎥ 1 M multidimensional BH 2 ⎜ ⎟ = ⎢ BH ⎥ R S (R.C. Myers and M.J. Perry, Ann. Phys. 172, + π ⎜ ⎟ M n 2 M ⎢ ⎥ ⎜ ⎟ 304, 1986) ⎝ ⎠ ⎣ ⎦ − − 1 1 D 3 = 4 + R ~ M ( E M ) , D n S D D σ BH production cross section d dL = σ → BH ˆ ( ab BH ) (S. Dimopoulos, G. Landsberg, 2 = ˆ s M dM dM Phys.Rev.Lett.87:161602, 2001 BH BH BH hep-ph/0106295v1) π 2 R S ⎛ ⎞ 1 2 dL 2 M dx M ∑ ∫ ⎜ ⎟ = BH a BH f ( x ) f ⎜ ⎟ a a b ⎝ ⎠ dM s x sx a , b 2 BH a a M s BH PDF’s 5 5

BH Production in pp collisions at the LHC BH Production in pp collisions at the LHC Increasing cross section, no suppression from small couplings 6 6

Hawking evaporation of BH Hawking evaporation of BH 1 ⎛ ⎞ + n 1 ⎜ ⎟ + + + Hawking temperature ⎜ M n 2 ⎟ n 1 n 1 = × = T M (R.C. Myers and M.J. Perry, ⎜ ⎟ ⎛ ⎞ + H π π n 3 M 4 R 4 Γ ⎜ ⎟ Ann. Phys. 172, 304, 1986) ⎜ BH 8 ⎟ S ⎝ ⎠ ⎝ ⎠ 2 − − ∝ 1 ( D 3 ) T M H Multiplicity of produced particles in BH decay = N M E BH Planckian spectrum (black body) 2 ∞ 1 x ∫ dx 1 1 ± a x x e c 0 = = x = E T 2 where E T x T ∞ ∫ H H H dx ± x e c 0 1 ⎛ ⎞ ⎛ ⎞ + + n 3 n 1 ⎜ ⎟ Γ ⎜ ⎟ + 8 n 2 ⎛ ⎞ π ⎝ ⎠ 2 M + ⎜ ⎟ 2 n 1 = ⎜ ⎟ BH N ⎜ ⎟ + ⎝ ⎠ + n 1 M n 2 ⎜ ⎟ ⎝ ⎠ 7 7

Grey Body Factors for BH Decay Grey Body Factors for BH Decay Γ dN + 1 n 1 = s , l , m s , l , m = T ω ω m H π 2 exp[ ] 1 d dt T 4 r H h Grey body factors Papers on GBF: P. Kanti, J. March-Russell, I. Olasagasti K. Tamvakis, 2002; G. Duffy, C. Harris, P. Kanti and E. Winstanley, 2005; M. Casals, P. Kanti and E. Winstanley, S. R. Dolan, 2006-2007 D. Ida, K.-y. Oda and S. C. Park, 2003-2006 dN dN ∑ dN dN dN ∑ ∑ − = 1 2 , l , m e − 2 = + 1 , l , m 0 , l , m W 2 ω ω ω ω ω d dt d dt d dt d dt d dt l , m l , m l , m # D.o.F. for e- # D.o.F. for GB 8 8

BH production in pp collisions at the LHC BH production in pp collisions at the LHC DL ‘01 For the LHC energies: a) Parton-level production cross section b) Differential cross section n=4 c) Hawking temperature d) Average decay multiplicity for Schwarzschild BH 9 9 (S. Dimopoulos, G. Landsberg, Phys.Rev.Lett.87:161602, 2001, hep-ph/0106295v1)

