1. Out-of-this-World Physics: From Particles to Black Holes
Greg Landsberg
L.G.Landsberg Symposium December 19, 2005

2. Outline A Word on Hierarchies Standard Model: Beauty and the Beast
How to Make Gravity Strong?
Looking for Extra Dimensions…
Production of Black Holes at Colliders
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

3. N.B. Large Hierarchies Tend to Collapse...
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

4. Hierarchy of the Standard Model
Beauty …
vev
MGUT
MPl
Gravitational
Force
E [GeV]
EM/Hypercharge
Weak Force
Strong Force
Inverse Strength
RGE evolution
1016
102
1019
and the Beast
Extra dimensions might get rid of the beast while preserving the beauty!
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

5. But Keep 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: / =
(HW Assignment: is it really numerology?)
But: beware the anthropic principle
Properties of the universe are special because we exist in it
Don’t give up science for philosophy: so far we have been able to explain how the universe works entirely by science
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

6. Math Meets Physics
Math physics: some dimensionalities are quite special
Example: Laplace equation in two dimensions has a logarithmic solution; for any higher number of dimensions it obeys the power law
Some of these peculiarities exhibit themselves in condensed matter physics, e.g. diffusion equation solution allows for long-range correlations in 2D-systems (cf. flocking)
Modern view in topology: one dimension is trivial; two and three spatial dimensions are special (properties are defined by the topology); any higher number is not
Do we live in a special space, or only believe that we are special?
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

7. The ADD Model
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)
Thus, the fundamental Planck scale could be as low as 1 TeV for n > 1
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

8. Longitudinal ED Simultaneously, another idea has appeared:
Explore modification of the RGE in (4+n)-dimensions to achieve low-energy unification of the gauge forces [Dienes, Dudas, Gherghetta, PL B436, 55 (1998)]
To achieve that, allow gauge bosons (g, g, W, and Z) to propagate in an extra dimension, which is “longitudinal” to the SM brane and compactified on a “natural” EW scale: R ~ 1 TeV-1 MZ
MGUT
MPl=1/GN MS
M’GUT
Gravitational
Force
logE
EM/Hypercharge
Weak Force
Strong Force
Real
GUT Scale
Virtual
Image
Inverse Strength
M’Pl
L ~ 1 TeV
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

9. Randall-Sundrum Scenario
Randall-Sundrum (RS) scenario [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 r
Planck brane (f = 0)
SM brane (f = p)
AdS5 f
k: AdS curvature
Reduced Planck mass:
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

10. Differences Between the Models
TeV-1 Scenario:
Pro: Lowers GUT scale by changing running of the couplings
Only gauge bosons (g/g/W/Z) “live” in ED’s
Size of ED’s ~1 TeV-1 or ~10-19 m
Con: Gravity is not in the picture
ADD Model:
Pro: “Eliminates” the hierarchy problem by stating that physics ends at a TeV scale
Only gravity lives in the “bulk” space
Size of ED’s (n=2-7) between ~100 mm and ~1 fm
Black holes at the LHC and in the interactions of UHE cosmic rays
Con: Doesn’t explain why ED are so large
RS Model:
Pro: A rigorous solution to the hierarchy problem via localization of gravity
Gravitons (and possibly other particles) propagate in a single ED, w/ special metric
Con: Size of ED as small as ~1/MPl or ~10-35 m G
Planck brane x5
SM brane
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

11. Kaluza-Klein Spectrum
ADD Model:
Winding modes with energy spacing ~1/r, i.e. 1 meV – 100 MeV
Can’t resolve these modes – they appear as continuous spectrum
TeV-1 Scenario:
Winding modes with nearly equal energy spacing ~1/r, i.e. ~TeV
Can excite individual modes at colliders or look for indirect effects
RS Model:
“Particle in a box” with a special metric
Energy eigenvalues are given by zeroes of Bessel function J1
Light modes might be accessible at colliders
Gravitational coupling per mode; many modes E E E
~1 TeV
~MGUT
~MPl
GN for zero-mode; ~1/Lp for others ge … … Mi Mi M1 M0 M0
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

