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THEORETICAL
PREDICTIONSFOR COLLIDER
SEARCHES
THEORETICAL
PREDICTIONSFOR COLLIDER
SEARCHES• “Big” and “little” hierarchy problems
• Supersymmetry
• Little Higgs
• Extra dimensions
G.F. Giudice CERN
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HIERARCHY PROBLEMHIERARCHY PROBLEM
2
22222
2
2
GeV200TeV 0.7
123624
SM
tHZWSMF
H mmmmG
m
nofine-tuning SM < TeV
“Big” hierarchy between SM and MPl
Cosmological constant
Cut off of quartic divergences at <10-3 eV
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LITTLE HIERARCHY LITTLE HIERARCHY
10
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
•Successful new physics at SM has to pass non-trivial tests
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SUPERSYMMETRYSUPERSYMMETRY
mH2 =
H H+
t~
exp
Ghilencea-Ross
t
can be extended to MPl
-Link with quantum gravity
-Successful scenario for GUTexp
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UNIFICATION WITHOUT DESERTUNIFICATION WITHOUT DESERT
• Accelerated running from extra dimensions• or from gauge group replication• Different tree-level expression for sin2W
GUT: trace over GUT irrep
Little running needed
4
1sin~~,~for
8
3
QTr
Tr sin
2312
12123
2
232
W
W
ggg
USUUSUSU
I
Dienes-Dudas-Gherghetta
Arkani Hamed-Cohen-Georgi
Dimopoulos-Kaplan
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SUPERSYMMETRYSUPERSYMMETRY
• Gauge-coupling unification• Radiative EW breaking• Light Higgs
• Satisfies “little” hierarchy LH~4SM
• Dark matter
• Sparticles have not been observed• Susy-breaking sector unspecified
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Degrassi-Heinemeyer-Hollik-Slavich-Weiglein
MGeV
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Giusti-Romanino-Strumia
%3sun
moonsun
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Supersymmetry-breaking sector unspecified
Susy flavour violations gauge, gaugino mediation
Connection with gravity supergravity, anomaly mediation
problem supergravity
Predictivity gauge, gaugino, anomaly med.
Scenarios with different spectra and different experimental signals
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y
R
NEW INGREDIENTS FROM EXTRA DIMENSIONSNEW INGREDIENTS FROM EXTRA DIMENSIONS
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
NEW INGREDIENTS FROM EXTRA DIMENSIONSNEW INGREDIENTS FROM EXTRA DIMENSIONS
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 SUSY SM compactified on S1/(Z2×Z2)
•Different susy breaking at each boundary
effective theory non-susy
(susy recovered at d<R)
• Higgs boson mass (rather) insensitive to UV
mH = 127 ± 10 GeV
Large corrections to ?
UV completion at ~ 5 TeV ?
AN INTERESTING EXAMPLEAN INTERESTING EXAMPLE
Barbieri-Hall-Nomura
Barbieri-Hall-Marandella-Nomura-Okui-Oliver-Papucci
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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
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USING WARPED DIMENSIONSUSING WARPED DIMENSIONS•Susy-breaking in Higgs sector is non-local finite effects
•AdS/CFT SM non-susy
Higgs sector: susy bound states of spontaneously broken CFT
•Light Higgs & higgsino
•New CFT states at L-1 ~ TeV
•Considerable fine tuning
states bound of size 4
1 11 LLmEW
Susy breaking
Higgs sector
SM
Gherghetta-Pomarol
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SUPERSYMMETRY:
CONCLUSIONS
SUPERSYMMETRY:
CONCLUSIONSSusy at EW scale can be realized in very different ways:
•ETmiss
• ETmiss +
•ETmiss + ℓ
•Stable charged particle
•Nearly-degenerate
•Stable stop
•Partial susy spectrum
0~ W
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HIGGS AS PSEUDOGOLDSTONE BOSON
HIGGS AS PSEUDOGOLDSTONE BOSON
22
/
forbids
symmetry realizedlinearly -Non
:
2
hmahh
ae
fef
ia
fi
Gauge, Yukawa and self-interaction are large non-derivative couplings
Violate global symmetry and introduce quadratic div.
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A less ambitious programme:
Explain only little hierarchy
At SM new physics cancels one-loop power divergences
LITTLE HIGGSLITTLE HIGGS
LH
224
4
22
222
2
TeV10 loops Two
TeV loop One
SMFSM
FH
F
SMSMSMF
H
mGm
Gm
Gm
Gm
“Collective breaking”: many (approximate) global symmetries preserve massless Goldstone bosonℒ1ℒ
2
H2
222
44
Hm
ℒ1 ℒ2
Arkani Hamed-Cohen-Georgi
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It can be achieved with gauge-group replication
•Goldstone bosons in
• gauged subgroups, each preserving a non-linear global symmetry
• which breaks all symmetries
Field replication Ex. SU2 gauge with doublets such that V(
) and
spontaneously break SU2
Turning off gauge coupling to
Local SU2(2) × global SU2() both spont. broken
HG /
21 GGG
21SM GG
loops two
42
4
42
gmH
Kaplan-Schmaltz
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Realistic models are rather elaborate
Effectively, new particles at the scale f ~ SM
canceling (same-spin) SM one-loop divergences with couplings related by symmetry
Typical spectrum:
Vectorlike charge 2/3 quark
Gauge bosons EW triplet + singlet
Scalars (triplets ?)
Arkani Hamed-Cohen-Georgi-Katz-Nelson-Gregoire-Wacker-Low-Skiba-Smith-Kaplan-Schmaltz-Terning…
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tuning-fine %1.0TeV 5
TeV 1422
ff
v
mm t
t
Bounds from: Tevatron limits on new gauge bosons
EW data ( from new gauge and top)
In minimal model:
Variations significantly reduce the fine tuning
Csaki-Hubisz-Kribs-Meade-Terning
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HIGGS AS EXTRA-DIM COMPONENT
OF GAUGE FIELD
HIGGS AS EXTRA-DIM COMPONENT
OF GAUGE FIELDAM = (A,A5), A5 A5 +∂5 forbids m2A5
2
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
•Do not reintroduce quadratic divergences
Csaki-Grojean-Murayama
Burdman-Nomura
Scrucca-Serone-Silvestrini
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EXTRA DIMENSIONSEXTRA DIMENSIONSForget about symmetries, about little hierarchy
cut off 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
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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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Graviton emission
Tree-level graviton
exchange
Graviton loops
Gauge/graviton loop
G.G.-Strumia
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√As s approaches MD, linearized gravity breaks down
underlying quantum gravity (strings?)
TRANSPLANCKIAN REGIMES>>MD RS>>Pl and (semi)classical effects dominate
over quantum-gravity effects
b > RS
b < RS
Gravitational scatteringG.G.-Rattazzi-Wells
Black-hole productionGiddings-Thomas, Dimopoulos-Landsberg
√
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SM PARTICLES IN EXTRA DIMENSIONS
SM PARTICLES IN EXTRA DIMENSIONS
Gauge bosons in 5D: Direct + indirect limits Mc > 6.8 TeV Cheung-Landsberg
At LHC up to 13-15 TeV
Weaker bounds in universal extra dimensions After compactification, momentum conservation in
5th dim KK number conserved KK particles pair produced; no tree-level exchange Mc > 0.3 TeV Appelquist-Cheng-Dobrescu
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CONCLUSIONSCONCLUSIONS
• Many open theoretical options for new physics at EW scale
• Direct searches + precision measurements no existing theory is completely free of fine-tuning
EWSUSY
GUT
E
Connection with MPl
Gauge coupling unification
Connection with MPl
Gauge coupling unification
LH orSM Need for UV
completion at