1 extra dimensions at future hadron colliders g.f. giudice cern
TRANSCRIPT
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LHC is the machine to study the scale of EW breaking
NEW THEORY
Desert, e.g. conventional susy need for precision
New thresholds around 10 TeV need for energy increase to make next step of discoveries
Multi-TeV linear collider?
VLHC ?
m < TeV measurements after LHC
VLHC not meant to push new-physics limits by an order of magnitude, but to explore a well-motivated
(after some LHC discoveries) energy region
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EXTRA DIMENSIONS offer good motivations for explorations with a √s ~ 100 TeV hadron collider
• Need to test the theory well above the EW breaking scale
• Existence of new thresholds (new physics, not just some more KK) in the 10 TeV region
Motivations and implementions of extra dimensions are quite different
Not a systematic review, but some examples relevant to VLHC
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GRAVITY IN EXTRA DIMENSIONS
GRAVITY IN EXTRA DIMENSIONSFundamental scale at SM
Any short-distance scale < SM
-1 explained by geometry
42/12/ DMRM DPl
KRPl eMM 5
FLAT Arkani Hamed-Dimopoulos-Dvali
WARPED Randall-Sundrum
5H
QUANTUM GRAVITY AT LHCQUANTUM GRAVITY AT LHC
Graviton emissionMissing energy (flat)
Resonances (warped)
TT
4
1
252
1ff
Contact interactions (loop dominates over tree if gravity is strong)
Higgs-radion mixing
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These processes are based on linearized gravity valid at √s <<MD ~TeV
• Suitable for LHC
• VLHC can extend limits, but the motivations are weak
VLHC can probe the region √s >>MD~TeV
(only marginal at LHC)
independent test, crucial to verify gravitational nature of new physics
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TRANSPLANCKIAN REGIME
2
1
3
c
GDP
1
1
3
1
1
2
3
2
81
c
sGR D
S
Planck length quantum-gravity scale
PSD
PS
RM
R
:slimit kian transplanc
:0 limit classical
Schwarzschild radius
classical gravity
same regime
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b > RS
Non-perturbative, but calculable for b>>RS (weak gravitational field)
Gravitational scattering: two-jet signal at hadron colliders
G.G.-Rattazzi-Wells
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b < RSGiddings-Thomas, Dimopoulos-Landsberg
At b<RS, no longer calculable
Strong indications for black-hole formation
At the LHC, limited space for transplanckian region and quantum-gravity pollution
At the VLHC, perfect conditions
See talk by T. Rizzo
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2-jets with large Minv and Black holes
Jets + missing ET 2-leptons
QUANTUM GRAVITY
Semi-classical approximation
Linearized gravity
Transplanckian
Cisplanckian
VLHC
LHC
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EXTRA DIMENSIONS AND THE THEORY OF ELECTROWEAK BREAKING
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5.6
9.2
9.7
4.6
7.3
6.1
4.3
4.5
3.2
6.4
9.3
5.0
12.4
FqdH
bbee
ee
LLHDiH
HDH
BWHH
LuudR
uuL
aa
2
55
2
2
1
LEP1
LEP2
MFV
Bounds on LH
LH > 5-10 TeV
+
O2LH
1L
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SM<1 TeV, LH>5-10 TeV
“Little” hierarchy between SM and LH
•New physics at SM is weakly interacting
•No (sizable) tree-level contributions from new physics at SM
•Strongly-interacting physics can only occur at scales larger than LH
2
22222
2
2 GeV200TeV
4228
3
SM
tHZWSMF
H mmmmG
m
13
y
R
EXTRA DIMENSIONS AND SYMMETRY BREAKING
Scherk-Schwarz breaking
symmetry -R is Q If
)(),(
conditionsboundary with expansion KK
),()2,(
2
22//
2
R
Qnmxeeyx
yxeRyx
nnn
RinyRyiQ
iQ
Supersymmetry is broken
Non-local susy breaking involves global structure
At short distances (<R), susy-breaking effects are suppressed
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y
R yZ2
Orbifold projection
R 0
n=1
n=2
0
n=0n=1
n=2
R
Z2 : y y cos(ny/R) sin(ny/R)
Chiral theories
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5D SM compactified on S1/(Z2×Z2)
•Different susy breaking at each boundary
effective theory non-susy
(susy recovered at d<R-1)
• Higgs boson mass (rather) insensitive to UV
mH = 127 ± 10 GeV
SUPERSYMMETRY BREAKING: AN INTERESTING EXAMPLE Barbieri-Hall-Nomura
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Mass spectrum is non-supersymmetric
• one Higgs and two sparticles for each SM particle
• LSP stable stop with mass 210 GeV
Interesting phenomenology at LHC
• Strong dynamics at 5/R ~ 1.7 TeV (5-10 TeV in other models)
• UV completion new unknown dynamics within VLHC range
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5-D SU(N) YANG-MILLS
Elastic gauge-boson scattering in spin-0 gauge-singlet channel
Chivukula-Dicus-He
KKMgN
s
Rgg
sgN
T
2
5
2500
23
96
2
1
192
23 Unitarity
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HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD
AM = (A,A5), A5 A5 +∂5 forbids m2A52
gauge HiggsHiggs/gauge unification as graviton/photon unification in Kaluza-Klein
Higgs/gauge unification as graviton/photon unification in Kaluza-Klein
Correct Higgs quantum numbers by projecting out unwanted states with orbifold
Yukawa couplings, quartic couplings without reintroducing quadratic divergences
Csaki-Grojean-Murayama
Burdman-Nomura
Scrucca-Serone-Silvestrini
EW BROKEN BY BOUNDARY CONDITIONS? Csaki et al.
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Calculable description of EW breaking with strong dynamics at 5-10 TeV
New realizations of technicolour theories with new elements (extra dimensions, AdS/CFT correspondence) allowing some calculability
“Little hierarchy” is satisfied
LHC will discover weak physics at SM
New strong-dynamics thresholds at LH within the reach of VLHC
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DESERT
• Connection with GUT, strings, quantum gravity
• Gauge-coupling unification
• Neutrino masses
• Suppression of proton decay and flavour violations
• Setup for cosmology (inflation, baryogenesis)
NON DESERT
• Low-scale string theory,…
• Accelerated running, different sin2W
• R in bulk
• Different location of quarks and leptons in bulk
• Low-scale inflation, EW baryogenesis
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• Extra dimensions ubiquitous ingredient in non-desert scenarios
• Physics goals of VLHC quite distinct from those of LHC
Examples:
• “Need to test the theory well above the EW breaking scale”
Transplanckian physics: new energy regime to test extra-dim gravity
• “Existence of new thresholds (new physics, not just some more KK) in the 10 TeV region”
Extra-dim theories of EW breaking require UV completion at a scale not far from EW
CONCLUSIONS