12. Using the ED Paradigm EWSB from extra dimensions:
Hall, Kolda [PL B459, 213 (1999)] (lifted Higgs mass constraints)
Antoniadis, Benakli, Quiros [NP B583, 35 (2000)] (EWSB from strings in ED)
Cheng, Dobrescu, Hill [NP B589, 249 (2000)] (strong dynamics from ED)
Mirabelli, Schmaltz [PR D61, (2000)] (Yukawa couplings from split left- and right-handed fermions in ED)
Barbieri, Hall, Namura [hep-ph/ ] (radiative EWSB via t-quark in the bulk)
Flavor/CP physics from ED:
Arkani-Hamed, Hall, Smith, Weiner [PRD 61, (2000)] (flavor/CP breaking fields on distant branes in ED)
Huang, Li, Wei, Yan [hep-ph/ ] (CP-violating phases from moduli fields in ED)
Neutrino masses and oscillations from ED:
Arkani-Hamed, Dimopoulos, Dvali, March-Russell [hep-ph/ ] (light Dirac neutrinos from right-handed neutrinos in the bulk or light Majorana neutrinos from lepton number breaking on distant branes)
Dienes, Dudas, Gherghetta [NP B557, 25 (1999)] (light neutrinos from right-handed neutrinos in ED or ED see-saw mechanism)
Dienes, Sarcevic [PL B500, 133 (2001)] (neutrino oscillations w/o mixing via couplings to bulk fields)
Many other topics from Higgs to dark matter
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

13. ED and Flavor Physics bulk SM bulk
gauge
fields
via gravity
ED models offer a powerful paradigm for explaining flavor sector and CP-violation
New amplitudes and phases could be transmitted to our world via gravity (or other bulk fields), thus naturally introducing small parameters needed for description of CP-violation, flavor physics, etc.
Some realizations of this class of models give realistic CKM matrix (e.g., Arkani-Hamed, Hall, Smith, Weiner [PRD 61, (2000)])
The idea of “shining” mentioned in the original ADD papers could explain why these effects were stronger in early universe
“shining”
bulk
“CP-brane” SM
big
bang
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

14. Flavor Physics from Geometry
Arkani-Hamed/Schmaltz [Phys. Rev. D61, (2000)] – split fermions embedded in a “fat” brane
Wave-functions of different families of quarks and leptons are spatially offset, thus the overlap areas are reduced exponentially
A fruitful paradigm to build models of flavor and mixing with automatically suppressed FCNC and stable proton
Possible to construct realistic CKM matrices via geometry of extra brane
Similar attempts in Randall-Sundrum class of models
In some of these models LFV decays of kaons are predicted and could be sought
Huber [NP 666, 269 (2003)]
Quark doublets of 3 generations
Quark singlets of 3 generations
Branco/de Gouvea/Rebelo [Phys. Lett. B506, 115 (2001)]
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

15. Tabletop Gravity Experiments
Sub-millimeter gravity measurements could probe only n=2 case only within the ADD model
The best sensitivity so far have been achieved in the U of Washington torsion balance experiment – a high-tech “remake” of the 1798 Cavendish experiment
R < 0.16 mm (MD > 1.7 TeV)
Sensitivity vanishes quickly with the distance – can’t push limits further down significantly
Started restricting ADD with 2 extra dimensions; can’t probe any higher number
Ultimately push the sensitivity by a factor of two in terms of the distance
No sensitivity to the TeV-1 and RS models
[J. Long, J. Price, hep-ph/ ]
E.Adelberger et al.
PRL 86, 1418 (2001) ~ ~
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

16. Astrophysical and Cosmological Constraints
Supernova cooling due to graviton emission – an alternative cooling mechanism that would decrease the dominant cooling via neutrino emission
Tightest limits on any additional cooling sources come from the measurement of the SN1987A neutrino flux by the Kamiokande and IMB
Application to the ADD scenario [Cullen and Perelstein, PRL 83, 268 (1999); Hanhart, Phillips, Reddy, and Savage, Nucl. Phys. B595, 335 (2001)]:
MD > TeV (n=2)
MD > 2-4 TeV (n=3)
Distortion of the cosmic diffuse gamma radiation (CDG) spectrum due to the GKK  gg decays [Hall and Smith, PRD 60, (1999)]:
MD > 100 TeV (n=2)
MD > 5 TeV (n=3)
Overclosure of the universe, matter dominance in the early universe [Fairbairn, Phys. Lett. B508, 335 (2001); Fairbairn, Griffiths, JHEP 0202, 024 (2002)]
MD > 86 TeV (n=2)
MD > 7.4 TeV (n=3)
Neutron star g-emission from radiative decays of the gravitons trapped during the supernova collapse [Hannestad and Raffelt, PRL 88, (2002)]:
MD > 1700 TeV (n=2)
MD > 60 TeV (n=3)
Caveat: there are many known (and unknown!) uncertainties, so the cosmological bounds are reliable only as an order of magnitude estimate
Still, n=2 is largely disfavored
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

