Observables of Extra Dimensions Sabine Hossenfelder ... · Observables of Extra Dimensions Sabine...

Why Extra DimensionsModels with Extra Dimensions

ObservablesSummary

Approaching the Planck ScaleObservables of Extra Dimensions

Sabine HossenfelderUniversity of Arizona

Sabine Hossenfelder Approaching the Planck Scale


ObservablesSummary

Beyond Standard

• Quantum gravity?

• Hierachies?

• SUSY, SUSY-breaking?

• 3 families?

• Neutrino masses?

• Cosmological constant?

• ...



ObservablesSummary

Beyond Standard

• Quantum gravity?

• Hierachies?

• SUSY, SUSY-breaking?

• 3 families?

• Neutrino masses?

• Cosmological constant?

• ...

−→ Can not be answered within the standard model



ObservablesSummary

Why Extra Dimensions



ObservablesSummary


Top down



ObservablesSummary


Top down

Bottom up



ObservablesSummary


Top down

Bottom up

Extra Dimensions



ObservablesSummary


Top down

Bottom up

Extra Dimensions

”Science may be described as the artof systematic over-simplification.”

Karl Popper, The Observer, August 1982



ObservablesSummary

ADDRSUniversalSplit

ADD

• d +3 space like dimensions (bulk)

• Compactified to radius R

• Only gravitons are allowed into all dimensions

• SM particles bound to 3-dimensional submanifold (brane)

+ Solves hierarchy problem m2p = RdMd+2

f

• Results in massive KK-tower for particles in the bulk

• Large radii 1/R ∼ eV .. 10 MeV

Arkani-Hamed, Dimopoulos and Dvali, Phys. Lett. B 429, 263 (1998)Antoniadis, Arkani-Hamed, Dimopoulos and Dvali, Phys. Lett. B 436, 257 (1998)Arkani-Hamed, Dimopoulos and Dvali, Phys. Rev. D 59, 086004 (1999)



ObservablesSummary

ADDRSUniversalSplit

ADD






f



V ∼ 1

m2p

1

r

V ∼ 1

Md+2f

1

rd+1→ 1

Md+2f

1

Rd

1

r



ObservablesSummary

ADDRSUniversalSplit

ADD






f





ObservablesSummary

ADDRSUniversalSplit

ADD






f



KK-expansion

ψ(x ,y) =+∞

∑n=−∞

ψ(n)(x)exp(iny/R)



ObservablesSummary

ADDRSUniversalSplit

ADD






f



KK-expansion leads to apparent mass-term:

[∂x∂x −

( n

R

)2]

ψ(n)(x) = 0



ObservablesSummary

ADDRSUniversalSplit

ADD






f



Why LARGE extra dimensions?



ObservablesSummary

ADDRSUniversalSplit

ADD






f



For Mf ∼ 1 TeV one obtains

d = 1 : R ≈ 1010 m ← excludedd = 2 : R ≈ 10−1 mmd = 3 : R ≈ 106 fmd = 4 : R ≈ 104 fm



ObservablesSummary

ADDRSUniversalSplit

ADD






f





ObservablesSummary

ADDRSUniversalSplit

ADD






f



Direct measurements:Hoyle (Washington)Chiaverini (Stanford)Long (Colorado)−→ R < 0.18 mm



ObservablesSummary

ADDRSUniversalSplit

Randall Sundrum

• Non factorizable (warped) geometry in 5 dimensions

ds2 = e−2kyηµνdxµdxν−dy2

+ Important because of AdS-CFT correspondence

• Allows non-compact extra dimensions (volume stays finite)

Randall and Sundrum, Phys. Rev. Lett. 83, 4690 (1999)Randall and Sundrum, Phys. Rev. Lett. 83, 3370 (1999)



ObservablesSummary

ADDRSUniversalSplit

Randall Sundrum

• Non factorizable (warped) geometry in 5 dimensions

ds2 = e−2kyηµνdxµdxν−dy2

+ Important because of AdS-CFT correspondence

• Allows non-compact extra dimensions (volume stays finite)



ObservablesSummary

ADDRSUniversalSplit

Universal Extra Dimensions

• Adds d extra spacelike dimensions

• Gauge, Higgs, Fermions propagate into all of them

• Radius ∼ 1/TeV

• Can be embedded into ADD as substructure

+ Accelerated running of coupling → early unification



ObservablesSummary

ADDRSUniversalSplit

Universal Extra Dimensions

• Adds d extra spacelike dimensions

• Gauge, Higgs, Fermions propagate into all of them

• Radius ∼ 1/TeV

• Can be embedded into ADD as substructure

+ Accelerated running of coupling → early unification

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



ObservablesSummary

ADDRSUniversalSplit

Split Fermion Scenario

• Localization of fermions at different positions inside ’fat’ brane

+ Solves proton decay problem with lowered fundamental scale

+ Explains hierarchies in Yukawa couplings

+ Suppresses flavor changing decays

Arkani-Hamed and Schmaltz, Phys. Rev. D 61, 033005 (2000)Mirabelli and Schmaltz, Phys. Rev. D 61, 113011 (2000)Arkani-Hamed, Grossman and Schmaltz, Phys. Rev. D 61, 115004 (2000).



