### The hidden dimensions of the Universe

I. Antoniadis

CERN

Joint Physics Colloquia, Taipei, 19 November 2013

### Particle physics:

structure of matter & fundamental forcesExperimental tools: Particle colliders at very high energies =>

physical laws of nature at very short distances
LEP2 (CERN): electron - positron collisions at 200 GeV→ 10^{−15} cm
TEVATRON (USA): protons - antiprotons at 2 TeV→ 10^{−16} cm
LHC (CERN):proton - proton collisions at 14 TeV^{∗} → 10^{−17} cm

Th description: simple mathematical theories with predictive power encoding the symmetries of physical phenomena

∗ for the moment 8 TeV

** at Accelerating Science and Innovation **

**at Accelerating Science and Innovation**

## the Large Hadron Collider (LHC)

### • Largest scientific instrument ever built, 27km of circumference

### • >10 000 people involved in its

### design and construction

superconducting magnets at 1.9^{o} K => accelerate protons at 0.99999999c
orbit LHC ring 11000 times/sec => several thousand billion protons

A billion p-p collisions per second

each collision has over a thousand particles produced

### … and also a telescope The LHC is the worlds most

### powerful microscope …

Big Bang

### Evolution of the Universe

Today 13.8 Billion Years

10^{28} cm

### Only particle

### physics can

### tell us what

### Standard Model of electroweak + strong forces

Quantum Field Theory Quantum Mechanics + Special Relativity Principle: gauge invariance U(1) × SU(2)×SU(3)

Very accurate description of physics at present energies 17 parameters

1 mediators of gaugeinteractions(vectors): photon, W^{±}, Z +8 gluons

2 matter(fermions): (leptons + quarks) × 3

electron, positron, neutrino (up, down)_{3 colors}

3 Higgs sector: new scalar(s) particle(s):

break the EW symmetryU(1) × SU(2) → U(1)γ at MW ∼ 100 GeV generate mass for all elementary particles Brout-Englert Higgs 1964

### Excellent LHC performance

Number of events = Cross section × Luminosity

### July 4

^{th}

### 2012 The discovery of a

### new particle

### Possible Higgs boson events

!"!"#$"

%&'()(&*$"

!"!"##"

$%&'('%)*"

### Higgs boson discovery at the LHC

m_{H} = 125.9 ± 0.4 GeV(average of Particle Data Group 2013)

### Couplings of the new boson vs SM Higgs

Agreement with Standard Model Higgs expectation at 1.5 σ
Most compatible with scalar 0^{+} hypothesis

Measurement of its properties and decay rates currently under way

Fran¸cois Englert Peter Higgs Nobel Prize of Physics 2013

↓ ↓

### Why Beyond the Standard Model?

Experimental indications:

Neutrino masses

Unification of gauge couplings ? Dark matter[23]

Two main theory reasons:

Include gravity Quantum Mechanics + General Relativity ? ^{[25]}

Mass hierarchy: M_{W}/M_{Planck} ≃ 10^{−17}^{[26]}

### Gauge coupling unification

Energy evolution of gauge couplings αi = g_{i}^{2}/4π =>

low energy data → extrapolation at high energies:

### Observable Universe

Ordinary baryonic matter: only a tiny fraction Non-luminous (dark) matter: 25%

Natural explanation: new stable WeaklyInteractingMassiveParticle[21]

## Classic Dark Matter Signature

### Missing transverse energy

### carried away by dark matter particles

### Newton’s law

m • ←−r−→ • m F_{grav}= GN

m^{2}

r^{2} G_{N}^{−1/2} = MPlanck = 10^{19} GeV
Compare with electric force: F_{el}= e^{2}

r^{2} =>

effective dimensionless coupling G_{N}m^{2} or in general G_{N}E^{2} at energies E

E = mproton => F_{grav}

F_{el} = G_{N}m^{2}_{proton}

e^{2} ≃ 10^{−40} => Gravity is very weak !
At what energy gravitation becomes comparable to the other interactions?

M_{Planck} ≃ 10^{19} GeV → Planck length: 10^{−33} cm
10^{15} × the LHC energy! ^{[21]}

### Mass hierarchy problem

Higgs mass: very sensitive to high energy physics

quantum corrections: δmH ∼ scale Λ of new physics/massive particles
stability requires adjustment of parameters at very high accuracy
to keep the physical mass (m^{tree}_{H} )^{2}+ δm_{H}^{2} at the weak scale

Λ = MGUT or MP => fine tuning at 28-32 decimal places ! Why gravity is so weak compared to the other interactions? [32]

### Standard picture: low energy supersymmetry

every particle has a superpartner with spin differ by 1/2 cancel large quantum corrections to the Higgs mass

=> superpartner mass splittings must be not far from M_{W}
Advantages:

natural elementary scalars
gauge coupling unification^{[22]}

LSP: natural dark matter candidate prediction of light Higgs

rich spectrum of new particles within LHC reach

### Problems of supersymmetry

too many parameters: soft breaking terms supersymmetry breaking mechanism: unknown Standard Model global symmetries are not automatic

conditions on soft terms for suppression of flavor changing processes no satisfactory model of supersymmetric grand unification

higgsino mass problem:

supersymmetric mass parameter but of the order of the soft terms
MSSM : already a % - %^{0} fine-tuning

‘little’ hierarchy problem

### String theory:

Quantum Mechanics + General Relativity point particle → extended objects• →

particles ≡ string vibrations - quantum gravity

- framework of unification of all interactions - “ultimate” theory: · ultraviolet finite

· no free parameters
mass scale(tension): Mstring ↔ size: l^{string}
rigid string : known particles (massless)
vibrations : infinity of massive particles

### At what energies strings may be observed?

Are there low energy string predictions testable at LHC ?

Very different answers depending mainly on the value of the string scale
Before 1994: M_{string} near M_{Planck} at ∼ 10^{18} GeV lstring≃ 10^{−32} cm

ց

✲
M_{W}

10^{2}

M_{Planck}

10^{18} GeV

↑

After 1994: M_{string} is an arbitrary parameter

High string scale: natural for supersymmetry and unification but no stringy test at LHC

Interesting possibility: M_{string} ∼ MW => nullify the hierarchy problem
low UV cutoff Λ ≃ Mstring ^{[26]}

### Extra dimensions and braneworlds

Consistency of string theory ⇒ 9 spatial dimensions !

=> six new dimensions of space

matter and gauge forces may be localized in less than 9 dimensions

=> our universe on a extended membrane ? [37]

p-brane: extended in p spatial dimensions

p = 0: particle, p = 1: string, p = 2: membrane,. . .

### Extra dimensions

how they escape observation?

finite size R Kaluza and Klein 1920

energy cost to send a signal:

E > R^{−1} ← compactification scale
experimental limits on their size
light signal ⇒ E >∼ 1 TeV

R <∼ 10^{−16} cm
how to detect their existence?

motion in the internal space => mass spectrum in 3d

### How many dimensions ?

example: - one internal circular dimension - light signal

5

plane waves e^{ipy} periodic undery → y + 2πR

=> quantization of internal momenta: p = _{R}^{k} ; k = 0, 1, 2, . . .

=> 3d: tower of Kaluza Klein particles with masses Mk = k/R
p_{0}^{2}− ~p^{2}− p_{5}^{2} = 0 => p^{2}_{0}− ~p^{2}= p_{5}^{2}= _{R}^{k}^{2}2

E >> R^{−1}: emission of many massive photons

⇔ propagation in the internal space

### Our universe on a membrane

Two types of new dimensions:

• longitudinal: along the membrane

• transverse: “hidden” dimensions
only gravitational signal => R_{⊥}<

∼ 1 mm !

Adelberger et al. ’06

R_{⊥}<∼ 45 µm at 95% CL

• dark-energy length scale ≈ 85µm ^{[52]}

### Low scale gravity

Extra large ⊥ dimensions can explain the apparent weakness of gravity total force = observed force × volume ⊥

↑ ↑ ↑

G_{N}^{∗} = G_{N} × V_{⊥}

G_{N}^{∗} = M_{∗}^{−(2+n)} : (4 + n)-dim gravitational constant

n dimensions of size R_{⊥}

=> V_{⊥}= R_{⊥}^{n}

total force ≃ O(1) at 1 TeV => M_{∗}≃ 1 TeV

n = 1 : R_{⊥}≃ 10^{8} km excluded

n = 2 : R_{⊥}≃ 0.1 mm ^{(10}^{−12} ^{GeV)}

possible
n = 6 : R_{⊥}≃ 10^{−13} mm (10^{−2}GeV)

### String theory realization: D-brane world

• gravity: closed strings propagating in 10 dims

• gauge interactions: open strings with their ends attached on D-branes Dimensions of finite size: n transverse 6 −n parallel

calculability => R_{k} ≃ lstring ; R_{⊥} arbitrary

G_{N}^{∗} =g_{s}^{2}l_{s}^{2+n} g_{s} : string coupling (≃ gauge coupling for D-branes)
M_{s} ∼ 1 TeV => R⊥^{n} = 10^{32}l_{s}^{n}

distances > R_{⊥} : gravity 3d but for < R_{⊥} : gravity (3+n)d[42]

strong gravity at 10^{−16} cm ↔ 10^{3} GeV

10^{30}× stronger than thought previously! ^{[43]}

### Braneworld

2 types of compact extra dimensions: • parallel (dk): <∼ 10^{−16} cm (TeV)^{[45]}

• transverse (⊥): <∼ 0.1 mm (meV)^{[51]}

open string

closed string

Extra dimension(s) perp. to the brane

Minkowski 3+1 dimensions

d extra dimensions||

p=3+d -dimensional brane//

3-dimensional brane

### Gravity modification at submillimeter distances

Newton’s law: force decreases with area

3d: force ∼ 1/r^{2}
(3+n)d: force ∼ 1/r^{2+n}

observable forn = 2: 1/r^{4} with r << .1 mm

### Gravitational radiation in the bulk = > missing energy

P

P γ or jet

present LHC bounds: M_{∗}>

∼ 3 − 5 TeV

Collider bounds on R⊥ in mm

n= 2 n= 4 n= 6

LEP 2 4.8 × 10^{−1} 1.9 × 10^{−8} 6.8 × 10^{−11}
Tevatron 5.5 × 10^{−1} 1.4 × 10^{−8} 4.1 × 10^{−11}
LHC 4.5 × 10^{−3} 5.6 × 10^{−10} 2.7 × 10^{−12}

### Black hole production

Giddings-Thomas, Dimopoulos-Landsberg ’01

String-size black hole energy threshold : MBH≃ Ms/g_{s}^{2}

Horowitz-Polchinski ’96, Meade-Randall ’07

weakly coupled theory => strong gravity effects occur much above Ms, M∗

g_{s} ∼ 0.1 (gauge coupling) => M_{BH}∼ 100M^{s}

Comparison with Regge excitations : M_{j} = M_{s}√
j =>

production of j ∼ 1/gs^{4} ∼ 10^{4} string states before reach MBH

### Other accelerator signatures

Large TeV dimensions seen by SM gauge interactions

=> KK resonances of SM gauge bosons[41] I.A. ’90

M_{n}^{2}=M_{0}^{2}+ k^{2}

R^{2} ; k = ±1, ±2, . . .
string physics and possible strong gravity effects

Massive string vibrations => e.g. resonances in dijet distribution [49]

M_{j}^{2} =M_{0}^{2}+ M_{s}^{2}j ; maximal spin: j + 1

higher spin excitations of quarks and gluons with strong interactions Anchordoqui-Goldberg-L¨ust-Nawata-Taylor-Stieberger ’08 extra U(1)’s and anomaly induced terms[50]

masses suppressed by a loop factor from M_{s}

Localized fermions (on brane intersections)

=> single production of KK modes I.A.-Benakli ’94

f

f _

n_ R

• strong bounds indirect effects: R^{−1}>

∼ 4 TeV

• new resonances ^{[48]}

Otherwise KK momentum conservation

=> pair production of KK modes (universal dims)

n_ R

-^{n}^{_}

R f

f _

• weak bounds R^{−1}>∼ 500 GeV

• no resonances

• lightest KK stable ⇒ dark matter candidate Servant-Tait ’02

### Standard Model on D-branes

I.A.-Kiritsis-Rizos-Tomaras ’02• U(1)^{4}⇒ hypercharge + global symmetries

• ν^{R} in the bulk ⇒ small neutrino masses

R^{−1}= 4 TeV^{[46]} I.A.-Benakli-Quiros ’94, ’99

1500 3000 4500 6000 7500

Dilepton mass
10^{-6}

10^{-5}
10^{-4}
10^{-3}
10^{-2}
10^{-1}
10^{0}

Events / GeV

γ + Z γ Z

Universal deviation from Standard Model in jet distribution

M_{s} = 2 TeV

Width = 15-150 GeV

Anchordoqui-Goldberg-
L¨ust-Nawata-Taylor-
Stieberger ’08 ^{[45]}

present LHC limits (2010 data): Ms>∼ 5 TeV

### Extra U(1)’s and anomaly induced terms

masses suppressed by a loop factor

usually associated to known global symmetries of the SM (anomalous or not) such as (combinations of)

Baryon and Lepton number, or PQ symmetry

in general they become massive due to anomalies but global symmetries remain in perturbation - Baryon number => proton stability

- Lepton number => protect small neutrino masses

### Standard Model on D-branes

R

L

LL

ER

QL

U , D

R R

W

gluon

### Sp(1) U(1)

### U(1) U(3)

### 1-Leptonic 3-Baryonic

### 2-Left 1-Right

≡ SU(2)

U(1)^{3} ⇒ hypercharge + B, L global

### microgravity experiments

change of Newton’s law at short distances^{[38]}

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 I.A.-Dimopoulos-Dvali ’98, I.A.-Benakli-Maillard-Laugier ’02 such as radion and lepton number

volume suppressed mass: (TeV)^{2}/M_{P} ∼ 10^{−4} eV → mm range
can 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: >∼ 10^{6}

### Experimental limits on short distance forces

V(r ) = −G ^{m}^{1}_{r}^{m}^{2} 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

10^{-2}
10^{-1}
10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}
10^{6}
10^{7}
10^{8}
10^{9}
10^{10}

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

U.Washington 1

Cantilever resonance (f_{0}): ~300 Hz
Drive frequency(f_{0}/3): ~100Hz

motion

Cantilever resonance (f_{0}): ~300 Hz
Drive frequency(f_{0}/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

Neutron scattering:

bounds in the range

∼ 1pm - 1nm

Nesvizhevsky-Pignol- Protasov ’07

**|****2****log|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 UCN gravitational level

gauge boson in extra dimensions Electroweak scale new boson

**LIMITS ON EXTRA YUKAWA FORCE**

** mass [eV]**

**1**

**2** **10**

**3** **10**

**4** **10**

**5** **10**
**10**

### Conclusions

Confirmation of the Higgs scalar discovery at the LHC : important milestone of the LHC research program

LHC and Particle physics in a new era with possible new discoveries unveiling the fundamental laws of Nature

Future plans to explore the 10-100 TeV energy frontier

The LHC timeline LS1 Machine Consolidation

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LS2 Machine upgrades for high Luminosity

• Collimation

• Cryogenics

• Injector upgrade for high intensity (lower emittance)

• Phase I for ATLAS : Pixel upgrade, FTK, and new small wheel

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LS3 Machine upgrades for high Luminosity

• Upgrade interaction region

• Crab cavities?

• Phase II: full replacement of tracker, new trigger scheme (add L0), readout electronics.

*Europe’s top priority should be the exploitation *
*of the full potential of the LHC, including the *
*high-luminosity upgrade of the machine and *
*detectors with a view to collecting ten times *
*more data than in the initial design, by around *
*2030. *

### Future accelerators

ILC project

The future of LHC

### VHE-LHC: location and size

A circumference of 100 km is being considered for cost-benefit reasons

This Master program, organized jointly by École Polytechnique (ParisTech) and ETH Zurich, will offer a coherent education in theoretical and experimental High Energy Physics.

2 year program (120 ECTS) 1 year in each institution CONTACTS:

Academic board:

Ignatios Antoniadis (EP Paris and CERN) Jean-Claude Brient (EP Paris) Günther Dissertori (ETH Zurich) Matthias Gaberdiel (ETH Zurich) Master’s administration offices:

master-hep@phys.ethz.ch masters@polytechnique.fr

ÉCOLE POLYTECHNIQUE - ETH Zurich

Particle & Astro-particle Physics

h e p . p o l y t e c h n i q u e . e d u

Quantum Grav

ity & String Theory

Strong & Electroweak Interactions

Theo retic

al &

Observation al Cosmology LHC P

hysics, Supersymmetry & Unifi cation Experimental methods & General Relativity

HOST INSTITUTIONS:

ETH Zurich - www.ethz.ch ÉCOLE POLYTECHNIQUE - www.polytechnique.edu