1. Planck Scale Physics - what we know and what we want to know
Sabine Hossenfelder
University of Arizona

2. The Standard Model These questions can not be answered within the SM !
Why is gravity so weak?
Where do the fermion masses come from?
How to explain EW symmetry breaking??
What is the origin of lepton and quark families??
Why is there CP-violation???
Quantum gravity????
The cosmological constant???!
...
These questions can not be answered within the SM !

3. ~ Karl Popper, The Observer, August 1982
"Science may be described
as the art of systematic
over-simplification."
Could now try to find a theory of everything exept the fact that this might be a very abspruchsvolle task, there is the
fact that physics is still about describing nature. Originally I studied mathematics so I am very aware of the striking beauty of supersymmetry and Stringtheory but the reason why I eventually skipped to physics is that I want do describe
nature and learn about it.
So insted of looking for the theory of everything we take the
progress that has been made on this topic and try to find a useful simplification of that, an approximation that includes
some of the main features, as there is the existence of extra Dimension, which is a very common feature. It seems, whatever way nature is, a theory behind the standardmodel is very likely to have extra dimensions.
I want to summarize the motivation to study the model I will present with this quotation...

4. Extra Dimensions 3+d spacelike dimensions
d dimensions compactified to d-torus with radii
fields in bulk come as KK-tower
KK-modes have apparent mass-term  

5. Large eXtra Dimensions
N. Arkani-Hamed, S. Dimopoulos & G. Dvali (1998)
only gravitons propagate into extra dimensions
SM fields live on brane

6. Large eXtra Dimensions
For = 1 TeV one finds:
 excluded
Hoyle (Washington)
Long (Colorado)
Chiaverini (Stanford) ...
 R < 0.18 mm
1st exitation in eV – MeV range

7. Universal eXtra Dimensions
SM gauge/matter fields are allowed in bulk
Xtra-momentum is conserved
KK-tower of massive fields
Dienes, Dudas, Gherghetta, Nucl. Phys. B 537, (1999) 47

8. The New Scale New fundamental scale At energies first effects occur!
This allows us to make predictions beyond the SM...
... which can be tested by experiment ...
... and verify /falsify the setting of the model...
... or constrain its parameters.

9. ~ Martin Luther King
„Knowledge is a process of piling up facts; wisdom lies in their simplification.“

10. Some References Arkani-Hamed-Dimopoulos-Dvali-model
N.Arkani-Hamed, S.Dimopoulos & G.Dvali, Phys. Lett. B 429, (1998)
I. Antoniadis, N. Arkani-Hamed et al, Phys. Lett. B 436, (1998)
N.Arkani-Hamed, S.Dimopoulos & G.Dvali ,Phys. Rev. D 59, , (1999)
Randall-Sundrum-model Type I and II
L.Randall & R.Sundrum, Phys. Rev. Lett. 83, (1999)
L.Randall & R.Sundrum, Phys. Rev. Lett (1999)
Universal eXtra Dimensions
A.Delgado, A.Pomarol and M.Quiros, Phys. Rev. D 60, (1999)
T.Appelquist, H.C.Cheng and B.A.Dobrescu, Phys. Rev. D 64, (2001)
K.R.Dienes, E.Dudas and T.Gherghetta, Phys. Lett. B 436, 55 (1998)

11. Effects The consequences of a lowered scale:
KK contributions get important at energies 
real KK production.
virtual KK exchange.
Increase of the gravitational strength at distances « R
Deviations from newtons law.
Modification of general relativity allow black holes to be produced at lowered matter densities.
The Planck length as minimal length is lowered to
Finite resolution of spacetime!
The uncertainty principle is modified at high energies!

12. Gravitons Coupling of gravitons to standard-model is straightforward
with small pertubations:
Lagrangian
The matter is on our brane:
Decomposition of metric in gravitons , vector and scalar-fields with :   
Tao Han, J.D.Lykken & Ren-Jie Zhang, Phys. Rev. D59; (1999)
J.L.Hewett, Phys.Rev.Lett. 82; (1999)
G.F.Guidice, R.Rattazzi & J.D.Wells, Nucl. Phys. B544, 3 (1999)

13. Observation of Gravitons
Exitations of gravitons are interpreted on our brane as
massive particles
Phase-space for energy E given by # of with is
this yields:
 Energy loss in collisions
 Modification of standard-model cross-sections

14. Black Holes  THE extremest state of matter not even light can escape
Schwarzschild-Solution of GR in Vakuum 
Redshift of photons sent from horizon is infinite:
the horizon is black

15. ! Black Holes   THE extremest state of matter
not even light can escape
Schwarzschild-Solution of GR in Vakuum  !
Higher Dimensions! 

16. Black Holes Astrophysics: M > earthmass ( 8 x 1048 TeV)
Colliders: M < earthmass
Modification of the gravitational law on distances « R
leads to an increase of the black hole radius

17. Black Hole Cross-section
Horizon-radius in 3+1 dimensions for
Horizon-radius in 3+d+1 dimensions for
 Partons which get closer than form a horizon !
Estimation for cross-section up to
At the LHC partons get so close that they may collaps!

18. Production of Black Holes
# Black Holes per year at LHC !!!
With CTEQ PDFs:

19. Production of Black Holes
# Black Holes per year at LHC !!!
Dimopoulos & Landsberg - “Black holes at the LHC” ... Cavaglia, Das & Maartens - “Will We Observe Black Holes at the LHC?” ... Mocioiu, Nara & Sarcevic - “Hadrons as signature of black hole production at the LHC” ... Ringwald - “Collider versus Cosmic Ray Sensitivity to Black Hole Production” ... Anchordoqui - “Black holes from cosmic rays” ... Giddings - “Black hole production in TeV-scale gravity” ... Rizzo, Casadio & Harms – “Black hole evaporation and compact extra dimensions'‘ ... Argyres, S.Dimopoulos & March-Russell - “Black Holes and Sub-millimeter Dimensions” ... Giddings - “Black Holes in the Lab” ... etc ... etc ...
# Total arXiv for “TeV + Black +Holes”: 135
Hossenfelder et al: Phys. Rev. D 66 (2002) , Phys. Lett. 548 (2002) 73

20. Thermodynamics of Black Holes
and yields
Astrophysics: the canonical ensemble (Hawking,1976)
Collider: the microcanonical ensemble (Harms, 1997) 

21. Evaporation of Black Holes
The Evaporation depends on the number of LXDs
Hossenfelder et al: Phys. Lett. 548 (2002) 73, J.Phys.G 28 (2002) 1657

22. Big Bang Machine: Will it destroy Earth?
The London Times July 18, 1999
Creation of a black hole on Long Island?
A NUCLEAR accelerator designed to replicate theBig Bang is under investigation by international physicists because of fears that it might cause "perturbations of the universe" that could destroy the Earth. One theory even suggests that it could create a black hole. [...]
The committee will also consider an alternative, although less likely, possibility that the colliding particles could achieve such a high density that they would form a mini black hole. In space, black holes are believed to generate intense gravita-tional fields that suck in all surrounding matter. The creation of one on Earth could be disastrous. [...]
John Nelson, professor of nuclear physics at Birmingham University who is leading the British scientific team at RHIC, said the chances of an accident were infinitesimally small - but Brookhaven had a duty to assess them. "The big question is whether the planet will disappear in the twinkling of an eye. It is astonishingly unlikely that there is any risk - but I could not prove it," he said.

23. In the Twinkling of an Eye
Mass loss:
Mass gain ratio, thermal only:
Mass gain ratio, high gamma-factor:

24. Observation of Black Holes

25. Observation of Black Holes
In high energetic collider experiments or UHECRs, resp.:
Cutoff in jet-spectrum at masses >
additional jets by emitted particles
Modification of particle spectra
due to evaporation
Ionisation by charged holes
Missing energy (Relics?)

26. Minimal Length D.J.Gross, P.F.Mende, Nucl.Phys. B 303, (1988) 407:
D.J.Gross [hep-th/ ]:
„In string theory [...] the probes themselves are not pointlike but rather extended objects, and thus there is another limitation as to how precisely we can measure short distances. As energy is pumped into the string it expands and thus there is an additional uncertainty proportional to the energy.“

27. Including the Minimal Length
The minimal length can be modeled by setting
with a minimal possible compton wavelength

28. Including the Minimal Length
Quantize via
with expansion this
yields:
 We get a generalized uncertainty principle !

29. Including the Minimal Length
Further
with the approximation for high energies
 The momentum measure is exponentially squeezed!

30. Experimental Constraints
to the Minimal Length
The modifications factorize and yield the relation:
 Modification of SM cross-section
at high energies, e.g. the minimal
length in
data from LEP2, D. Bourikov et al.,
LEP2ff/01-02 (2001).
Hossenfelder et al, Phys. Lett. B 575 (2003) 85-99

31. Suppression of Black Hole Production
S. Hossenfelder, Phys. Lett. B 598, 92 (2004)

32. Running Coupling with Minimal Length
Higher dimensional loops 
S. Hossenfelder, PRD ??

33. Renormalization of Selfenergy
Looking closer, the propagator exhibits complex structures 
Expansion in series of one-particle-irreducible contributions
Can be summarized in

34. Minimal Length versus Cut-off

35. Minimal Length versus Cut-off
no arbitrariness in computation
no pure power law but mixtures
running stagnates at energies
confirmation of hard cut-off results BUT
+ physical interpretation of regulator

36. Lorenz Invariance and GZK
Lorentz-covariance?
Lorentz-covariance?!
Modification of Lorentz-Transformation
observer independend length scale
“Doubly Special Relativity”
Amelino-Camelina, Speciale, etc
Boost traveling UHE proton:
photon soup does not get arbitrarily dense!
longer mean free path

37. ~ Konrad Lorenz
"Truth in science can best be defined as the working hypothesis best suited to open the way to the next better one."

38. Summary Soon we might be able to look behind the SM.
Simple models like LXD + minimal length dont claim to be
a TOE ...
... but they provide a useful basis to check out general features of spacetime:
value of new scale
# and size of extra dimensions
existence of a minmal length
the model yields predictions for astro+collider
and may help to learn about
the general structure of quantum gravity
and the mechanism of unification
Sabine Hossenfelder – University Of Mississippi – 02/11/04