Black Holes at Accelerators

Transcription

1 Black Holes at Accelerators Black hole production Measuring the Planck scale Black hole decay Event simulation & model uncertainties Measuring black hole mass Bryan Webber, SSI5 Determining the number of extra dimensions 1

2 Black hole production Parton-level cross section: ˆσ(ŝ = M 2 BH) = F n πr 2 S r S = Schwarzschild radius in 4+n dimensions: r S = ) MBH [ ( 1 8Γ n+3 2 πmpl (n + 2)M PL ] 1 n+1 F n = form factor of order unity (hoop conjecture) Usually set Planck scale MPL = 1 TeV in this study (Dimopoulos-Landsberg MPL [G(4+n)] -(n+2) ) 2

3 BH formation factor (1) b b max = 2r h = 2r s [ 1 + a 2 ] 1 n+1 a = (n + 2)J 2r h M BH, J bm BH /2 ˆσ = F n πr 2 S πb 2 max [ ( ) ] 2 2 n+1 n + 2 F n ( geometric ) 3

4 BH formation factor (2) Yoshino-Rychkov Yoshino-Nambu geometric H Yoshino & Y Nambu, gr-qc/293 H Yoshino & VS Rychkov, hep-th/

5 BH cross section vs Planck mass! (nb) < MBH=5 TeV YN form factor n=2 n=3 n=4 n=5 n=6 n= M PL (TeV) Little sensitivity to n Measuring σ and M BH gives MPL 5

6 BH cross sections at LHC Topology Total Cross Section (fb) n = 2 62, 5 TeV black hole n = 4 37, n = 6 34, n = TeV black hole n = 4 31 n = 6 27 n = TeV black hole n = n = Several 5 TeV BH per minute at LHC! 6

7 Black hole decay (1) Balding phase loses `hair and multipole moments, mainly by gravitational radiation Spin-down phase loses angular momentum, mainly by Hawking radiation Schwarzschild phase loses mass by Hawking radiation, temperature increases Planck phase mass and/or temperature reach Planck scale: remnant =?? 7

8 Black hole decay (2) We assume Schwarzschild phase is dominant all types of SM particles emitted with Hawking spectrum Hawking temperature dn de γe 2 (e E/T H 1)T n+6 H T H = n + 1 4πr BH (M BH ) 1 n+1 γ is (4+n)-dimensional grey-body factor 8

9 1 8 Grey-body factors 1 n= scalar 8 spinor! () abs(") [#r 2 H] 6 4 n=1! (1/2) abs (") [#r 2 H] 6 4 n=6 n=4 n=2 2 n=6 2 n= " r H " r H 1 8 vector Emission on brane only! (1) abs(") [#r 2 H] 6 4 n= n=2 n=6 Low-energy vector suppression CM Harris, hep-ph/ " r H 9

10 Integrated Hawking flux n r h F () r h F (1/2) r h F (1) r h F tot N.B. r h F tot 1 at large n Transit time time between emissions Decay no longer quasi-stationary at large n 1

11 Black hole lifetime τm BH n M BH = 5M PL M BH = 1M PL ( ) M BH = 5 TeV MBH s N.B. τm BH 1 at large n Black hole no longer well-defined? 11

12 Spin-down phase Few results available for spinning BH Power spectrum for scalar emission on brane (n=1).1.8 a = (n + 2)J 2r h M BH a * =1.5 rh d 2 E/dt dω Geometrical optics a * = a * =1. a * = ω r h CM Harris & P Kanti, hep-th/531 12

13 LHC Event Simulation 13

14 HERWIG Event Generator Most important SM & MSSM processes at LO spin correlations included parton showers at leading log (LL) no showering from SUSY particles provides some SM processes at NLO see S Frixione & BW, hep-ph/56182 & refs therein Interface to CHARYBDIS black hole generator 14

15 Main CHARYBDIS parameters Name Description Values Default TOTDIM Total dimension (n+4) GTSCA Use scale (1/rS) not MBH logical.false. TIMVAR Use time-dependent T H logical.true. MSSDEC Include t,w,z(2), h(3) decay GRYBDY Include grey-body factors logical.true. KINCUT Use kinematic cutoff logical.false. NBODY Multiplicity from remnant

16 Effects of grey-body factors Photons/25 GeV/1 events 6 4 Primary photons from 5 TeV BH (n=2) neglecting g.b.f. neglecting T var. including both Energy of photon (GeV) Particle emissivity (%) GRYBDY=.TRUE.GRYBDY=.FALSE. Particle type Generator Theory Generator Theory Quarks Gluons Charged leptons Neutrinos Photon Z W + and W Higgs boson Vector boson suppression 2-3% Generator-theory differences due to masses & charge conservation 16

17 Exploring Higher Dimensional Black Holes at the Large Hadron Collider C.M. Harris, M.J. Palmer, M.A. Parker, P. Richardson, A. Sabetfakhri and B.R. Webber Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 HE, UK. Institute for Particle Physics Phenomenology, University of Durham, DH1 3LE, UK. hep-ph/41122, JHEP5(25)53; see also CM Harris, PhD thesis, hep-ph/525; CM Harris et al (CHARYBDIS event generator) hep-ph/3735, JHEP8(23)33 earlier work: SB Giddings & S Thomas, hep-ph/16219; S Dimopoulos & G Landsberg, hep-ph/

18 Missing transverse energy Arbitrary Scale p p! QCD SUSY 5 TeV BH (n=6) 5 TeV BH (n=2) (P T > 6 GeV) (SUGRA point 5) Missing P T (GeV) Typically larger E than SM or even MSSM T 18

19 Measuring black hole masses Event 1 Constant.8685E+5 Mean Sigma 22.1 Event 4 Constant Mean Sigma TeV BH 8 TeV BH M rec. True BH - M BH (GeV) M rec. True BH - M BH (GeV) Need E < 1 GeV for adequate resolution T ΔM BH M BH 4% 19

20 Effect of energy cutoff E < M /2 BH Particle Energy (GeV) n= n= Particle Energy (GeV) M BH (GeV) M BH (GeV) Energy distribution of primary emissions vs M BH Cutoff affects spectrum at low mass and/or high n 2

21 T H (GeV) Effects of time dependence TIMVAR off (a) T H (GeV) 2 Fit: n = 1.7 ±.3 19 Fit: n = 3.8 ± TIMVAR on (b) M BH (GeV) Fits to primary electron spectrum for n=2 M BH (GeV) Neglecting time variation of TH leads to over-estimate of n 21

22 A possible observable sensitive to n P(E max > M BH /2 4 GeV) p.14 p M BH (GeV) (a) Test case (see section 3) M BH (GeV) (b) No time variation p.14 p M BH (GeV) (c) Kinematic cut on M BH (GeV) (d) 4-body remnant decay Not highly sensitive to model assumptions 22

23 Combined measurement of M and n PL n n % 68%, 1! 86.6%, 1.5! 95%, 2! 99.7%, 3! Mean x 129 Mean y RMS x RMS y M PL (GeV) ΔMPL MPL 15%, Δn.75 23

24 Conclusions Large cross section if Planck mass ~ 1 TeV Clear signature, with large E T But BH mass measurement needs small BH decay not well understood: early phases, time variation, spectrum cutoff, Planck-scale remnant... Measuring n difficult but may be possible E T 24