1 extra dimensioni e la fisica elettrodebole g.f. giudice napoli, 9-10 maggio 2007
TRANSCRIPT
1
Extra dimensioni e la fisica elettrodebole
G.F. Giudice
Napoli, 9-10 maggio 2007
2
SPACE DIMENSIONS AND UNIFICATION
Minkowski recognized special relativistic invariance of Maxwell’s eqs connection between unification of forces and number of dimensions
Electric & magnetic forces unified in 4D space time
€
r∇ ⋅
rE = ρ
r ∇ ×
r E = −
∂r B
∂tr
∇ ⋅r B = 0
r ∇ ×
r B =
∂r E
∂t+
r J
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
€
space - time t,r x → x μ = (t,
r x )
EM potentials r E = −
r ∇φ −
∂r A
∂t,
r B =
r ∇ ×
r A → Aμ = (φ,
r A )
EM fields r E ,
r B → Fμν = ∂μ Aν −∂ν Aμ =
0 −Ex −Ey −E z
Ex 0 Bz −By
Ey −Bz 0 Bx
E z By −Bx 0
⎛
⎝
⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟
current ρ,r J → Jμ = ( ρ,
r J )
Maxwell's eqs → ∂μ F μν = Jν
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3
UNIFICATION OF EM & GRAVITYNext step:
New dimensions?
1912: Gunnar Nordström proposes gravity theory with scalar field coupled to T
1914: he introduces a 5-dim A to describe both EM & gravity
1919: mathematician Theodor Kaluza writes a 5-dim theory for EM & gravity. Sends it to Einstein who suggests publication 2 years later
1926: Oskar Klein rediscovers the theory, gives a geometrical interpretation and finds charge quantization
In the ‘80s the theory, known as Kaluza-Klein becomes popular with supergravity and strings
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4
GRAVITY
In General Relativity, metric (4X4 symmetric tensor) dynamical variable describing space geometry (graviton)
€
ds2 = gμν dx μ dxν
€
gμν
Dynamics described by Einstein action
€
SG =1
16π GN
d4∫ x −g R(g)
• GN Newton’s constant
• R curvature (function of the metric)
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5
Consider GR in 5-dim
€
ˆ S G =1
16π ˆ G Nd5∫ x −ˆ g R( ˆ g )
Choose
€
ˆ g MN ( ˆ x ) =gμν + κ 2φ Aμ Aν κ φ Aμ
κ φ Aν φ
⎛
⎝ ⎜
⎞
⎠ ⎟( ˆ x )
€
ˆ g MN ⇔ gμν , Aμ , φDynamical fields
Assume space is M4S1
• First considered as a mathematical trick
• It may have physical meaning
(t,x)
x5
R
6
Extra dim is periodic or “compactified”
€
x5 + 2π R = x5
All fields can be expanded in Fourier modes
€
ϕ ( ˆ x ) =ϕ (n )(x)
2π Rn=−∞
+∞
∑ exp in x5
R
⎛
⎝ ⎜
⎞
⎠ ⎟
5-dim field set of 4-dim fields: Kaluza-Klein modes
€
ϕ (n )(x)
Each has a fixed momentum p5=n/R along 5th dim
€
ϕ (n )
4-d space
extra dimensions
mass
D-dim particle
E2 = p 2 + p2extra + m2
KK mass
From KK mass spectrum we can measure the geometry of extra dimensions
7
R
r << R r >> R
2-d plane
1-d line
Suppose typical energy << 1/R only zero-modes can be excited
Expand SG keeping only zero-modes and setting ϕ=1
€
ˆ S G ( ˆ g MN ) = SG (g(0)μν ) + SEM (A(0)
μ )
€
SG (g) =1
16π GN
d4 x −g R(g)∫
SEM (A) = −1
4d4 x Fμν F μν∫
⎧
⎨ ⎪
⎩ ⎪
To obtain correct normalization:
€
SG →1
GN
=dx5∫ˆ G N
=2π R
ˆ G N
SEM → κ = 16π GN
Gravity & EM unified in higher-dim space: MIRACLE?
