1. Out-of-this-World Physics: Black Holes at Future Colliders
Greg Landsberg
Space Telescope Science Institute Spring Symposium April 23, 2007

2. Outline Astroparticle Connections The Hierarchy Problem Some Solutions
Production of Black Holes at Future Colliders
Conclusions
STSci, 4/23/07
Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

3. Astro-Particle Physics
Last decade emphasized remarkable connection between the astrophysics and particle physics:
Searches for dark matter
QFT connections to early universe and inflation
Black hole thermodynamics
The landscape
The more we study these seemingly different subjects, the more connections we discover
Physics at the very large distances may be inherently connected to the physics at the shortest ones
More similarities:
Microscopes vs. telescopes
Large international collaborations
Complicated detectors
We are (hopefully!) doing the things via two complementary means
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

4. Microscopes vs. Telescopes
dr ~ 1/E
Dq = 1.22 l/D
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

5. Beautiful Instruments
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

6. Spectacular Launches STSci, 4/23/07
Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

7. Deep Fields Quantum vacuum texture Hubble Deep Field Survey
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

8. Mass and Gravity F +Q -q F M m R R
Isaac Newton: the force that makes the apple fall is the same force that keeps the moon going around the Earth!
Charles Coulomb: opposite electric charges attract! +Q -q F R m M R F
Isaac Newton
Mass is similar to electric charge?!
But gravity is 1038=100,000,000,000,000,000,000,000,000,000,000,000,000 (hundred billion billion billion billions) times WEAKER than electricity! Why?
The hierarchy problem (MPl = GN-½ = 1016 TeV » MEW ~ 1 TeV ~ 1000 Mp)
Charles Coulomb
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

9. N.B. Large Hierarchies Tend to Collapse...
The eighties
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

10. Gravitational Hierarchy Collapse
With thanks to Chris Quigg and the B44 restaurant in San Francisco
Human Castles in Catalonia
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

11. More Large Hierarchies
Collapse of the Soviet Union
The nineties…
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

12. Note: Some Hierarchies are Surprisingly Stable…
The 2000-ies
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

13. And Bear in Mind…
Fine tuning (required to keep a large hierarchy stable) exists in Nature:
Solar eclipse: angular size of the sun is the same as the angular size of the moon within 2.5% (pure coincidence!)
Politics: Florida recount, 2,913,321/2,913,144 =
(!!)
Numerology: / =
(!!!)
(Food for thought: is it really numerology?)
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

14. Solutions to the Hierarchy Problem
Several classes of solutions exist in particle physics:
Introduction of intermediate energy scales with new particles and interactions (e.g., Technicolor)
Introduction of new symmetries, which guarantee high degree of cancellation of various effects, thus providing fine-tuning by the means of symmetry (e.g., SUSY)
Ignorance or not the right question (e.g., anthropic principle)
New class of solutions was found in the late 90-ies, requiring modification of space itself to make gravity fundamentally strong force (MPl ~ 1 TeV), which only appears weak at low energies
Two such models: large and warped extra dimensions
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

15. Large Extra Dimensions
Arkani-Hamed, Dimopoulos, Dvali (ADD) [PLB 429, 263(1998)]
SM fields are localized on the (3+1)-brane; gravity is the only force that “feels” the bulk space
What about Newton’s law?
Ruled out for infinite extra dimensions, but does not apply for sufficiently small compact ones
Gravity is fundamentally strong force, bit we do not feel that as it is diluted by the volume of the bulk
G’N = /MD2; MD  1 TeV
More precisely, from Gauss’s law:
Amazing as it is, but no one has tested Newton’s law to distances less than  1mm (as of 1998)
Current limits: n = 2 nearly ruled out; for n > 2 limits are: MD > 1.4 TeV ~
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

16. Randall-Sundrum Model
Randall-Sundrum (RS) model [PRL 83, 3370 (1999); PRL 83, 4690 (1999)]
+ brane – no low energy effects
+– branes – TeV Kaluza-Klein modes of graviton
Low energy effects on SM brane are given by Lp; for kRC ~ 10, Lp ~ 1 TeV and the hierarchy problem is solved naturally x5
SM brane G
AdS
Planck brane
Anti-deSitter space-time metric: Rc
Planck brane (f = 0)
SM brane (f = p)
AdS5 f
k – AdS curvature
Reduced Planck mass:
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

