Large eXtra Dimensionsand theMinimal Length Sabine Hossenfelder University of Arizona
The Standard Model • 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."
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.
„Knowledge is a process of piling up facts;wisdom lies in their simplification.“ ~ Martin Luther King
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 • Astrophysics: earthmass ( 8 x 1048 TeV) • Colliders: earthmass «R Modification of the gravitational law on distances 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 Dimopoulos & Landsberg - “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 ... • # Black Holes per year at LHC !!! • # Total hits @ arXiv for “TeV + Black +Holes”: 132 Hossenfelder et al: Phys. Rev. D 66 (2002) 101502, Phys. Lett. 548 (2002) 73
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 gain ratio, high gamma-factor: • Massloss: • Mass gain ratio, thermal only:
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. B575 (2003) 85-99
Running Couplingwith Minimal Length • Higher dimensional loops
Renormalization of Selfenergy • Looking closer, the propagator exhibits complex structures • Expansion in series of one-particle-irreducible contributions • Can be summarized in
Running Couplingwith Minimal Length • At one loop order the important graph is • Dienes, Dudas, Gherghetta, • Nucl. Phys. B 537, (1999) 47
What else? • Black Hole production with minimal length? • Violation of Lorentz-covariance? • Non-commutative geometries? • Real gravitons with minimal length? • Graviton loops? • ... ArXiv:hep-th/0404232
~ Konrad Lorenz "Truth in science can best be defined as the working hypothesis best suited to open the way to the next better one."
LXD-Group ITP Frankfurt/Germany Marcus Bleicher, Benjamin Koch, Ulrich Harbach, Sabine Hossenfelder, Stefan Hofmann(Stockholm), Lars Gerland (Tel Aviv), Kerstin Paech, Christoph Rahmede, Jörg Ruppert, Horst Stöcker, Sascha Vogel
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 Arizona – 05/04/04