Black Hole in LHC

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Black Hole in LHC

• Weigang Geng, Hui Wang, Kaijie Xu and Li Yang
• Department of Physics Astronomy
• Michigan State University

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What is the black hole?

• A black hole is defined to be a region of
  space-time where escape tothe outside universe
  is impossible. The outer boundary of this
  regionis called the event horizon. Nothing can
  move from inside the eventhorizon to the
  outside, even briefly, due to the extreme
  gravitationalfield existing within the region.

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Three Types of BHs

• Stellar BHs - ten times the mass of our Sun
• Supermassive BHs - millions or billions of times
  mass of our sun
• Micro BHs - 2 10-8 kg or 1.1 1019 GeV (Planck
  mass)

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The Large Hadron Collider

• Under Construction at CERN opens 2007
• Proton-proton collider
• Designed to find the Higgs boson or exclude its
  existence
• CM energy 14 TeV

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Formation of BH

• General Relativity Vs. Quantum Field Theory
• Randall-Sundrum Model
• Suppression of Cross Section
• Generalized Uncertainty Principle
• Low limit of BH mass

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General Relativity Quantum Field Theory

• Space-time of GR QFT
• Quantum Gravity Theory
• String, Superstring, M-theory, etc.
• Extra dimension
• Randall-Sundrum model

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Randall-Sundrum Model(1)

• Original Randall-Sundrum Model
• Extra dimension
• TeV brane and Planck Brane
• Cross Section

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Randall-Sundrum Model(2)

• 5-d Cross Section
• Cross Section in the Collisions
• Improved Randall-Sundrum Model

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Suppression of Cross Section

• gg ? BH
• ff ? BH
• gf ? BH

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General Uncertainty Principle

• Heisenberg Uncertainty Principle
• General Uncertainty Principle
• d-dimensional Schwarzschild BH horizon

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Low Limit of BH mass
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Planck Scale Physics

• Planck mass 1.221019 GeV
• Planck length 1.61610-35 m
• The Planck scale is believed to be the scale
  at which both general relativity and quantum
  mechanics simultaneously become important.

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Extra Dimension

• Several models using extra dimensions indicate
  the observed huge Planck-scale as a
  geometrical feature of the space-time, while the
  true fundamental scale of gravity may be as low
  as 1 TeV.
• All SM particles are confined to our 31
  dimensional brane, while gravitons are allowed to
  propagate freely in the (3d) 1 dimensional
  bulk.
• The Planck mass mp and the fundamental mass
  Mf are related by
• mp2Mfd2Rd

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Evolution of the Black Hole

• Balding Phase
• Evaporation Phase
• Planck Phase

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Balding Phase

• In this phase the black hole radiates away the
  multipole moments it has inherited from the
  initial configuration, and settles down in a
  hairless state.

During this stage, a certain fraction of the
initial mass will be lost in gravitational
radiation.
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Evaporation Phase

• The Hawking radiation carries away the angular
  momentum, and then it proceeds with emission of
  thermally distributed quanta until the black hole
  reaches Planck mass.

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Evaporation Phase

• The black hole decay via the semi-classical
  Hawking evaporation process
• It emits modes both along the brane and into
  the extra dimensions, as illustrated in the Fig.

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Evaporation Phase
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Evaporation Phase

• The decay of the BH is governed by its
  Hawking temperature , which is proportional to
  the inverse radius, and given by

Where RS is the Schwarzschild radius of an (4d
)dimensional black hole.
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Evaporation Phase

• The black hole decays according to Planck's
  law of black body radiation with the Hawking
  temperature, as the BH decays, it gets lighter
  and hotter and its decay accelerates.
• The parametric dependence of the black hole
  lifetime on mass follows directly from

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Planck Phase

• When the Hawking temperature reaches the
  fundamental scale THMp , the semi-classical
  Hawking theory breaks down. At this point the
  black hole reaches a final Planck phase of decay.
  

The decay falls into the regime of quantum
gravity and predictions become increasingly
difficult.
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Experimental Signature

• Very large total cross section with production
  rates at the LHC approaching up to of order 1 Hz
  possible.
• Large multiplicity events, with up to many dozens
  of relatively hard jets and leptons.
• Some events contain a few hard visible quanta
  with energy up to order the fundamental Planck
  scale from the Planck decay phase.
• Suppression of hard perturbative scattering
  processes at energies for which black hole
  production becomes important.

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Black hole decay feature

• The evaporation phase have high multiplicity
  the typical decay involves a large number of
  particles, the BH emits all the 120 standard
  model (SM) particles and antiparticles.

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Black hole decay feature

• Another feature is the BH decay with roughly
  equal probability to all of the SM particles, as
  long as all local conservation laws are obeyed.
• 75 quarks and gluons
• 10 charged leptons
• 5 photons or W_Z bosons
• 5 neutrinos
• also get new particles around 100GeV,
  including light higgs.

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Simulation of BH production decay
CHARYBDIS hep-ph/0307305 An event generator
which simulates the production and decay of
miniature black holes at hadronic colliders as
might be possible in certain extra dimension
models. PYTHIA 6.225 ATLFAST (v1.10) the
Atlas Fast Simulation package
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Event selection

• For a precise reconstruction of the BH, it is
  necessary to remove particles produced in the
  stage of initial state radiations (ISRs).
• pT 30 GeV for µ, e

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Event selection

• For a precise reconstruction of the BH, it is
  necessary to remove particles produced in the
  stage of initial state radiations (ISRs).
• pT 50 GeV for ?, jet

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Event selection

• For a precise reconstruction of the BH, it is
  necessary to remove particles produced in the
  stage of initial state radiations (ISRs).
• Pseudorapidity
• ?

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Event selection

• To suppress backgrounds, more than three
  particles are required to have energy larger than
  300 GeV,and moreover, at least one of them has to
  be either an electron or a photon .

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Event selection

• We require the event shape variable R2 to be
  less than 0.8

?ij is the opening angle between particles i and
j, Evis is the total visible energy of the event .
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Event selection
Emissmass, events with high missing energy are
rejected here. The black hole mass is then
reconstructed from the 4-momenta of the remaining
muons, electrons, gammas and jets as follows

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Possible Risk

• High probability of micro black holes produced in
  the LHC
• Validity of Hawking evaporation
• Cosmic ray model is not valid for LHC
• Lower speed MBHs created in colliders could be
  captured by earth

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Summary

• Formation of black hole in LHC is formulated in
  large extra dimension model. The low limit of the
  mass of the black hole is obtained from
  uncertainty principle
• The evolution of BH contains three main phases
  Balding phase, Hawking evaporation and the Planck
  phase.
• Black-hole production at the LHC offer
  low-background environment for searches of new
  particles with mass 100 GeV

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