Transcript Document 7277939

Production and detection of
Black Holes at the LHC
Sven Vahsen
Overview
• “Introduction”
–
–
–
–
General Relativity
Cosmic black holes
The Hierarchy Problem
Extra dimensions
• BH production at the LHC
• BH decay and detection with ATLAS.
For more information
(=material taken from):
•
Black holes at the LHC
– Overview / introduction: Greg Landsberg (Brown Univ.): EPS
(European Physical Socienty) 2003 meeting. See both Talk and
procedings.
•
Extra-dimension studies by ATLAS collaboration
– Nothing in Detector and physics Performance TDR
 because the topic is wacky or because it is new?
– Exotics working group webpage:
• http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/EXOTICS/
• many studies underway within ATLAS
•
ATLAS studies on Black Holes written up by several groups:
–
Harris, C M; Palmer, M J; Parker, M A; Richardson, P; Sabetfakhri, A; Webber, B R
Exploring Higher Dimensional Black Holes at the Large Hadron Collider ATL-PHYS-2004-033
–
Tanaka, J; Yamamura, T; Asai, S; Kanzaki, J :
Study of Black Holes with the ATLAS detector at the LHC -- ATL-PHYS-2003-037
–
J. Grain
Search for Gauss-Bonnet Black Holes, Dec. 2003 meeting
–
LBL?
General Relativity
“Spacetime tells matter how to move, matter tells spacetime how to curve”
John Wheeler
Newtonian Gravity
General Relativity
•
Overall distribution of mass at a certain time determines
gravitational field throughout space.
•
Overall distribution of mass/energy (not only rest mass) in
universe determines curvature of spacetime.
•
An object with mass experiences force proportional to
gravitatiol field and mass. (Mass is graviational charge).
•
At each point in time and space, the local curvature of
spacetime tells matter how to move.
•
The curvature of spacetime propagates with the speed of light
 gravity waves
•
Since spacetime’s curvature tells matter how to move, all
matter, regardless of restmass, experiences the same
acceleration by gravity.
•
This “Universality of graviational coupling” experimentally
verified to 1 part in 1012
•
Gravitational lensing is one consequence of gravity’s effect on
photons. There’s a talk on this at LBL today.
–
•
F = G mM / r2
Inertia is the same as mass  all massive objects experience
same acceleration in gravitational field.
–
g = F/m = GM / r2
•
One may wonder why any object’s gravitational mass and
inetertia are the same.
•
Action at a distance is instantaneous. Example: The Sun
somehow instantaneously “tells” the earth how to move.
(Newton apparently thought this was absurd.)
•
What about massless particles - photons and neutrinos?
This includes light (photons)
Black Holes (BH’s)
•
Once you accept that gravity accelerates/deflects light, as well as massive particles…it’s not far fetched to imagine
a gravitational field strong enough to retain photons
•
If enough mass/energy MBH contained within a volume of radius RS  2MGN/c2, gravity is so strong that nothing
inside RS can get out. RS is the Swarzschild radius, and the surface at R=RS is the “eventhorizon” of the black hole.
•
•
•
GR established in 1915 by Einstein
Black Holes predicted by Karl Schwarzschild in 1916
Name “Black Hole” by John A. Wheeler in 1967
How is a black hole formed?
•
Given a certain amount of mass, one needs to somehow compress it within the Schwarzschild radius
–
•
Example: RS of the earth is 8.8mm
1) Stellar evolution
–
–
–
A Star’s fuel, hydrogen, subject to fusion (pressure outward) and gravitational pull inward.
Once hydrogen is burned up, gravity dominates
The further fate of the star depens on the mass
•
•
•
A star less than 1.4 times the mass of the sun will become a white dwarf.
A star between 1.4 and 3 times the mass of the sun will become a neutron star.
It's only those stars greater than 3 times the mass of the sun that become black holes upon collapse.
•
2) Additionally, a black hole can be formed by compression through external forces. This type of black hole is called
a primordial black hole.
•
3) Collisions of highly energetic particles: Cosmic rays and particle accelerators
–
Since all energy (not only restmass) is gravitational in GR, all we need is large sqrt(s).\
- need √s > ~ M_plank = 1019 GeV  No chance at any future colider!
- need impact parameter < Rs
Black Hole Evolution
•
Naїvely, black holes would only grow once
they are formed
•
In 1975 Steven Hawking showed that this
is not true, as the black hole can
evaporate by emitting pairs of virtual
photons at the event horizon, with one of
the pair escaping the BH gravity
•
These photons have a black-body
spectrum (Plank) with the Hawking
temperature:
c
TH 
4 kRS
•
The smallest black holes are the hottest!
•
Usual Stefan-Boltzmann blackbody
formula givess the Luminosity: L~TH4
The smallest are also the brightest!
•
•
•
If the Hawkings Temperature is
high enough, then particle/
antiparticle pairs (other than two
photons) are created as well, and
the black hole luminosity
increases.