17. Collider Signatures for Large ED
Kaluza-Klein gravitons couple to the energy-momentum tensor, and therefore contribute to most of the SM processes
For Feynman rules for GKK see:
[Han, Lykken, Zhang, PRD 59, (1999)]
[Giudice, Rattazzi, Wells, NP B544, 3 (1999)]
Since graviton can propagate in the bulk, energy and momentum are not conserved in the GKK emission from the point of view of our 3+1 space-time
Depending on whether the GKK leaves our world or remains virtual, the collider signatures include single photons/Z/jets with missing ET or fermion/vector boson pair production
Graviton emission: direct sensitivity to the fundamental Planck scale MD
Virtual effects: sensitive to the ultraviolet cutoff MS, expected to be ~MD (and likely < MD)
The two processes are complementary
Real Graviton Emission
Monojets at hadron colliders
GKK g q
Single VB at hadron or e+e- colliders
GKK V
Virtual Graviton Effects
Fermion or VB pairs at hadron or e+e- colliders V
GKK f
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

18. Virtual Graviton Exchange
L’EPilogue (Large ED)
e+e-  gG
e+e-  ZG
Experiment
n=2
n=3
n=4
n=5
n=6
ALEPH
1.28
0.97
0.78
0.66
0.57
0.35
0.22
0.17
0.14
0.12
DELPHI
1.38
1.02
0.84
0.68
0.58 L3
0.81
0.67
0.51
0.60
0.38
0.29
0.24
0.21
OPAL
1.09
0.86
0.71
0.61
0.53
Color coding
184 GeV
189 GeV
>200 GeV
l=-1 l=+1 GL
All limits are in TeV
Virtual Graviton Exchange
Experiment
e+e-
m+m-
t+t- qq
f f gg WW ZZ
Combined
ALEPH
0.53/0.57
0.46/0.46 (bb)
0.75/1.00 (<189)
DELPHI
0.60/0.76 (ff) (<202) L3
1.0/1.1 (<202)
OPAL
1.15
1.00
0.62
0.66
1.17/1.03 (<209)
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes
LEP Combined: 1.2/1.1 TeV

19. Colliders: Graviton Emission
85 pb-1
ee  g + GKK at LEP
g + MET final state
MP > TeV (ADLO), for n=2…7
qq/gg  q/g + GKK at the Tevatron
jets + MET final state
Z(nn)+jets is irreducible background
Challenging signature due to large instrumental backgrounds from jet mismeasurement, cosmics, etc.
DØ pioneered this search and set limits [PRL, (2003)] MP > TeV for n=2…7
Later, CDF achieved slightly better limits
Expected reach for Run II/LHC:
Theory:
[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/ ]
[Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]
[PRL 90, (2003)]
GKK g q n
MD reach, Run I
MD reach, Run II
MD reach, LHC 100 fb-1 2
1100 GeV
1400 GeV
8.5 TeV 3
950 GeV
1150 GeV
6.8 TeV 4
850 GeV
1000 GeV
5.8 TeV 5
700 GeV
900 GeV
5.0 TeV
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

20. Tevatron: Virtual Graviton Effects
GKK f
Expect an interference with the SM fermion or boson pair production
High-mass, low |cosq*| tail is a characteristic signature of LED [Cheung, GL, PRD (2000)]
Best limits on the effective Planck scale come from new DØ Run II data:
MPl > TeV (n=2-7)
Combined with the Run I DØ result:
MPl > TeV – tightest to date
Sensitivity in Run II and at the LHC:
Run II, 200 pb-1
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

