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
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 1.9o 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
1028 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
th2012 The discovery of a
new particle
Possible Higgs boson events
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Higgs boson discovery at the LHC
mH = 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: MW/MPlanck ≃ 10−17[26]
Gauge coupling unification
Energy evolution of gauge couplings αi = gi2/4π =>
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 Fgrav= GN
m2
r2 GN−1/2 = MPlanck = 1019 GeV Compare with electric force: Fel= e2
r2 =>
effective dimensionless coupling GNm2 or in general GNE2 at energies E
E = mproton => Fgrav
Fel = GNm2proton
e2 ≃ 10−40 => Gravity is very weak ! At what energy gravitation becomes comparable to the other interactions?
MPlanck ≃ 1019 GeV → Planck length: 10−33 cm 1015 × 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 (mtreeH )2+ δmH2 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 MW 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: lstring 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: Mstring near MPlanck at ∼ 1018 GeV lstring≃ 10−32 cm
ց
✲ MW
102
MPlanck
1018 GeV
↑
After 1994: Mstring is an arbitrary parameter
High string scale: natural for supersymmetry and unification but no stringy test at LHC
Interesting possibility: Mstring ∼ 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 eipy periodic undery → y + 2πR
=> quantization of internal momenta: p = Rk ; k = 0, 1, 2, . . .
=> 3d: tower of Kaluza Klein particles with masses Mk = k/R p02− ~p2− p52 = 0 => p20− ~p2= p52= Rk22
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 ⊥
↑ ↑ ↑
GN∗ = GN × V⊥
GN∗ = 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⊥≃ 108 km excluded
n = 2 : R⊥≃ 0.1 mm (10−12 GeV)
possible n = 6 : R⊥≃ 10−13 mm (10−2GeV)
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 => Rk ≃ lstring ; R⊥ arbitrary
GN∗ =gs2ls2+n gs : string coupling (≃ gauge coupling for D-branes) Ms ∼ 1 TeV => R⊥n = 1032lsn
distances > R⊥ : gravity 3d but for < R⊥ : gravity (3+n)d[42]
strong gravity at 10−16 cm ↔ 103 GeV
1030× 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/r2 (3+n)d: force ∼ 1/r2+n
observable forn = 2: 1/r4 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/gs2
Horowitz-Polchinski ’96, Meade-Randall ’07
weakly coupled theory => strong gravity effects occur much above Ms, M∗
gs ∼ 0.1 (gauge coupling) => MBH∼ 100Ms
Comparison with Regge excitations : Mj = Ms√ j =>
production of j ∼ 1/gs4 ∼ 104 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
Mn2=M02+ k2
R2 ; k = ±1, ±2, . . . string physics and possible strong gravity effects
Massive string vibrations => e.g. resonances in dijet distribution [49]
Mj2 =M02+ Ms2j ; 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 Ms
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
• νR 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 10-1 100
Events / GeV
γ + Z γ Z
Universal deviation from Standard Model in jet distribution
Ms = 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/MP ∼ 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: >∼ 106
Experimental limits on short distance forces
V(r ) = −G m1rm2 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 10-1 100 101 102 103 104 105 106 107 108 109 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
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
Neutron scattering:
bounds in the range
∼ 1pm - 1nm
Nesvizhevsky-Pignol- Protasov ’07
|2log|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
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