Introduction to Black Holes, Extra Dimensions and Colliders

Transcription

1 Introduction to Black Holes, Extra Dimensions and Colliders James Frost Institute of Physics Half-day Meeting Thursday 9th December 2010 James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

2 Welcome Thankyou all for coming, despite the weather and proximity to the end of university term and Christmas. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

3 Programme With thanks to the IoP Introduction James Frost (University of Cambridge) Colliding Black Holes in 3+1 and higher dimensional spacetimes Ulrich Sperhake (California Institute of Technology) CMS status from the 2010 run James Jackson (Rutherford Appleton Laboratory) Coffee Break Astrophysical and Cosmological Impact of Extra Dimensions Malcolm Fairbairn (Kings, London) Quantum black holes and gravity Xavier Calmet (University of Sussex) Extra dimensions and black holes at the LHC Ryan Buckingham (University of Oxford) James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

4 Outline Extra Dimensions Black Hole Formation Hawking Phase - Black Hole Evaporation Evolution and Phenomenology Summary James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

5 Why Extra Dimensions? Motivation The Hierarchy Problem Why is the fundamental scale for gravity: M Pl TeV, so large compared to the electroweak energy scale: M EW 1TeV Why is gravity so weak? See e.g. N.Arkani-Hamed et al. hep-ph/ , L. Randall & R. Sundrum hep-ph/ James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

6 The Extra Dimensions Solution Solve with Extra Dimensions Assume spacetime is (4+n) dimensional., Take M EW 1,TeV - M 4+n as fundamental scale 4D gravity diluted Two main classes of models: Large extra dimensions (ADD) (Usually a) Single warped extra dimension (RS). N.B. Deviations at short distances, KK modes. constraints (see Malcolm s talk) James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

7 Black Hole Formation The black disk approach Thorne s hoop conjecture (Magic without Magic 231 (1972)): For a given concentration of matter/energy, if it fits inside a hoop with the Schwarzchild radius r S for that mass, then a black hole forms. Black disk cross section: S. B. Giddings and S. D. Thomas, hep-ph/ S. Dimopoulos and G. Landsberg, hep-ph/ James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

8 Production - Short-comings Why not b>2r S? Angular momentum? Losses in gravitational radiation? Spin and charge of the partons. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

9 Production Model I Ideally, set up the spatial metric for two highly boosted particles (modelled as black holes). Include spin and charge. Evolve system. Obtain final metric and radiation. see Ulrich s talk. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

10 Production Model II Trapped Surface Results Trapped surface methods give bounds on the maximum impact parameter and hence parton-level cross section. Bounds on the mass (M) and angular momentum (J) trapped for a given impact parameter, b. Mass bounds compared with approximate methods for b=0 James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

11 Production Losses H. Yoshino, V. S. Rychkov hep-th/ For each value of impact parameter b, a maximum bound can be placed on the fraction of the black hole mass and angular momentum lost in radiation. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

12 Inelasticity Black hole cross-sections can be large. But assuming the maximum allowed losses reduces the differential cross section dramatically. Large uncertainties. When is the semi-classical approach valid-how far above M Pl? Can argue the Compton wavelength of colliding particle of energy E/2 must lie within the Schwarzschild radius bounds on E/M Pl, particularly in the RS case. Expect interactions, with lower entropy and multiplicity below this - with similar cross sections. Randall, Meade arxiv: James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

13 Open Issues Formation Numerical relativity simulations in (3+1) and higher dimensions, (see Ulrich s talk) Shibata and Yoshino arxiv: , Sperhake et al. arxiv: , Effects of brane tension, thickness and extra dimensional geometry not completely modelled. Quantum gravity effects (see Xavier s talk) - input partons have charges. What is the threshold for equilibrium black hole production? Randall, Meade arxiv: James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

14 Black Hole Lifecycle Black holes formed will be rapidly rotating, asymmetric, and hairy. Four stages of subsequent evolution. Balding Phase Spin-down Phase Schwarzschild Phase Planck (Quantum) Phase Question: Is this still true for very light black holes? James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