Entropy, BH decay and M Entropy, BH decay and M min (BH) ) min (BH BH Entropy 1 ⎛ ⎞ − n 3 ⎛ + ⎞ + n 1 3 n ⎜ ⎟ π Γ ⎜ ⎟ n + 2 n 2 2 ⎛ ⎞ π ⎜ ⎝ ⎠ ⎟ 4 M + (R.C. Myers and M.J. Perry, 2 n 1 = ⎜ ⎟ BH S Ann. Phys. 172, 304, 1986) ⎜ ⎟ BH + ⎝ ⎠ + 2 2 n M n ⎜ ⎟ ⎝ ⎠ S BH must be large enough to K. Cheung, PR D66, 036007 (2002). reproduce thermal BH decay 1 ⇒ << > 1 S 25 BH S BH (S.B. Giddings, hep-ph/0110127v3, K. Cheung, Phys. Rev. Lett. 88, 221602, 2002) BH ≥ min M 5 M Democratic decay blinded to flavor: probabilities are the same for all species 10 10 (violation of some conservation laws)

# D.o.f D.o.f. counting and . counting and “ “democracy democracy” ” of decay of decay # ± ± ± ± γ µ τ ν ν µ ν Z , W , , g , H ; e , , , , , ; u , d , s , c , b , t τ e ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 3 6 2 16 1 4 4 4 2 2 2 12 12 12 12 12 12 ± u , d , s , c , b , t l 1 4 2 4 3 × × 6 4 3 ↓ ↓ 1 1 + − 2 ; flavor color 2 2 (Gauge+Higgs) : (Leptons) : (Quarks) = 28 : 18 : 72 The ratio of hadronic/leptonic is 5 : 1 11 11

Black Hole or String Ball? Black Hole or String Ball? Picture by Kingman Cheung M BH >> M D : semiclassical well-known description for BH’s. What happens when M BH approach M D ? BH becomes “stringy”, their properties become complex. Matching: = σ = σ min 2 ( SB ) ( BH ) M M g 2 2 BH s s = = M M g M M g SB s s BH s s S. Dimopoulos and R. Emparan, Phys. Lett. B526, 393 (2002), hep-ph/0108060 12 12

Production cross section for BH, SB and p- -brane brane Production cross section for BH, SB and p K. Cheung, PR D66, 036007 (2002), hep-ph/0305003 13 13

Final state of the SM process vs vs typical BH decay typical BH decay Final state of the SM process spectra spectra BH decay SM Pictures by Sabine Hossenfelder Multi-jet and hard leptons events, spherical, typical temperature about 200 GeV 14 14

BH Experimental Signatures BH Experimental Signatures • Potentially large cross sections, approaching 10 3 fm or more • An increase of cross sections with energy, according to an absense of gauge coupling suppression (will be hard to see at the LHC) • Relatively high sphericity for final states • High multiplicity as proportional to the BH entropy of particles produced (primaries) • Hard trasverse leptons and jets, in significant numbers • Approximately thermally determined ratios of species (democratic decay) • Suppression of highest-energy jets • Decrease of decay primary (lepton/parton) energy with total event transverse energy (resulting from decreasing Hawking temperature with mass) 15 15

Part II. Optimism Is fading… … Part II. Optimism Is fading BH not as spectacular as advertized!! • BH Production near the threshold and careful counting • Conventions on a fundamental mass • Inelasticity for BH formation at the LHC and in the UHECR • Minimal M for a sensible definition of a BH • LHC unlikely to make classical BH with thermal decay spectra. So, what can we see, then? • Two-body final states and QG … but it is not the end of the story but it is not the end of the story … 16 16

Conventions on a fundamental mass Conventions on a fundamental mass 1 1 ∫ ∫ = − ℜ + − D D S d x g d x g L π 8 G 2 Just numerical coefficients D At least three definitions: But: there is essential difference between M about 1 TeV and 2 TeV for the LHC! − π D 4 − = ( 2 ) 2 D M P π 4 G 1 D = − D 2 M 2 M P D − π D 4 − = ( 2 ) D 2 M D π 8 G D D=6 = M 1 . 3 M p DL 1 − = − DL = D 2 − − − M π D 2 D 6 D 5 D 2 M 2 M G P DL D=10 = M 2 . 9 M D p DL 17 17

At what energy can we safely speak about “ “true true” ” BH BH At what energy can we safely speak about production? production? Clearly E > M D . But how much large? 18 18 From the talk by Lisa Randall at String’2007