17. Examples of Compact Dimensions
M.C.Escher, Relativity (1953)
M.C.Escher, Mobius Strip II (1963)
[All M.C. Escher works and texts copyright © Cordon Art B.V., P.O. Box 101, 3740 AC The Netherlands. Used by permission.]
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

18. The Large Hadron Collider
LHC- the new energy frontier proton-proton collider being built at the border of France and Switzerland, near Geneva
Proton-proton collisions at the c.o.m. of 14 TeV
Luminosity (event rate) of 1034 cm-2s-1 = 0.01 Hz/pb
Two general-purpose experiments: ATLAS and CMS
Scheduled to start operating at full energy in Spring 2008
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

19. Black Holes on Demand N.B. Also possible in the Randall-Sundrum model
NYT, 9/11/01
N.B. Also possible in the Randall-Sundrum model
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

20. Black Holes in General Relativity
Naїvely, a black hole would only grow once it’s formed
In 1975 Hawking showed that this is not true [Commun. Math. Phys. 43, 199 (1975)], as the black hole can evaporate by emitting virtual pairs at the event horizon, with one particle of the pair escaping the BH
These particles have a black-body spectrum at the Hawking temperature:
In natural units ( = c = k = 1), one has: RSTH = (4p)-1
If TH is high enough, massive particles can also be produced in the process of evaporation
Black holes (BH) are direct prediction of Einstein’s General Relativity (GR)
It’s somewhat ironical that Einstein himself never believed in BH!
Schwarzschild showed (1916) that the space-time metric for a massive body has a singularity at r = RS  2MGN/c2
r and t essentially swap places for r < RS
Hence, if the mass M is enclosed within its Schwarzschild radius RS, a “black hole” is formed
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

21. Brief History of Holes
Note, that Rs can be derived from Newtonian gravity by taking the escape velocity, vesc = (2GNM/RS)1/2 to be equal to c – first noticed by Pierre-Simon Laplace in his famous 1796’s “Exposition du Systeme du Monde”
A few years earlier (1783) John Michell presented similar qualitative idea (“dark star”) to the Royal Society:
“If the semi-diameter of a sphere of the same density with the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it, would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to the vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity”
The name, “Black Hole,” was coined only half-a-century after Schwarzschild by John Wheeler (in 1967)
Previously these objects were often referred to as “frozen stars” due to the time dilation at the event horizon
Pierre Laplace
John Wheeler
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

22. Looking for Black Holes
The most straightforward evidence, Hawking radiation, is not likely to ever be observed for astronomical black holes (TH ~ 100 nK, l ~ 100 km, P ~ W: ~1014 years for a single g to reach us!)
LIGO/VIRGO/LISA hope to observe gravitational waves from black hole collisions (cf. Joan Centrella’s talk)
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

23. Black Hole Evaporation
As the BH evaporates, its mass becomes smaller, RS decreases, and Hawking temperature increases
Consequently, as the BH evolves, the radiation spectrum becomes harder and harder, until the BH evaporates completely in a giant flash of light
Ergo, the BH spends most of its time at the lowest temperature, when the radiation is soft (cf. Gary Horowitz’s talk)
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

24. Black Holes at Colliders
Based on work done with Dimopoulos a few years ago [PRL 87, (2001)] and a related study by Giddings/Thomas [PRD 65, (2002)]
Extends previous, more formal studies by Argyres/Dimopoulos/March-Russell [PL B441, 96 (1998)], Banks/Fischler [JHEP, 9906, 014 (1999)], Emparan/Horowitz/Myers [PRL 85, 499 (2000)] to collider phenomenology
Big surprise: BH production is not an exotic remote possibility, but the dominant effect!
Main idea: when the c.o.m. energy reaches the fundamental Planck scale, a BH is formed!
Artist’s view: RS
quark
M2 = s ^
s ~ pRS2 ~ 1 TeV -2 ~ m2 ~ 100 pb
Corresponds to ~1 Hz BH rate!
Cross section is given by a black disk approximation: p p
Black hole
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

25. Assumptions and Approximation
Fundamental limitation: our lack of knowledge of quantum gravity (QG) effects close to the Planck scale
Consequently, no attempts for partial improvement of the results, e.g.:
Grey body factors
BH spin, charge, color hair
Relativistic effects and time-dependence
The underlying assumptions rely on two simple qualitative properties:
The absence of small couplings;
The “democratic” nature of BH decays
We expect these features to survive for light BH
Use semi-classical approach strictly valid only for MBH » MPl; only consider MBH > MPl
Clearly, these are important limitations, but there is no way around them without detailed knowledge of QG features
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