15 The Hawking Phase Particle Creation The central result of Hawking s calculation is: Classically, black hole do not emit, only accrete. However, in 1974, Hawking found a quantum instability. Effectively, the large gravitational field leads to spontaneous emission of particle via pair creation at the event horizon (cf. e + e pairs in a strong electric field). Black hole evaporates and slowly loses mass Gravity couples universally, so all SM particles can be emitted. The spectrum is that of a grey-body, with a characteristic temperature T H (non-rotating case): T H = n+1 4πr S James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

16 Hawking Radiation Non-rotating case Has a thermal, black-body character, with Planckian factor and temperature T H modified by a transmission coefficient (grey-body factor), codifying the probability of escaping the gravitational field. Spin-dependent - through helicity label h. Isotropic angular distribution. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

17 Particles emitted Qualitative Features Universal thermal spectrum for particles emitted (modulo spin). Particle type spin-0 spin-1/2 spin-1 Quarks Gluons Charged Leptons Neutrinos Photon Z W + and W Higgs boson Total Integrating the spectrum gives a high multiplicity. Implications for colliders - expect signature to have multiple hadronic jets. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

18 Grey-Body Progress and Status Hawking Radiation from Rotating Black Holes Rotating black holes have spectra that depend upon black hole oblateness (a ). In order to simulate rotating black holes, their grey-body factors are needed. Current Status Brane emission of scalar, fermion and gauge bosons done - rotating and non-rotating Bulk emission of scalars done - rotating and non-rotating Graviton emission onto brane and into bulk - done in non-rotating case, very limited results in rotating case Black holes radiate mainly on the brane Emparan, Horowitz and Myers, hep-th/ Casals et al. arxiv: James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

19 Rotation Effects I Once the grey-body factors are known, the power fluxes and angular distributions can be determined. Power spectrum of fields for brane emission with n=6 and a range of BH oblateness. Rotation increases the mean energy and total flux dramatically. Harder spectrum. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

20 Rotation Effects II Rotation breaks the isotropic emission spectrum. Higher energy emissions are more equatorial in character. Low energy vector emissions are more axial with each polarisation contriubting differently to the angular distribution. Azimuthal symmetry remains. Angular power fluxes for scalars, fermions and vectors. hep-th/ ,hep-th/ ,hep-th/ hep-th/ ,hep-th/ ,hep-th/ James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

21 Black Hole Evolution Semi-classical limit: BH mass 50 TeV JF et al. arxiv: Shows expected semi-classical behaviour: Schwarzschild: steady loss of mass until Planck phase. Rotating: mass lost more rapidly during spin-down phase. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

22 Black Hole Evolution II LHC energies: BH mass 10 TeV JF et al. arxiv: Evaporation is less smooth, due to fewer emissions. Statistical fluctuations are larger, and trends less definite. James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

23 Open Issues Hawking Phase Gravitational modes in the rotating case missing. Requires full gravitational perturbation equations. Recent work only for tensor modes arxiv: , arxiv: Black hole not exactly neutral (at least initially) Hawking calculation does not take into account recoil of the black hole Effects of brane tension, thickness and warped extra dimensions not completely modelled. Final stage - quantum gravity effects important. Recent reviews: Kanti arxiv: , Gregory arxiv: James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

24 Experimental Signature What s different about black holes? Signatures of semi-classical black holes: Potentially very high cross sections. High multiplicity events, with multiple very high p T objects. Rotation slightly reduced multiplicity but harder spectrum Wide range of SM particles - many hadronic jets, but also highly boosted photons and leptons hard to replicate through other BSM scenarios. Potentially large missing energy from losses in formation. see Ryan and James talk James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

25 Phenomenology Rotating versus Non-rotating black holes Very high p T objects. Multiple objects in the final states. Harder spectrum, but correspondingly lower multiplicity from rotating black holes James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25

26 Summary Much theoretical progress recently in the description of both the formation and evaporation of mini black holes. Still uncertainties in their formation. Semi-classical Hawking radiation analysis complete apart from graviton modes for rotating black holes. End point of black hole evolution not fully understood - Planck phase and quantum effects. New tools and Monte-Carlo to simulate these processes. JF et al. arxiv: , D. Dai et al. arxiv: Study of mini black holes merits further study, both from Collider produced black holes have an interesting and distinct phenomenology - rotation effects, Will be probed experimentally at the LHC! Enjoy the rest of the meeting! James Frost (University of Cambridge) IOP Half-Day Meeting Thursday 9th December / 25