Total luminosity directly
proportionally to the degrees of
freedom available.
Do Black Holes Exist?
•
•
•
•
•
•
While there is little doubt that BHs exist,
we don’t have an unambiguous evidence
for their existence so far
Many astronomers believe that quasars
are powered by a BH (from slightly above
the Chandrasekhar limit of 1.5 M to
millions of M), and that there are
supermassive (~106 M) black holes in
the centers of many galaxies, including
our own
The most crucial evidence, Hawking
radiation, has not been observed
(TH ~ 100 nK, l ~ 100 km, P ~ 10-27 W:
~1014 years for a single g to reach us!)
The best indirect evidence we have is
spectrum and periodicity in binary
systems
Astronomers are also looking for “flares”
of large objects falling into supermassive
BHs
LIGO & VIRGO hope to observe
gravitational waves from black hole
collisions
Some Black Hole Candidates
Cygnus X-1
Name of
Binary System
Companion
Star
Spectral Type
Orbital
Period
(days)
Black Hole
Mass
(Solar Units)
Cygnus X-1
B supergiant
5.6
6-15
LMC X-3
B main
sequence
1.7
4-11
A0620-00 (V616
Mon)
K main
sequence
7.8
4-9
GS2023+338
(V404 Cyg)
K main
sequence
6.5
>6
GS2000+25 (QZ
Vul)
K main
sequence
0.35
5-14
GS1124-683 (Nova
Mus 1991)
K main
sequence
0.43
4-6
GRO J1655-40
(Nova Sco 1994)
F main
sequence
2.4
4-5
H1705-250 (Nova
Oph 1977)
K main
sequence
0.52
>4
Dates?
Chandra X-ray Spectrum
Circinus galaxy
The hierarchy problem
“Why is gravity so much weaker than the other forces of nature”?
– The electroweak scale:
– The Plank scale:
MZ,W ≈ 100 GeV.
MPlank ≈ 1019GeV (≈ 2^10-8 kg)
– PDG review: “MPlank is defined to be the energy scale where the gravitational
interactions of elementary particles become comparable to gauge interactions”
– In plain terms: Can “derive” MPlank as follows: Comparing electrostatic and
gravitation forces between two test particles of charge=e, at what mass does the
gravitational force equal the electrostatic?
– PDG review: “It is possible that supersymmetry may ultimately explain the origin of
this hierarchy.”
– Why? Supersymmetry can make the hierarchy stable, while in the Standard Module
alone this is not possible.
– Today, we’ll look at an alternative, proposed solution to the hierarchy problem, i.e.
to why gravity is so weak.
Proposal solution:
Gravity may not be weak!
Gravity may be strong, but appear
weak, because it is leaking into
extra dimensions!
Extra dimensions
•
•
•
•
•
•
Extra dimensions in physics date back to 1920’s, when Kaluza tried to unify relativity
and EM by adding a 5th dimension to Einstein’s spacetime.
In order to “hide” the extra dimension, Klein proposed that the extra dimension may
be undetectable because it’s “compactified.”, e.g. rolled up, with a very small radius
In 1970’s and 1980’s, renewed interest in (multiple) extra dimensions:
supersymmetry and string theory
In recent years (1998 to now), we have seen the appearance of new models with
extra dimensions, which address the hierarchy problem by exploiting the geometry
of space time
These models may have verifiable consequences at the TeV (=LHC) scale
Common features of these models:
–
–
–
–
•
•
We live in a 3+1 dimensional subspace: “3-brane” (as in “membrane”).
The brane is embedded in a D(=3+d+1) - dimensional space time: “the bulk”
The d dimensions transverse to the brane hava a common size R
All fields/particles which propagate in the bulk are replicated in Kaluza-Klein Towers,
corresponding to states with non-zero momentum in the bulk
Size / geometry of bulk, and which particles are allowed to propagate in the bulk and
on the brane is model dependent.
Example: Universal Extra Dimensions (UED). See Joes talk.
“Gravity may appear weak, because
it’s leaking into extra dimensions.”
In 1998, N. Arkani-Hamed, S. Dimopoulus, G. Dvali suggested: What if gravity is the
only force aware of the extra dimension?
•
Using Gauss’ law, and geometrical arguments, we can check that the behavior of
gravity now depends on which length-scale on is probing! (let’s try derivation on the
blackboard?)
•
at distances smaller than R (compactification scale), gravity will low follow a F ~ G/r2+n
force law
Compact
Dimension
•
Flat Dimension
•
At distances larger than R, gravity will go as F~G/Rn x 1/r2
•
 Classical gravity, with diluted coupling G’ ≈ G/Rn recovered at large distances
•
Can switch this around and vary R,n to tune G, the undiluted coupling as desired:
G~G’ Rn. More dimensions & larger radius  stronger gravitation coupling  lower
planck scale (MPl2 = 1/G)
Now let’s (re)move the hierarchy
problem: We’d like MPl≈ MW,Z
• Setting MPlank = 1 TeV, one obtains:
8  1012 m , n  1
2/ n

1  M Pl 
0.7 mm , n  2

  
R
2 MS  MS 
3 nm , n  3
6  1012 m , n  4
• Experimentally, it turns out that (~1/r^2) has only been
verified down to distances 1 mm (as of 1998) or 0.15 mm
(2002)
• Therefore, large spatial extra dimensions, compactified at
a sub-millimeter scale are, in principle, allowed!
• If this is the case, gravity can be ~1038 times stronger than
what we think!
Remember the black holes?
If gravity is actually strong, it becomes much easier to create black holes.
•requirements:
–√s ~ MPl ~1 TeV (now within LHC reach)
–Impact parameter b < RS
•Black disc approximation, strictly valid for √s >> MPl
s ~ RS2 ~ 1 TeV 2 ~ 1038 m2 ~ 100 pb
M2 = ^s
parton
RS
parton
•Folding this with parton distribution functions at LHC givess the total cross section
for production of BH’s with MBH> MPl:
• 15 pb < s < 1 pb, for 1 TeV< MPl <5 TeV
• Varies ~10% for n between 2 and 7, and with choice of fi(xi)
•production rate at LHC for MPl =1 TEV ≈ 15 pb = 1.5x10-35 cm-2
at expected luminosities of 10-33 to 10-34, we’ll see several BH’s per minutes
If LHC is not far above plank scale, (unkown) quantum corrections to GR properties
expected to be large  BH studies should focus on robust effect, and may as well
disregard spin, BH quantum number, grey factors etc
What would a mini-black hole
produced at the LHC look like?
•
Decay process
– Mini black holes produced at LHC would be light & tiny, compared to cosmic black
holes. (~TeV versus >3 Solar masses)
– As a result, they would be extremely hot (T~100 GeV) and evaporate almost
instantaneously, mainly via Hawking radiation. [Decay involvates other stages
(balding, spin down), but we won’t get into that.]
– Democratic production: Hawking radiation produces particle/antiparticle pairs for all
degrees of freedom accessible around ~ 100 GeV, at roughly equal rates.
•
Decay Signature
– Average of ~ 6 particles for each decay, emitted spherically
– ~120 Particle degrees of freedom  ~ 1% chance for each.
– Summing over spin and color gives:
–
–
–
–
–
75 % quarks and gluons
10 % charged leptons
5 % neutrinos
5 % photons or W/Z bosons
Also get new particles around 100GeV, including light highs (1% ?)
– Small fraction of invisible neutrinos and gravitons  BH’s easy to reconstruct
– 10% high PT leptons  trigger
A simulated black hole event in the
ATLAS detector
Surprise: courtesy Laurent Vacavant!
LHC as a Black Hole Factory
Spectrum of BH produced at the LHC w/ subsequent decay into final states tagged with
an electron or a photon [Dimopoulos, G. Landsberg, PRL 87, 161602 (2001)]
100 fb-1
(Before cuts?)
n=2
n=7
Drell-Yan
g+X
For Planck scale up to ~ 5TeV, clean and large samples of BH’s at the LHC
Given abundant production black
holes… what to do with them?
• Obvious: Counting experiment to detect BH production over
background
• Reconstruct black hole mass and temperature  verify process of
Hawking Radiation
• Use MBH vs TH to measure MPL& n, independent of shape of extra
dimensions
• Discover the Higgs with M≈130 GeV.
• Note: At √s >> MPL BH production becomes the dominant process:
“The End of short distance physics”
BH discovery potential, including
detector simulation
[Robindra Pabhu, Univ. of Oslo, Atlas Exotics WG meeting Nov ’04]
Discovery luminosity defined by: S/√B>5.0 and S>10.0
(confusing labels!)
• Strong dependence on MPL, weak dependence on n
• We could see something very early!
Shape of Gravity at the LHC
[Dimopoulos, GL, PRL 87, 161602 (2001)]
log TH  
1
log M BH  const
n 1
• Relationship
between logTH and
logMBH allows to
find the number of
ED; n
• This result is
independent of
their shape!
• This approach
drastically differs
from analyzing
other collider
signatures and
would constitute a
“smoking cannon”
signature for a TeV
Planck scale
Conclusion
•
Large Extra dimensions (ED) provide an alternative to SUSY in addressing
the hierarchy problem
•
If Large ED’s realized in nature, gravity could be stronger than we think
•
In that case, the actual plank scale may be within reach of the LHC
•
Black hole production could be abundant, and we could see something
early on
•
Black hole production could become the dominant process at the LHC, or
future colliders - “The end of short distance physics”
•
BH production would provide an unexpected window into geometry of
spacetime, as well as a new production process for other undiscovered
particles