21. Interesting Candidate Events
While the DØ data are consistent with the SM, the two highest-mass candidates have anomalously low value of cosq* typical of ED signal:
Event Callas: Mee = 475 GeV, cosh* = 0.01
Event Farrar: Mgg = 436 GeV, cosh* = 0.03
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

22. Antoniadis, Benaklis, Quiros [PL B460, 176 (1999)]
TeV-1 Extra Dimensions
Intermediate-size extra dimensions with TeV-1 radius
Introduced by Antoniadis [PL B246, 377 (1990)] in the string theory context; used by Dienes, Dudas, Gherghetta [PL B436, 55 (1998)] to allow for low-energy unification
Expect ZKK, WKK, gKK resonances at the LHC energies
At lower energies, can study effects of virtual exchange of the Kaluza-Klein modes of vector bosons
Current indirect constraints come from precision EW measurements: 1/r ~ 6 TeV
No dedicated experimental searches at colliders to date
Antoniadis, Benaklis, Quiros [PL B460, 176 (1999)]
ZKK
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

23. First Dedicated Search for TeV-1 Extra Dimensions
While the Tevatron sensitivity is inferior to indirect limits, it explores the effects of virtual KK modes at higher energies, i.e. complementary to those in the EW data
DØ has performed the first dedicated search of this kind in the dielectron channel based on 200 pb-1 of Run II data (ZKK, gKK  e+e-)
The 2D-technique similar to the search for ADD effects in the virtual exchange yields the best sensitivity in the DY production [Cheung, GL, PRD 65, (2002)]
Data agree with the SM predictions, which resulted in the following limit:
1/R > % CL
R < 1.75 x m
200 pb-1, e+e-
Event
Callas
Interference effect
1/R = 0.8 TeV
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

24. Randall-Sundrum Model Observables
Need only two parameters to define the model: k and rc
Equivalent set of parameters:
The mass of the first KK mode, M1
Dimensionless coupling
To avoid fine-tuning and non-perturbative regime, coupling can’t be too large or too small
0.01 ≤ ≤ 0.10 is the expected range
Gravitons are narrow
Expected Run II sensitivity in DY
Drell-Yan at the LHC M1
Davoudiasl, Hewett, Rizzo [PRD 63, (2001)]
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

25. First Search for RS Gravitons
Already better limits than sensitivity for Run II, as predicted by phenomenologists!
[PRL 95, (2005)]
Assume fixed K-factor of 1.3 for the signal
The tightest limits on RS gravitons to date
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

26. Black Holes on Demand NYT, 9/11/01 December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

27. Theoretical Framework
Based on the work done with Dimopoulos a few years ago [PRL 87, (2001)] and a related study by Giddings/Thomas [PRD 65, (2002)]
Extends previous theoretical 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; cross section is given by the black disk approximation:
Geometrical cross section approximation was argued in early follow-up work by Voloshin [PL B518, 137 (2001) and PL B524, 376 (2002)]
More detailed studies showed that the criticism does not hold:
Dimopoulos/Emparan – string theory calculations [PL B526, 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)]
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)] RS
parton
M2 = s ^
s ~ pRS2 ~ 1 TeV -2 ~ m2 ~ 100 pb
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

28. Assumptions and Approximation
Fundamental limitation: our lack of knowledge of quantum gravity 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 » MP; only consider MBH > MP
Clearly, these are important limitations, but there is no way around them without the knowledge of QG
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

29. 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)]
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

30. Black Hole Decay
Hawking temperature: RSTH = (n+1)/4p (in natural units  = c = k = 1)
BH radiates mainly on the brane [Emparan/Horowitz/Myers, hep-th/ ]
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
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

31. 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
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

32. 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
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

33. 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]
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

34. Conclusions
If you still think that gravity is weak force, you may be spending too much time in the lab!
Stay tuned – next generation of collider experiments has a good chance to solve the mystery of large extra dimensions!
If large extra dimensions are realized in nature, black hole production at future colliders is likely to be the first signature for quantum gravity at a TeV
Many other exciting consequences from effects on precision measurements to detailed studies of quantum gravity
If any of these new ideas is correct, we might see a true “Grand Unification” – that of particle physics, astrophysics and cosmology – in just a few years from now!
December 19, 2005
Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes