Large eXtra Dimensionsand the

Minimal Length

Large eXtra Dimensionsand the

Minimal Length

Sabine Hossenfelder

University of Arizona

Sabine Hossenfelder

University of Arizona

The Standard ModelThe 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???!• ...

• 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 !These questions can not be answered within the SM !

~ Karl Popper, The Observer, August 1982~ Karl Popper, The Observer, August 1982

"Science may be described as the art of systematic over-simplification."

"Science may be described as the art of systematic over-simplification."

Extra DimensionsExtra 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

• 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

0

d

i

d

ii

i

R

n

112

2

Rn

p ˆ

R

Large eXtra DimensionsLarge eXtra Dimensions

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

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

dd RMm 22 fp

dd RMm 22 fp

12

11 dd rMm

V

f rRM dd

1112

f

rmmV 11

2p

fM

fm

fm

mm

m

4

6

1

12

10:4

10:3

10:2

10:1

Rd

Rd

Rd

Rd excluded excluded

• For = 1 TeV one finds:• For = 1 TeV one finds:

1st exitation in eV – MeV range 1st exitation in eV – MeV range

Large eXtra DimensionsLarge eXtra Dimensions

• Hoyle (Washington)• Long (Colorado)• Chiaverini (Stanford) ...

R < 0.18 mm

• Hoyle (Washington)• Long (Colorado)• Chiaverini (Stanford) ...

R < 0.18 mm

GeV300/1 R

• SM gauge/matter fields are allowed in bulk • Xtra-momentum is conserved• KK-tower of massive fields

• 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• Dienes, Dudas, Gherghetta, Nucl. Phys. B 537, (1999) 47

Universal eXtra DimensionsUniversal eXtra Dimensions

The New ScaleThe 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.

• 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.

fMTeVf M

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

~ Martin Luther King ~ Martin Luther King

Some ReferencesSome 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)

• 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)

EffectsEffects 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!

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!

fM

fm4-10

GravitonsGravitonsCoupling 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 :

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 :

IJ IJ IJ g

ARTM LLL )()( yxTT JIIJ

ij ii

2

1

2

1i

i VVhhL

jiij

iiVh

ThT2

1

h iV

- 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)

- 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 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:

• Exitations of gravitons are interpreted on our brane as

massive particles

• Phase-space for energy E given by # of with

is

• this yields:

REnidEREn )()(

),...,( 1 dnn

)()( 2 snm

Geep

Energy loss in collisions

Modification of standard-model cross-sections

Energy loss in collisions

Modification of standard-model cross-sections

2

d

Ms

s f

Black HolesBlack Holes

• Astrophysics: earthmass

( 8 x 1048 TeV)

• Colliders: earthmass

• Astrophysics: earthmass

( 8 x 1048 TeV)

• Colliders: earthmass

HR

EarthRRRH »

EarthRRRH «

Modification of the gravitational law on distances

leads to an increase of the black hole radius Modification of the gravitational law on distances

leads to an increase of the black hole radius « R

M

M

Black Hole Cross-sectionBlack Hole Cross-section

• Horizon-radius in 3+d+1 dimensions for

Partons which get closer than form a horizon !

• Estimation for cross-section up to

• Horizon-radius in 3+d+1 dimensions for

Partons which get closer than form a horizon !

• Estimation for cross-section up to

fm38102 HR

fm4102 HR

),( dMRH

f10Ms

1TeVf MM

2)( BHXX HR

At the LHC partons get so close that they may collaps!At the LHC partons get so close that they may collaps!

• Horizon-radius in 3+1 dimensions for• Horizon-radius in 3+1 dimensions for

fMM

Production of Black HolesProduction of Black Holes• # Black Holes per year at LHC !!!• # Black Holes per year at LHC !!!

),ˆ()ˆ,()ˆ,(ddd

21ˆ2

1

01

111

dssyfsxfxM BAsx

s

BA

With CTEQ PDFs:With CTEQ PDFs:

910

Production of Black HolesProduction of Black Holes• # Black Holes per year at LHC !!!• # Black Holes per year at LHC !!!

910

Hossenfelder et al: Phys. Rev. D 66 (2002) 101502, Phys. Lett. 548 (2002) 73Hossenfelder et al: Phys. Rev. D 66 (2002) 101502, Phys. Lett. 548 (2002) 73

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 ...

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 ...

• # Total hits @ arXiv for “TeV + Black +Holes”: 132• # Total hits @ arXiv for “TeV + Black +Holes”: 132

Evaporation of Black HolesEvaporation of Black Holes

The Evaporation depends on the number of LXDsThe Evaporation depends on the number of LXDs

Hossenfelder et al: Phys. Lett. 548 (2002) 73, J.Phys.G 28 (2002) 1657 Hossenfelder et al: Phys. Lett. 548 (2002) 73, J.Phys.G 28 (2002) 1657

Big Bang Machine: Will it destroy Earth?

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 EyeIn the Twinkling of an Eye

• Mass gain ratio, high gamma-factor:• Mass gain ratio, high gamma-factor:

fmGeV

fmGeV 2862 101010

dd vR

tM

H

fmGeV

fmGeV 244mH

9842 101010d

d TRt

M

• Mass gain ratio, thermal only:• Mass gain ratio, thermal only:

• Mass loss:• Mass loss: )7(10)3(1d

d 3 ddt

Mfm

TeV , ... ,

fmTeV

Observation of Black Holes Observation of Black Holes

Observation of Black Holes Observation of Black Holes

• 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?)

• 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?)

fM

In high energetic collider experiments or UHECRs, resp.:In high energetic collider experiments or UHECRs, resp.:

Minimal LengthMinimal Length

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.“

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.“

D.J.Gross, P.F.Mende, Nucl.Phys. B 303, (1988) 407:D.J.Gross, P.F.Mende, Nucl.Phys. B 303, (1988) 407:

NE string of surface

Including the Minimal LengthIncluding the Minimal Length

• The minimal length can be modeled by setting

• with a minimal possible compton wavelength

• The minimal length can be modeled by setting

• with a minimal possible compton wavelength

.../)( 52

31 papappkk

ff ML /1

• Quantize via

• with expansion this yields:

• Quantize via

• with expansion this yields:

)ˆ(ˆ kpp j

i

kp

ji px iˆ,ˆ

2

fMp

px2

12 ,

2

f

Mp

px2

1iˆ,ˆ

We get a generalized uncertainty principle ! We get a generalized uncertainty principle !

ijji kx iˆ,ˆ ][

Including the Minimal LengthIncluding the Minimal Length

3)/(/)( ff MpMppk

• Further

• with the approximation for high energies

• Further

• with the approximation for high energies

, )( ppkp

pp

pkp

k

d

d

fM

p

pk

e

The momentum measure is exponentially squeezed! The momentum measure is exponentially squeezed!

Including the Minimal LengthIncluding the Minimal Length

Experimental ConstraintsExperimental Constraints

• The modifications factorize and yield the relation: • The modifications factorize and yield the relation:

to the Minimal Lengthto the Minimal Length

pp

pk

n n

nE

d

~d

ffee

Modification of SM cross-section at high energies, e.g. the minimal length in

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).data from LEP2, D. Bourikov et al., LEP2ff/01-02 (2001).

Hossenfelder et al, Phys. Lett. B 575 (2003) 85-99 Hossenfelder et al, Phys. Lett. B 575 (2003) 85-99

Running Couplingwith Minimal Length

Running Couplingwith Minimal Length

• Higher dimensional loops • Higher dimensional loops

0

22

4

lnd

qpp

p

d

qpp

pd

0

d22

4

p

k

qpp

pd

22

4d

pq

Renormalization of SelfenergyRenormalization of Selfenergy

• Looking closer, the propagator exhibits complex structures• Looking closer, the propagator exhibits complex structures

• Expansion in series of one-particle-irreducible contributions• Expansion in series of one-particle-irreducible contributions

DeDDD ~ii~ii~i 2 ...~ii~ii~i 22

DeDeD

D~2/)( qgqD

gDegq ~22

• Can be summarized in• Can be summarized in

Running Couplingwith Minimal Length

Running Couplingwith Minimal Length

• At one loop order the important graph is• At one loop order the important graph is

][)()( 2 qqqgqq

1ln)()(

iniini

ini 2

~

2

~11

ddiii bbb

ii

• Dienes, Dudas, Gherghetta, Nucl. Phys. B 537, (1999) 47• Dienes, Dudas, Gherghetta, Nucl. Phys. B 537, (1999) 47

IntegralIntegral

~

Power SeriesPower Series

Minim

al Length versus Cut-off

Minim

al Length versus Cut-off

1.10 7.21

1.2 2.5

TeV1/

TeV

f 100

1/1

L

R

What else?What else?

• Black Hole production with minimal length?

• Violation of Lorentz-covariance?• Non-commutative geometries?• Real gravitons with minimal length?• Graviton loops?• ...

• 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~ Konrad Lorenz

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

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

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

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

LXD-Group ITP Frankfurt/GermanyLXD-Group ITP Frankfurt/Germany

SummarySummary

• 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

• 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

Soon we might be able to look behind the SM.Soon we might be able to look behind the SM.

Sabine Hossenfelder – University Of Arizona – 05/04/04Sabine Hossenfelder – University Of Arizona – 05/04/04