parker

Extra Dimensions and Black Holes: 

Extra Dimensions and Black Holes Andy Parker Cavendish Laboratory Cambridge

Two views of the world….: 

Two views of the world…. Supersymmetry …. Extra dimensions…. ….hidden perfection …different scales

Epicycles: 

Epicycles Typical Ptolemaic planetary model Symmetry is assumed: all orbits are based on circles But the Earth is not at the centre of the circle (the eccentric) The planet moves on an epicycle The epicycle moves around the equant From Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution.

Supersymmetry: 

Supersymmetry Conventional method to fix Higgs mass: Invoke SUSY Double the number of states in model Invoke SUSY breaking Fermion/boson loops cancel (GIM) Higgs mass stabilised! 105 new parameters (MSSM) +48 more free parameters if RP not conserved => SUSY is a good pension plan for experimentalists!

Extra Dimensions: 

Extra Dimensions Hypothesize that there are extra space dimensions Volume of bulk space >> volume of 3-D space Hypothesize that gravity operates throughout the bulk SM fields confined to 3-D Then unified field will have “diluted” gravity, as seen in 3-D If we choose n-D gravity scale=weak scale then… Only one scale -> no hierarchy problem! Can experimentally access quantum gravity! But extra dimension is different scale from “normal” ones -> new scale to explain Extra dimensions are more of a lottery bet than a pension plan!

Kaluza Klein modes: 

Kaluza Klein modes Particles in compact extra dimension: Wavelength set by periodic boundary condition States will be evenly spaced in mass “tower of Kaluza-Klein modes” Spacing depends on scale of ED For large ED (order of mm) spacing is very small - use density of states For small ED, spacing can be very large. 4-D brane Compactified dimension r M 1/R

Why are SM fields confined to 3-D space?: 

Why are SM fields confined to 3-D space? Interactions of SM fields measured to very high precision at scales of 10-18 m If gauge forces acted in bulk, deviations would have been measured KK modes would exist for SM particles For large ED, mass splitting would be small.

Pioneer 10: 

Pioneer 10 Pioneer 10 is leaving the solar system after 30 years in flight. Orbit shows deccelaration from force of 10-10 g Radiation pressure? Solar? Antenna? Heat? Gas leaks Time dependence?

Signatures for Large Extra Dimensions at Colliders: 

Signatures for Large Extra Dimensions at Colliders ADD model (hep-ph/9803315) Each excited graviton state has normal gravitational couplings -> negligible effect LED: very large number of KK states in tower Sum over states is large. => Missing energy signature with massless gravitons escaping into the extra dimensions G

Warped 5-d spacetime: 

Warped 5-d spacetime Planck scale brane Our brane 5th space dimension r Higgs vev suppressed by “Warp Factor” Gravity

Warped Extra dimensions: 

Warped Extra dimensions Consider Randall and Sundrum type models as test case Gravity propagates in a 5-D non-factorizable geometry Hierarchy between MPlanck and MWeak generated by “warp factor” Need : no fine tuning Gravitons have KK excitations with scale This gives a spectrum of graviton excitations which can be detected as resonances at colliders. First excitation is at where Analysis is model independent: this model used for illustration

Slide12: 

Signal and background for increasing graviton mass 500 GeV 2.0 TeV 1.5 TeV 1000 GeV

Production Cross Section: 

Production Cross Section 10 events produced for 100fb-1 at mG=2.2 TeV. With detector acceptance and efficiency, search limit is at 2080 GeV, for a signal of 10 events and S/√B>5 10 events

Angular distribution observed in ATLAS: 

Angular distribution observed in ATLAS 1.5 TeV resonance mass Production dominantly from gluon fusion Statistics for 100fb-1 of integrated luminosity (1 year at high luminosity) Acceptance removes events at high cos q*

Graviton discovery contours: 

Graviton discovery contours Confidence limits in plane of Lp vs graviton mass Coupling = 1/ Lp Test model has k/MPl=0.01, giving small coupling. For large k/MPl coupling is large enough for width to be measured. (Analysis assumes width<<resolution)

Measurement of the graviton coupling to m+m-: 

Measurement of the graviton coupling to m+m- Ds.B/s.B Confidence limits in plane of Lp vs graviton mass Coupling = 1/ Lp Test model has k/MPl=0.01, giving small coupling. For large k/MPl coupling is large enough for width to be measured. (Analysis assumes width<<resolution)

Photon analysis: 

Photon analysis Graviton mass (GeV) Photon pair mass resolution as good as electrons But background uncertain. For standard model (ptmin=150 GeV) sHERWIG=0.36 pb Included: Not included: for example FNAL data indicates sHERWIG is 5x too small  use 1.8 pb Do not trust cosq distribution for background.

