the physics of extra dimensions Enrico Fermi Institute/UofC Club the physics of extra dimensions Maria Spiropulu Enrico Fermi Institute/UofC may 3 2002

2014 : extra dimensions centennial from the Standard Model to extra dimensions many “flavors” of extra dimensions direct and indirect effects of extra dimensions at the TeV scale current results and upcoming discoveries

: Gunnar Nordstrom Uber die Moglichkeit das electromagnetiche Feld und das Gravitationsfeld zu vereiningen Phys. Z. 15, 504 1914 : : Abstract. It is shown that a unified treatment of the electromagnetic and gravitational fields is possible if one views the four dimensional space time as a surface in a five dimensional world

Thedor Kaluza Oscar Klein Kaluza Th.Sitzungsber. Press.Akad.Wiss.Math K1 (1921) 966 Klein O. Z.Phys. 37 (1926) 895

Kaluza and Klein started from 5-dim gravity and derived 4-dim gravity plus electromagnetism They compactified the 5th dimension around a circle of radius R (“cylinder condition”) 5 GN=1/(MP)2 4

the Standard Model a list of particles with their “quantum numbers”, about 20 numbers that specify the strength of the various particle interactions, a mathematical formula that you could write on a napkin. 20s

LEPTONS R L QUARKS L R GAUGE BOSONS g Higgs Graviton

R L QUARKS L R GAUGE BOSONS g Higgs Graviton

R L L R GAUGE BOSONS g Higgs Graviton

Higgs Graviton + all antiparticles

what does the Standard Model not explain ? quantum gravity HST image of an 800 light-year wide spiral shaped disk of dust fueling a 1.2x10^9 solar mass black hole in the center of NGC 4261 10s

what does the Standard Model not explain ? quantum gravity dark matter and dark energy Sean Carroll 10s

what does the Standard Model not explain ? quantum gravity dark matter and dark energy Higgs G.t’Hooft 10s Arrange it so delicately that it will fall down in 19 minutes.

the Bigger Big picture The Standard Model describes everything that we have seen to extreme accuracy. Michelangelo Antonioni on Ferrara: “...it is a city that you can only see partly and the rest disappears and can only be imagined...” (beyond the clouds)

the Bigger Big picture (even) extra dimensions strings supersymmetry Ian Shipsey Now we want to extend the model to higher energies and get the whole picture For this we need new experiments and ideas

how many dimensions we live in what is an electron? how many dimensions we live in

32? 7? 6? extra dimensions? Experiments can actually discover them! String theory demands extra dimensions. 20sec

strong, weak, electromagnetic forces have comparable strengths hierarchy of scales 10-17 cm Electroweak scale range of weak force mass is generated (W,Z) strong, weak, electromagnetic forces have comparable strengths 10-33 cm Planck scale GN ~lPl2 =1/(MPl)2 1028 cm Hubble scale size of universe lu 16 orders of magnitude puzzle 1m

signals from extra dimensions in short range gravity observations in particle collision observations in astrophysical/cosmological observations how do we see a hidden dimension? what particles can move in that dimension how big is that dimension what is its shape

Frameworks ADD type of models: the extra dimension(s) are finite (i.e. compactified), the world is a “braneworld”, gravity (or SM singlets) propagate in the bulk. Hierarchy is generated by a large volume of the extra dimensions. Direct emission/virtual exchange. RS type of models: the extra dimension(s) are infinite. Hierarchy is generated from a strong curvature of the extra dimensional space. Direct resonant production of the spin-2 states in the graviton KK tower. Universal (Yale) type of models : No branes. Momentum conservation; Pair production of KK excitations.

compactification Nima Arkani-Hamed Savas Dimopoulos Gia Dvali hiding the extra dimensions (I) compactification Nima Arkani-Hamed Savas Dimopoulos Gia Dvali 1m

Gauss’s Law If the n extra dimensions are compactified down to sizes R, then Gauss’s Law 1m

Kaluza-Klein modes If a spatial dimension is periodic then the momentum in that dimension is quantized: From our dimensions of view the KK modes get mass: KK momentum tower of states (n is the mode number, for 2 extra dimensions two modes etc…) p

Pick the effective (higher dimensional) Planck Scale at 1TeV, then

hiding the extra dimensions (II) brane-worlds There could be other branes which would look like dark matter to us Standard Model particles are trapped on a brane and can’t move in the extra dimensions

Infinite Randall - Sundrum G Mother brane Our world brane 5th dimension Zero mode graviton is trapped on the mother brane (Planck brane)

gravity gets stronger at extremely high energies (or short distances). (4+n)d gravity it gets stronger at lower energies if there are extra dimensions…. 4d gravity force strength energy

Grand Unification Force Strength new gravity Higher Energy strong weak electromagnetic new Higher Energy

gravity is so weak that we have never even seen a graviton. gravitons are the most robust probe of extra dimensions gravity is so weak that we have never even seen a graviton. F=GN melectronmelectron r2 r melectron The gravitational attraction between two electrons is about 1042 times smaller than the electromagnetic repulsion.

Fermion or VB pairs at hadron or e+e- colliders graviton production in collider experiments: graviton emission Each KK-graviton state couples to the wall with Planck supressed strength The number of KK-states ~(ER)d The sum over all KK-states is not MPl supressed but MPl(4+d) supressed i.e. MEWK supressed so we have sizable cross sections graviton Exchange Fermion or VB pairs at hadron or e+e- colliders

Collider Detector at Fermilab

graviton emission in particle collisions www.columbia.edu/~lab71

graviton emission simulation:

concentric cylindrical layers energy deposited from the particle debris of the collision in the middle

“lego” event display

Two events are graviton simulation and one is real CDF data: Can you pick the gravitons?

two events are real CDF data and one is graviton simulation; Can you pick the graviton?

Lykken/Matchev/Burkett/Spiropulu qqbar->g G (d=2, M=1TeV, s=1.8TeV) [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] Lykken/Matchev/Burkett/Spiropulu

Case d=6 Only qqbar->g G (PYTHIA 6.115 + graviton process), d=6, M=1TeV, s=1.8TeV

qq  Gg LHC 100fb-1 8.5 TeV 6.8 TeV 5.8 TeV 5.0 TeV 900 GeV 700 GeV 5 4 1150 GeV 950 GeV 3 1400 GeV 1100 GeV 2 MS reach, Run II MSreach,Run I n [Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)] very very optimistic estimates 8.5 TeV 6.8 TeV 5.8 TeV 5.0 TeV

Monojet+missing energy: DØ limit

Monojet+missing energy: CDF Expected number of gravitons for 84pb-1 Result very soon

e+e-  gG @L3 (GMSB analyses) [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and cor. version: hep ph/9811291] (GMSB analyses)

Total cross section analysis e+e-GZ ( a la Higgs analyses) [Balazs, Dicus, He, Repko, Yuan, hep-ph/9904220, Z width] [Cheung, Keung, hep-ph/9903294, recoil mass] MET+jets n sZG(pb) e sZG95%(pb) Ms(TeV) 2 0.64 0.56 0.29 0.60 3 0.08 0.56 0.30 0.38 4 0.01 0.55 0.30 0.29 L3: Phys. Lett. B470, 281 (1999) Visible Mass analysis ALEPH-CONF-99-027 Total cross section analysis

Monojet + missing energy: LHC reach Ian Hinchliffe

Pair production via virtual graviton exchange e.g 2 > Gravity effects interfere with SM effects > 3 terms in the production cross section: SM, intrerference, gravity > the sum over the KK states is divergent and a cutoff is required (Ms)

Virtual exchange: dielectron and diphoton D0 limits

M(gg) = 574 GeV cosq* = 0.86

Virtual exchange: diphoton CDF analysis

(anomalous Zgg couplings analyses,WW x-section,Zg) e+e- gg,VV Standard Model Interference Term Gravity Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] Agashe, Deshpande, Phys. Lett. B456, 60 (1999)

Two-photon measurements at LEP-II

Virtual Graviton Exchange Summary LEP 184 GeV 189 GeV Graviton Emission 202 GeV e+e-  gG e+e-  ZG n=2 n=3 n=4 n=5 n=6 n=2 n=3 n=4 n=5 n=6 A D L3 1.28 0.97 0.78 0.66 0.57 0.35 0.22 0.17 0.14 0.12 1.38 1.02 0.84 0.68 0.58 1.02 0.81 0.67 0.58 0.51 0.60 0.38 0.29 0.24 0.21 Virtual Graviton Exchange e+e- m+m- t+t- qq f f gg WW ZZ Combined ALL 0.80 1.03 0.63 0.68 0.57 0.59 0.66/0.61 0.55/0.55 (bb) 0.82 1.04 0.91 0.92 0.84/1.12 (<189) 0.75/1.00 A D L3 O 0.59 0.73 0.56 0.65 0.60 0.76 0.69 0.71 0.60/0.76 (ff) (<202) 0.91 0.99 0.56 0.69 0.58 0.54 0.49 0.49 0.84 1.00 0.80 0.79 0.68 0.79 0.76 0.77 0.87/1.07 (<189) 0.82/0.89 (VV) 0.63 0.60 0.50 0.63 0.61 0.68 0.63 0.64 0.61/0.68 (ff) (<189)

and neutral gauge boson excitations RS phenomenology 1500 GeV KK graviton/ its tower of states at LHC e+e-m+m- 500 GeV KK graviton/ its tower of states at a lepton collider 500 GeV KK graviton and neutral gauge boson excitations Davoudiasl, Hewett,Rizzo

A spin 2 graviton: Can we tell? 1.5 TeV graviton in Randal Sundrum at LHC

new accelerators for new physics Large Hadron Collider (CERN, 2006) Linear Collider (?,~2012)

Plethora of new models that involve extra dimensions Use Extra Dimensions Geomerty to solve: EWKB hierarchy problem SUSY Breaking flavor Breaking neutrino masses proton decay supression Grand Unification the cosmological problem More ideas are being explored

hiding the extra dimensions (III) no need to hide them extra-new ideas (Arkani-Hamed et al, Hill et al…..) Deconstructing dimensions and sting theories: The extra dimension(s) emerges from the theory, is well used, and then the theory comes back to the normal 4 dimensions serviced and healthy and with all the necessary Higgses. No tricks.

what is the physics that connects the gravitational scale and the scale of the typical mass of the elementary particles what are the dimensions and dynamics behind spacetime how is string theory connected to the world

Space and time may be doomed. E. Witten I am almost certain that space and time are illusions. N. Seiberg The notion of space-time is clearly something we’re going to have to give up. A. Strominger If you ask questions about what happened at very early times, and you compute the answer, the answer is: Time doesn’t mean anything. S. Coleman

Nima Arkani-Hamed

D. Gross

think w a y different

SCIENCE: The Glorious Entertainment …for any important assertion evidence must be produced; …prophecies and bugaboos must be subjected to scrutiny; … guesswork must be replaced by exact count; ….accuracy is a virtue and inquiry is a moral imperative To the hegemony of science we owe a feeling for which there is no name, but which is akin to the faith of the innocent that the truth will out and vindication will follow. In its purest form science is justice as well as reason. Jacques Barzun

: Eot-Wash Group Measured gravity at the sub-mm level (down 0.2 mm) Adelberger et al Measured gravity at the sub-mm level (down 0.2 mm)

1030 1023 PRL 86 1418 (2001) 10-10 Purdue (AFM experiment 2001) Fischbach et al 1023 PRL 86 1418 (2001) 10-10

short range gravity measurements l<150 mm M*>4 TeV C.D. Hoyle, Ph.D thesis University of Washington, 2001

short range gravity measurements

(Price &Long) 100u

e+e-  ff Terms ~cos3q, ~cos4q make differential cross (QED analyses) e+e-  ff Terms ~cos3q, ~cos4q make differential cross sections a unique signature For ff other than ee the integrated interference term for scattering angles from 0 to p is ZERO. The interference between graviton and t-channel SM Bhabha is giving sizable contributions good sensitivity Every author and every experiment choose their Ms, LT,sign conventions as different ap from the others... [Hewett, Phys. Rev. Lett. 82, 4765 (1999) - DY] [Giudice, Rattazzi, Wells Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291 – DY, Bhabha] [Rizzo, Phys. Rev. D59, 115010 (1999) - Bhabha]

Bhabha scattering results ALEPH,OPAL,DELPHI,L3 combined: (Bourilkov hep-ph/9907380) MS>1.26 TeV (l=+1) Ms>960 TeV (l=-1)

Black Hole production at high energy collisions (Banks et al., Dimopoulos et al. Giddings et al.) L. BORISSOV

Collider Black Hole Production? If the Planck scale is the TeV scale, gravity becomes strong at the TeV scale : In high energy particle collisions short-lived microscopic black holes will be created These decaying black holes could be observed in future colliders, such as CERN’s LHC! ( bets?) p p