8
Gauge transformation has a geometrical meaning
€
dˆ s 2 = ˆ g MN ( ˆ x ) dˆ x M dˆ x N
€
ˆ g MN ( ˆ x ) =gμν + κ 2φ Aμ Aν κ φ Aμ
κ φ Aν φ
⎛
⎝ ⎜
⎞
⎠ ⎟( ˆ x )
Keep only zero-modes:
€
dˆ s 2 = g(0)μν dx μ dxν + φ(0) dx 5 + κ A(0)
μ dx μ( )
2
Invariant under local
€
x 5 → x 5 −κ Λ
A(0)μ → A(0)
μ + ∂μ Λ(where g and ϕ
do not transform)
• Gauge transformation is balanced by a shift in 5th dimension
• EM Lagrangian uniquely determined by gauge invariance
9
CHARGE QUANTIZATION
Matter EM couplings fixed by 5-dim GR
Consider scalar field
€
S = d5 ˆ x −ˆ g ˆ g MN∂Mϕ∫ ∂Nϕ
Expand in 4-D KK modes:
€
S = dx5 d4 x −g(0) ∂ μ − inκ
RA(0)μ ⎛
⎝ ⎜
⎞
⎠ ⎟ϕ (n )
2
−n2
R2
ϕ (n )2
φ
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
∫n
∑∫
€
2π R
Each KK mode n has: mass n/R charge n/R
• charge quantization
• determination of fine-structure constant
• new dynamics open up at Planckian distances
€
α = 2
4π R2=
4GN
R2⇒ R =
4GN
α≈ 4 ×10−31 m = 5 ×1017 GeV( )
−1
10
Not a theory of the real world
ϕ=1 not consistent (ϕ dynamical field leads to inconsistencies: e.g. F(0)
F(0)=0 from eqs of motion)
• Charged states have masses of order MPl
• Gauge group must be non-abelian (more dimensions?)
Nevertheless
• Interesting attempt to unify gravity and gauge interactions
• Geometrical meaning of gauge interactions
• Useful in the context of modern superstring theory
• Relevant for the hierarchy problem?
11
Usual approach: fundamental theory at MPl, while W is a derived quantity
Alternative: W is fundamental scale, while MPl is a derived effect
New approach requires• extra spatial dimensions
• confinement of matter on subspaces
Natural setting in string theory Localization of gauge theories on defects (D-branes: end points
of open strings)
We are confined in a 4-dim world, which is embedded in a higher-dim space where gravity can propagate
12
COMPUTE NEWTON CONSTANT
Einstein action in D dimensions
€
SED =
1
16π ˆ G NdD x −ˆ g R( ˆ g )∫
Assume space R4SD-4: g doesn’t depend on extra coordinates
Effective action for g
€
SE =VD−4
16π ˆ G Nd4 x −g R(g)∫
⇒1
GN
=VD−4
ˆ G N
€
MPl = MD RMD( )D−4
2
€
ˆ G N =1
MDD−2
VD−4 = RD−4
13
Suppose fundamental mass scale MD ~ TeV
€
MPl = MD RMD( )D−4
2 very large if R is large (in units of MD-1)
Arkani-Hamed, Dimopoulos, Dvali
€
5 ×10−4 eV( )−1
≈ 0.4 mm D − 4 = 2
R = 20 keV( )−1
≈10−5 μ m D − 4 = 4
7 MeV( )−1
≈ 30 fm D − 4 = 6
Radius of compactified space
• Smallness of GN/GF related to largeness of RMD
• Gravity is weak because it is diluted in a large space (small overlap with branes)
• Need dynamical explanation for RMD>>1
14
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€
V (r) = −GN
m1m2
r1+ α exp −r λ( )[ ]
α
Gravitational interactions modified at small distances
€
FN (r) = GN
m1m2
r2 at r > R
At r < R, space is (3+)-dimensional (=D-4)
€
FN (r) = ˆ G N(4 +δ ) m1m2
r2+δ=
= GN Rδ m1m2
r2+δ
From SN emission and neutron-star heating:
MD>750 (35) TeV for =2(3)
15
Probability of producing a KK graviton
€
≈E 2
MPl2
€
σ pp → G(n ) jet( ) =α s
πGN =10−28 fb 1 event ⇒ run LHC for 1016 tU
Number of KK modes with mass less than E (use m=n/R)
€
∝ nD−4 ≈ ER( )D−4
≈E D−4 MPl
2
MDD−2
Inclusive cross section
€
σ pp → G(n ) jet( ) ≈α sE
D−4
π MDD−2
n
∑
graviton
gluon
It does not depend on VD (i.e. on the Planck mass)
Missing energy and jet with characteristic spectrum
Testing extra dimensions at high-energy colliders
16
17
Contact interactions from graviton exchange
€
L = ±4π
ΛT4
T
T =1
2Tμν T μν −
1
D − 2Tμ
μTνν ⎛
⎝ ⎜
⎞
⎠ ⎟
• Sensitive to UV physics
• d-wave contribution to scattering processes
• predictions for related processes