26. Black Hole Production LHC n=4
Schwarzschild radius is given by Argyres et al. [hep-th/ ], after Myers, Perry [Ann. Phys. 172 (1986) 304]; it leads to:
Hadron colliders: use parton luminosity w/ MRSD-’ PDF (valid up to the VLHC energies)
Note: at c.o.m. energies ~1 TeV the dominant contribution is from qq’ interactions
stot = 0.5 nb
(MP = 2 TeV, n=7)
LHC
n=4
stot = 120 fb
(MP = 6 TeV, n=3)
[Dimopoulos, GL, PRL 87, (2001)]
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

27. Black Hole Decay
BH radiates mainly in our 3D world: Emparan/Horowitz/Myers [PRL 85, 499 (2000)]
l ~ 2p/TH > RS; hence, the BH is a point radiator, producing s-waves, which depends only on the radial component
The decay into a particle on the brane and in the bulk is thus the same
Since there are much more particles on the brane, than in the bulk, decay into gravitons is largely suppressed
Democratic couplings to ~120 SM d.o.f. yield probability of Hawking evaporation into g, l±, and n ~2%, 10%, and 5% respectively
Averaging over the BB spectrum gives average multiplicity of decay products:
Note that the formula for N is
strictly valid only for N » 1 due
to the kinematic cutoff E < MBH/2;
If taken into account, it increases multiplicity at low N
[Dimopoulos, GL, PRL 87, (2001)]
Stefan’s law: t ~ s
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

28. Black Hole Factory Black-Hole Factory
Dimopoulos, GL [PRL 87, (2001)]
Black-Hole Factory
n=2
n=7
g+X
Drell-Yan
Spectrum of BH produced at the LHC with subsequent decay into final states tagged with an electron or a photon
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

29. Shape of Gravity at the LHC
Dimopoulos, GL [PRL 87, (2001)]
Relationship between logTH and logMBH allows to find the number of ED,
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
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

30. Randall-Sundrum Black Holes
Not nearly as studied as ADD BH
Originally suggested by Anchordoqui, Goldberg, Shapere [PRD 66, (2002)]
A few authors extended work to various cases: Rizzo [JHEP 0501, 28 (2005); hep-ph/ ; hep-ph/ ] Stojkovic [PRL 94, (2005)]
The event horizon has a pancake-like shape (squashed in the 5th dimension by e-kpRc)
Nevertheless comparison with the ADD BH is trivial GL [J. Phys. G32, R337 (2006)]
For BH production, Lp in the RS model plays the same role as the fundamental Planck scale MD in the ADD model
Then if one sets Lp = MD and k = 1/8p  0.04, the RS case turns into the ADD one!
TH = 1/(2pRS) (the ADD formula in 5D)
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

31. Wien’s Law ~ k = 1/8p Lp = MD Impressive precision in proving n=1!
100 the LHC
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

32. Black Hole Events First studies already initiated by ATLAS and CMS
ATLAS –CHARYBDIS HERWIG-based generator with more elaborated decay model [Harris/Richardson/Webber]
CMS – TRUENOIR [GL]
Simulated black hole event in the ATLAS detector [from ATLAS-Japan Group]
Simulated black hole event in the CMS detector [A. de Roeck & S. Wynhoff]
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

33. Conclusions
Black hole production at future colliders is likely to be the first signature for quantum gravity at a TeV
Large production cross section, low backgrounds, and little missing energy would make BH production and decay a perfect laboratory to study strings and quantum gravity
Precision tests of Hawking radiation may allow to determine the shape of extra dimensions and distinguish between various scenarios
Properties of black holes in the Randall-Sundrum model are similar to those in models with large extra dimensions
A possibility of studying black holes at future colliders is an exciting prospect of ultimate ‘grand unification’ – that of astro-particle physics and cosmology!
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

34. Backup Slides

35. Fine Tuning Explained…
Numerology: / = ?
Numerology it is not!
Seeing is believing:
In hexadecimal system, FEDCBA / ABCDEF =
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