ObservablesSummary

ADDRSUniversalSplit

Split Fermion Scenario

• Localization of fermions at different positions inside ’fat’ brane

+ Solves proton decay problem with lowered fundamental scale

+ Explains hierarchies in Yukawa couplings

+ Suppresses flavor changing decays



ObservablesSummary

KK-modesGravitonsBlack HolesMinimal Length

KK-modes

• Compactification leads to quantized momenta

• Tower of apparently massive particles on brane

• Real pair production (KK # conserved)

• Virtual exchange divergent for d > 1:

∑n

Zd4p

1

p2 +(n/R)2→ ∞

• UXD: equally spaced, RS: not equally spaced

Tightest constraints from precision electroweak: 1/R > 4 TeV (ford = 1, depends on precise scenario).

Rizzo and Wells, Phys. Rev. D61, 016007 (2000)



ObservablesSummary


Gravitation as Effective Theory

• Philosophy: treat naively quantized gravity as effective theory

• Valid in weak coupling, examine first new effects

• Perturbation of metric: gAB = ηAB +ΨAB

• Decompose: spin-2 hµν, vector Vµi , scalar φij ( trace φii = φ)

• Coupling L = LGR +LM

• Energy momentum tensor on brane TAB = ηµAην

BTµν(x)δ(y)• Yields coupling terms: Lint =−1

2Tφ−T µνhµν

T. Han, J. D. Lykken and R. J. Zhang, Phys. Rev. D 59 (1999) 105006S. Cullen, M. Perelstein and M. E. Peskin, Phys. Rev. D 62, 055012 (2000)T. G. Rizzo, Phys. Rev. D 64, 095010 (2001)J. Hewett and M. Spiropulu, Ann. Rev. Nucl. Part. Sci. 52, 397 (2002)



ObservablesSummary


Massive Gravitons

• Yields tower of massive gravitons

• Tiny spacing but large phase space makes contributions important

• # of excitations with energy E is N(E )∼ (ER)d

• Brane breaks Poincare invarianz and momentum conservation on brane

E.g. e+e−→ γG :

σ ∼ αm2

pN(√

s)

∼ αs

(√s

Mf

)d+2



ObservablesSummary


Signatures of Gravitons

Collider physics:

• Real gravitons lead to missing energy (Mf in LHC-range)

• Virtual exchange modifies cross sections (depends on cutoff)

Astrophysical bounds are weak for d > 4, strong for d ≤ 4: Mf > 10 TeV

• Enhanced cooling of supernovae/red giants due to graviton emmission

• Cooling in early universe and addidional contributuins to backgroundfrom decay of bulk excitations

• Anomalous re-heating of neutron stars by decay of gravitationally trappedmassive gravitons



ObservablesSummary


Signatures of Gravitons

Collider physics:

• Real gravitons lead to missing energy (Mf in LHC-range)

• Virtual exchange modifies cross sections (depends on cutoff)

Astrophysical bounds are weak for d > 4, strong for d ≤ 4: Mf > 10 TeV

• Enhanced cooling of supernovae/red giants due to graviton emmission

• Cooling in early universe and addidional contributuins to backgroundfrom decay of bulk excitations

• Anomalous re-heating of neutron stars by decay of gravitationally trappedmassive gravitons

Approximation breaks down if graviation becomes strongly coupled=⇒ black holes!!



ObservablesSummary


Black Holes

In large extra dimensions (ADD)

• Gravity stronger at small distances ⇒ horizon radius larger

• For mass M ∼ 1 TeV :

RH ∼ 2×10−38fm without RH ∼ 2×10−4fm with extra dim.

• Two cases: RH � R (astro) and RH � R (collider)

• At the LHC partons can come closer than their Schwarzschildhorizon−→ a black hole can be created!



ObservablesSummary


Black Holes







Case 1:

Astrophysical black holes

radius RH � R

masses > earthmass ≈ 1048 TeV



ObservablesSummary


Black Holes







Case 2:

Collider produced black holes

radius RH � R

masses ∼ TeV



ObservablesSummary


Black Holes









ObservablesSummary


Cross-section of Black Holes

• Cross section σ∼ πR2H is function of

√s

• Threshold Θ(M−Mmin), one expects Mmin ∼Mf

• Model with colliding wave-packets in Aichelburg-Sexlgeometry and examine spacetime for horizons

• Integrate over PDFs for hadron collisions



ObservablesSummary


Production of Black Holes

=⇒ estimation yields ≈ 109 black holes per year, one per second



ObservablesSummary


Evaporation of Black Holes

Evaporation proceeds in 3 stages:

1 Balding phase: hair loss – the black holes radiates offangular momentum and multipole moments

2 Hawking phase: thermal radiation into allparticles of the standard model as well as gravitons

3 Final decay or remaining black hole relic

Black hole thermodynamics: T = κ/2π and dS/dM = 1/T

Numerical investigation: black hole event generator CHARYBDIS



ObservablesSummary


Evaporation Rate and Mass evolution

S.H. et al, Phys. Lett. 548 (2002) 73, J. Phys. G. 28 (2002) 1657



ObservablesSummary


Observables of Black Holes

• Multi-jet like events

• Momentum cut-off at ∼Mf

• Thermal spectrum → yields d and Mf

• Virtual black holes: baryon/flavor non-conservation


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 the Big Bang isunder investigation by international physicists because of fears thatit might cause ’perturbations of the universe’ that could destroy theEarth. One theory even suggests that it could create a black hole.[...]The committee will also consider an alternative, although lesslikely, possibility thatthe colliding particles could achieve sucha high density that they would form a mini black hole. In space,black holes are believed to generate intense gravita-tional fieldsthat suck in all surrounding matter. The creation of one on Earthcould be disastrous. [...]

John Nelson, professor of nuclear physics at Birmingham Univer-sity who is leading the British scientific team at RHIC, said thechances of an accident were infinitesimally small - but Brookhavenhad a duty to assess them.”The big question is whether the planetwill disappear in the twinkling of an eye. It is astonishingly un-likely that there is any risk - but I could not prove it,”he said.


ObservablesSummary


Evaporation faster than mass gain

The mass loss of the black hole from the evaporation

dM−dt∼ 103GeV/fm

is much larger than any possible mass gain even in a very densemedium (QGP, neutron star),

dM+

dt∼ R2

HT 4 ∼ 10−9GeV/fm

(even with high γ-factor ∼ 108).

−→ the black hole decays and can not grow



ObservablesSummary


Minimal Length Scale

Lowering the Planck mass means raising the Planck length!

• Fluctuations of spacetime itself disable resolution at smalldistances

• Follows e.g. from string theory, LQG, NGC, etc.

• Minimal length scales acts as UV cutoff



ObservablesSummary







→ →Sabine Hossenfelder Approaching the Planck Scale


ObservablesSummary









ObservablesSummary


Effective Model for Minimal Length

Use effective model to incorporate minimal length effects in QFT:

• For large momenta, p, Compton-wavelength λ can not getarbitrarily small λ > Lf = 1/Mf

• Modify wave-vector k and commuation relationsk = k(p) = h̄p +a1p

3 +a2p5...⇒ [pi ,xj ] = i∂pi/∂kj

• Results in a generalized uncertainty principle

∆x∆p ≥ 1

2h̄

(1+

p2

M2f

)

• And a squeezed phase space at high energies

〈p|p′〉= ∂p

∂kδ(p−p′)⇒ dp→ dk

h̄

∂p

∂k=

dk

h̄e|p|Mf



ObservablesSummary


Consequences of Minimal Length

• High precision: hydrogen, g −2,...

• Stagnation of energy dependence of cross sections

• Black hole production becomes more difficult

• Regulator!



ObservablesSummary






• Regulator!

SH, M. Bleicher, S. Hofmann, S. Scherer, J. Ruppertand H. Stoecker, Phys. Lett. B598 (2004) 92-98



ObservablesSummary






• Regulator!

SH, Phys. Lett. B598 (2004) 92-98



ObservablesSummary






• Regulator!

dpd+4→ dkd+4∣∣∣∂p

∂k

∣∣∣SH, Phys. Rev. D70 (2004) 105003



ObservablesSummary


Konrad Lorentz

”Truth in science can best be defined as theworking hypothesis best suited to open theway to the next better one.”

– Konrad Lorenz



ObservablesSummary

Summary

• Extra dimensions are effective theories beyond standard

• Useful to examine first effects and make predictions

* KK-excitations* Gravitons* Black holes

• Parametrize influence of space-time properties (d ,R) onobservables and constrain scenarios

• Working hypothesis to proceed from bottom to top...


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