Measurement of the graviton coupling to gg: 

Measurement of the graviton coupling to gg Confidence limits in plane of Lp vs graviton mass Coupling = 1/ Lp Test model has k/MPl=0.01, giving small coupling. For large k/MPl coupling is large enough for width to be measured. (Analysis assumes width<<resolution)

Graviton to jet-jet backgrounds: 

Graviton to jet-jet backgrounds k/MPl = 0.08 (64x higher cross-section)

Graviton to jet-jet search reach : 

Graviton to jet-jet search reach Reach is limited because of high background

Graviton to WW: 

Graviton to WW Look for Select 1e, 0 m, 2 jets, PTmiss from ATLFAST hjet <2 Require Mjj compatible with W mass take highest pT pair in mass window Solve for pzn using W mass constraint Plot MWW look for resonance above SM background SM background from WW, WZ and ttbar

Graviton to WW: signal and background: 

Graviton to WW: signal and background WW channel is viable for graviton ttbar W+jj

Graviton to WW channel: 

Graviton to WW channel Reach of W+jets channel

Exploring the extra dimension: 

Exploring the extra dimension Check that the coupling of the resonance is universal: measure rate in as many channels as possible: mm,gg,jj,bb,tt,WW,ZZ Use information from angular distribution to separate gg and qq couplings Estimate model parameters k and rc from resonance mass and s.B For example, in test model with MG=1.5 TeV, get mass to ±1 GeV and s.B to 14% from ee channel alone (dominated by statistics). Then measure

Conclusions: 

Conclusions Graviton resonances can be detected at the LHC with ATLAS For 100fb-1 (1 year at full luminosity) expect search to detect graviton masses up to 2080 GeV, using conservative assumptions for e+e- channel alone. Angular distributions allow graviton to be distinguished from any spin-1 resonance, up to 1720 GeV. Angular distribution also gives information on production mechanism. Universality of couplings can be checked for leptons and photons and IVBs. Quark couplings under study. Extra dimensions at the Planck length can be explored!

Black hole production : 

Black hole production Low scale gravity in extra dimensions allows black hole production at colliders. Decay by Hawking radiation (without eating the planet) 8 TeV mass black hole decaying to leptons and jets in ATLAS 8 partons produced with pT>500 GeV Work in progress: Richardson, Harris

Black hole production cross-sections at LHC: 

Black hole production cross-sections at LHC Classical approximation to cross-section (Controversial…) Very large rates for n=2-6 hep-ph/0111230 10000 evs/yr

Black hole decay: 

Black hole decay Decay occurs by Hawking radiation Hawking Temperature TH Black Hole radius rh Use observed final state energy spectrum to measure TH and hence n?

Particle spectra from black hole decays: 

Particle spectra from black hole decays Example: n=6 extra dimensions MD = 2 TeV Mh = 7-7.5 TeV Hawking Temperature TH= 400 GeV Multiplicity N~ Mh/2 TH ~ 9 Electron spectrum deviates from Black body effect of isolation cut? recoil effect? Fit gives 388 GeV All jets Isolated e’s Black body Fit

Extracting n from Black Holes: 

Extracting n from Black Holes Fit TH against Black Hole mass No experimental resolution yet (500 GeV bins…) Effect of heating? Input n=6 Fit gives n=5.7+-0.2 Preliminary!

Black hole production at the Tevatron: 

Black hole production at the Tevatron Rate expected to be large at Tevatron n=4 extra dimensions Cross-section drops rapidly at high mass Assume 10fb-1 Non-observation implies MD>1.4 TeV hep-ph/0112186 105 102 100 10-2 10-5 pb 0.7 1.0 1.3 1.6 MD Events/yr s

Conclusions: 

Conclusions Extra dimensional theories provide an exciting alternative to the normal picture of physics beyond the standard model A wide variety of new phenomena are predicted within reach of experiments. Exciting times ahead for experimentalists!