36. Black Holes in the Cosmic Rays
Discussed by Feng/Shapere [PRL 88 (2002) ]; Anchordoqui/ Goldberg [PRD 65, (2002)]; Emparan/ Massip/Rattazzi [PRD 65, (2002)]; …
Proton primaries have very high SM interaction rate; consider BH production by quasi-horizontal UHE neutrinos
Detect them, e.g. in the Pierre Auger fluorescence experiment or AGASA
A few to a hundred BHs can be detected before the LHC turns on
Might be possible to establish the uniqueness of the signature by comparing several neutrino-induced processes
Auger, 5 years of running
MBH = 1 TeV, n=1-7
[Feng & Shapere, PRL 88 (2002) ]
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

37. Other Recent Developments
Phenomenology of mini-BH became a popular subject (~380 citations of the original papers)
There have been a lot of studies of various second-order effects in BH formation and decay
Many of the estimates suffer from the intrinsic lack of knowledge of the quantum gravity effects, which will affect these fine features tremendously
Grey-body factor calculation has been attempted by many authors [e.g., Kanti, March-Russell, PRD 66, (2002); PRD 67, (2003)]
Kerr black holes have been considered extensively [e.g., Ida, Oda, Park, PRD 67, (2003), erratum PRD 69, (2004)]
Accounting for recoil effects [e.g. Frolov, Stojkovic, PRD 66, (2002), PRL 89, (2002)]
Number of people discussed the effect of Gauss-Bonnet terms, which arise naturally in perturbative expansion of string theory [e.g., Torii, Maeda, hep-ph/ and hep-ph/ ]
Randall-Sundrum BH studies [Anchordoqui, Goldberg, Shapere, PRD 66, (2002)]
Exploring AdS/QFT duality to relate formation of black holes in AdS to QCD colorless scattering and Froissart unitarity bound saturation [Giddings, PRD 67, (2003); Kang, Nastase, hep-th/ , hep-th/ ]
RHIC fireball/BH duality [Nastase, hep-th/ ]
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

38. String Balls at the LHC
Dimopoulos/Emparan, [PL B526, 393 (2002)] – an attempt to account for stringy behavior for MBH ~ MS
GR is applicable only for MBH > Mmin ~ MS/gS2, where gS is the string coupling; MP is typically less than Mmin
They show that for MS < M < Mmin, a string ball, which is a long jagged string, is formed
Properties of a string-ball are similar to that of a BH: it evaporates at a Hagedorn temperature: in a similar mix of particles, with perhaps a larger bulk component
Cross section of the string ball production is numerically similar to that of BH, due to the absence of a small coupling parameter:
It might be possible to distinguish between the two cases by looking at the missing energy in the events, as well as at the production cross section dependence on the total mass of the object
Very interesting idea; more studies of that kind to come!
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

39. Geometrical Cross Section Suppression?
Geometrical cross section approximation was argued in early follow-up work by Voloshin [PL B518, 137 (2001), PL B524, 376 (2002)]
More detailed studies showed that the criticism does not hold:
Dimopoulos/Emparan – string theory calculations [PLB 526, 393 (2002)]
Eardley/Giddings – full GR calculations for high-energy collisions with an impact parameter [PRD 66, (2002)]; extends earlier d’Eath and Payne work
Yoshino/Nambu - further generalization of the above work [PRD 66, (2002); PRD 67, (2003)]
Further improved by Yoshino/Rychkov [hep-th/ ]
Hsu – path integral approach w/ quantum corrections [PL B555, 29 (2003)]
Jevicki/Thaler – Gibbons-Hawking action used in Voloshin’s paper is incorrect, as the black hole is not formed yet! Correct Hamiltonian was derived: H = p(r2 – M)  ~ p(r2 – H), which leads to a logarithmic, and not a power-law divergence in the action integral. Hence, there is no exponential suppression [PRD 66, (2002)]
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

40. New Physics in BH Decays
Example: Higgs with the mass of 130 GeV decays predominantly into a bb-pair
Example: 130 GeV Higgs boson – tag BH events with leptons or photons, and look at the dijet invariant mass; does not even require b-tagging!
Use typical LHC detector response to obtain realistic results
s = 15 nb
boost W t
MP = 1 TeV, 1 LHC-hour (!)
Higgs observation in the black hole decays is possible at the LHC as early as in the first day of running even with the incomplete and poorly calibrated detectors!
For MP = 1, 2, 3, and 4 TeV one needs 1 day, 1 week, 1 month, or 1 year of running to find a 5s signal
Higgs is just an example – this applies to most of the new particles with the mass ~100 GeV
W/Z h t
GL, PRL 88, (2002)
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Greg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders