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

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 !

~ 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...

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  

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

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

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

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.

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

Some References Arkani-Hamed-Dimopoulos-Dvali-model N.Arkani-Hamed, S.Dimopoulos & G.Dvali, Phys. Lett. B 429, 263-272 (1998) I. Antoniadis, N. Arkani-Hamed et al, Phys. Lett. B 436, 257-263 (1998) N.Arkani-Hamed, S.Dimopoulos & G.Dvali ,Phys. Rev. D 59, 086004, (1999) Randall-Sundrum-model Type I and II L.Randall & R.Sundrum, Phys. Rev. Lett. 83, 3370-3373 (1999) L.Randall & R.Sundrum, Phys. Rev. Lett. 83 4690-4693 (1999) Universal eXtra Dimensions A.Delgado, A.Pomarol and M.Quiros, Phys. Rev. D 60, 095008 (1999) T.Appelquist, H.C.Cheng and B.A.Dobrescu, Phys. Rev. D 64, 035002 (2001) K.R.Dienes, E.Dudas and T.Gherghetta, Phys. Lett. B 436, 55 (1998)

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!

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; 105006 (1999) J.L.Hewett, Phys.Rev.Lett. 82; 4765-4768 (1999) G.F.Guidice, R.Rattazzi & J.D.Wells, Nucl. Phys. B544, 3 (1999)

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

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

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

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

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!

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

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 hits @ arXiv for “TeV + Black +Holes”: 135 Hossenfelder et al: Phys. Rev. D 66 (2002) 101502, Phys. Lett. 548 (2002) 73

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

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

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.

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

Observation of Black Holes

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?)

Minimal Length D.J.Gross, P.F.Mende, Nucl.Phys. B 303, (1988) 407: D.J.Gross [hep-th/9704139]: „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.“

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

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

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

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

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

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

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

Minimal Length versus Cut-off

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 »

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

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

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