Universal extra dimensions · 2020. 2. 7. · Universal extra dimensions All Standard Model ﬁelds...

Universal extra dimensions

All Standard Model fields propagate in the extra dimension(s)

Translation invariance => momentum conservation

e.g. 〈φnφmφl 〉 ∝ δn+m+l ,0 φn : n-th KK excitation of φ

No tree-level contribution to SM processes involving only 0-modes

However chirality => orbifolding e.g. S1 (circle) → S1/Z2 (interval)=> translation invariance is broken

But KK-parity remains : KK-number even/odd → KK-parity +/-1=> lightest KK-odd particle is stable

All SM gauge bosons have internal components AM ,M = 0 . . .D − 1- one gets eaten to give mass to 4d KK-vectors

- the remaining D − 5 form adjoint scalars (no extra scalar in D = 5)

I. Antoniadis (Extra dimensions) 21 / 44

Orbifolds

S1 : y ≡ y + 2πR / y → −y −→ S1/Z2

R0 πR 0 πR

Z2 acts also on fermion chirality (L→ L,R → −R) => 4d chiral 0-modes

Fields can be even or odd under Z2

Z2 even : Φe(xµ, y) =

∑

nΦ(n)e (x) cos

nRy

Z2 odd : Φo(xµ, y) =

∑

nΦ(n)o (x) sin

nRy

Odd fields have no 4d zero-modes


Mass spectrum

Radiative corrections => mass shifts that lift degeneracy at lowest KK level

divergent sum over KK modes in the loop => cutoff scale Λ ≃ 10/R


Lightest KK Particle (LKP)

1st KK of hypercharge boson Bµ1 in D = 5 or adjoint scalar B1H in D = 6


UED hadron collider phenomenology

large rates for KK-quark and KK-gluon production

LHC: 1-100 pb for R−1

Production at hadron colliders


SUSY vs UED signals

Example: jet dilepton final state [25]

SUSY UED


microgravity experiments

change of Newton’s law at short distances

detectable only in the case of two large extra dimensions

new short range forces

light scalars and gauge fields if SUSY in the bulk

or broken by the compactification on the brane

such as radion and lepton number

volume suppressed mass: (TeV)2/MP ∼ 10−4 eV → mm rangecan be experimentally tested for any number of extra dimensions

- Light U(1) gauge bosons: no derivative couplings

=> for the same mass much stronger than gravity: >∼ 106


Experimental limits on short distance forces

V (r) = −G m1m2r

(

1 + αe−r/λ)

Radion ⇒ M∗ >∼ 6 TeV 95% CL Adelberger et al. ’06


improved bounds in the range 5-15 µm

Geraci-Smullin-Weld-Chiaverini-Kapitulnik ’08

1 10 100 100010

-2

10-1

100

101

102

103

104

105

106

107

108

109

1010

Excluded by

experiment

Lamoreaux

U.Colorado

Stanford 2

Stanford 1

U.Washington 2

gauged

B#

Yukawa messengers

dilaton

KK gravitons

strange

modulus

gluon

modulus

heavy q

moduli

Stanford 3

α

λ (µm)

U.Washington 1


Cantilever resonance (f0): ~300 Hz

Drive frequency(f0/3): ~100Hz

motion

Cantilever resonance (f0): ~300 Hz

Drive frequency(f0/3): ~100Hz

motion

z

x

y

Piezo actuator

(+/- 120 µm at f /3)0

Fiber

Drive mass

T est mass

Cantilever

Silicon nitride

shield (cutaway)


improved bounds from Casimir effect in the nm range

Decca-Fischbach et al ’07, ’08

5: Colorado 4: Stanford 3: Lamoureaux 1: Mohideen et al.


Neutron scattering:

bounds in the range

∼ 1pm - 1nm

Nesvizhevsky-Pignol-

Protasov ’07

[m]λ-1210 -1110 -1010 -910 -810 -710

|2lo

g|g

-26

-24

-22

-20

-18

-16

-14

-12

-10

-8

Random potential model

Comparing forward and backward scattering

Comparing forward scattering and total X-section

Asymmetry of scattering on noble gases

EXCLUDED

REGION

antiprotonic atoms

Ederth

Mohideen

Purdue

Unseen extra U

CN

gravitational level

gauge boson

in extra dimensions

Electroweak scale new boson

LIMITS ON EXTRA YUKAWA FORCE mass [eV]

110210310410510


Neutron whispering gallery

Centrifugal quantum states of neutrons


Randal Sundrum models

spacetime = slice of AdS5 : ds2 = e−2k|y |ηµνdx

µdxν + dy2 k2 ∼ Λ/M35

UV-brane IR-brane

y = 0 y = rc

MP MW−|Λ|

bulk

fine-tuned tensions: T = −T ′ = 24M35k

exponential hierarchy: MW = MPe−2krc M2P ∼ M35/k

M5 ∼ MGUT

4d gravity localized on the UV-brane, but KK gravitons on the IR


main prediction: spin-2 resonances at the TeV scale

mn = cn k e−2krc ∼ TeV cn ≃ (n + 1/4) for large n

=> spin-2 TeV resonances in di-lepton or di-jet channels

weakly coupled for mn < M5 e−2krc => k < M5

viable models: SM gauge bosons in the bulk, Higgs on the IR-brane

AdS/CFT duals to strongly coupled 4d field theories

composite Higgs models, technicolor-type gYM = M5/k > 1


RS2

IR-brane can move to infinity: rc →∞

M2P = M3 1−e−2πkrc

k← internal volume V finite =>

• always 4d gravity localized on the UV-brane

potential: 1r+ 1

k2r3← deviations (rc →∞)

k−1 108 GeV, T 1/4 > 1 TeV


Universal extra dimensions · 2020. 2. 7. · Universal extra dimensions All Standard Model ﬁelds...

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