• Limits from Bhabha/di- at LEP and Drell-Yan/ di- at Tevatron: T > 1.2 - 1.4 TeV
• Loop effect, but dim-6 vs. dim-8
• only dim-6 generated by pure gravity
• > 15 - 17 TeV from LEP
€
L = ±4π
ΛΥ2
Υ
Υ =1
2f γ μγ 5 f
f = q,l
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
18
TRANSPLANCKIAN REGIME2
1
3
+⎟⎠
⎞⎜⎝
⎛=
c
GDP
h
1
1
3
1
1
2
3
2
81 ++
⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ +Γ
+=
π c
sGR D
S
Planck length quantum-gravity scale
€
classical limit h → 0( ) : RS >> λ P
transplanckian limit s >> MD( ) : RS >> λ P
Schwarzschild radius
classical gravity
same regime
G-emission is based on linearized gravity, valid at s << MD2
The transplanckian regime is described by classical physics (general relativity) independent test, crucial to verify
gravitational nature of new physics
19
b > RS
Non-perturbative, but calculable for b>>RS (weak gravitational field)
€
θ ≈∂b
∂L≈
bcδ
mvbδ +1 rel . ⏐ → ⏐ GD s
bδ +1θE =
4GD s
b
D-dim gravitational potential:
€
V (r) =GDmM
rδ +1D = 4 + δ
Quantum-mechanical scattering phase of wave with angular momentum mvb
€
b = −bc
b
⎛
⎝ ⎜
⎞
⎠ ⎟
δ
bc ≈GDmM
vh
⎛
⎝ ⎜
⎞
⎠ ⎟
1
δ
Gravitational scattering
θbvm
20
Diffractive pattern characterized by
€
bc ≈GDs
h
⎛
⎝ ⎜
⎞
⎠ ⎟
1
δ
Gravitational scattering in extra dimensions: two-jet signal at the LHC
21
b < RS At b<RS, no longer calculable
Strong indications for black-hole formation
Characteristic events with large multiplicity (<N> ~ MBH / <E> ~ (MBH / MD2)/(+1)) and typical energy <E> ~ TH
BH with angular momentum, gauge quantum numbers, hairs (multiple moments of the asymmetric distribution of gauge charges and energy-momentum)
σ ~ πRS2 10 pb (for MBH=6 TeV and MD=1.5 TeV)
Gravitational and gauge radiation during collapse spinning Kerr BH
Hawking radiation until Planck phase is reached TH ~ RS
-1 ~ MD (MD / MBH)1/1)
Evaporation with ~ MBH(+3)/(+1) / MD
2(+2)/(+1) (10-26 s for MD=1 TeV)
Transplanckian condition MBH >> MD ?
22
WARPED GRAVITY
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A classical mechanism to make quanta softer
For time-indep. metrics with g0=0 E |g00|1/2 conserved . (proper time d2 = g00 dt2)
€
Schwarzschild metric g00 =1−2GN M
r⇒
Eobs − Eem
Eem
= g00 −1= −GN M
rem
On non-trivial metrics, we see far-away objects as red-shifted
23
Randall Sundrum
Consider observer & emitter as 3-d spaces (branes) embedded in non-trivial 5-D space-time geometries
5th dim S1 / Z2: identify y y+2πR, y -y
y
0 πR
y
0 πR
-y
0 πR
Two 3-branes on boundaries & appropriate vacuum-energy terms
€
ds2 = e−2K |y|η μν dx μ dxν + dy 2
24
GRAVITATIONAL RED-SHIFT
€
ds2 = e−2K |y|η μν dx μ dxν + dy 2
Masses on two branes related by
€
mπR
m0
= e−πRK
Same result can be obtained by integrating SE over y
€
R ≈10 K−1 ⇒mπR
m0
≈MZ
MGUT
y=0 g00=1
y=πR g00=e-2πRK
25
PHYSICAL INTERPRETATION• Gravitational field configuration is non-trivial
• Gravity concentrated at y=0, while our world confined at y=πR
• Small overlap weakness of gravity
WARPED GRAVITY AT COLLIDERS• KK masses mn = Kxne-πRK [xn roots of J1(x)] not equally spaced
• Characteristic mass Ke-πRK ~ TeV
• KK couplings
• KK gravitons have large mass gap and are “strongly” coupled
• Clean signal at the LHC from G l+l- €
L = −T μν Gμν(0)
MPl
+Gμν
(n )
Λπn=1
∞
∑ ⎛
⎝ ⎜
⎞
⎠ ⎟ Λπ ≡ e−πRK MPl ≈ TeV
26
Spin 2
Spin 1
27
A SURPRISING TWISTAdS/CFT correspondence relates 5-d gravity with
negative cosmological constant to strongly-coupled 4-d conformal field theory
Theoretical developments in extra dimensions have much contributed to model building of 4-dim theories
of electroweak breaking: susy anomaly mediation, susy gaugino mediation, Little Higgs, Higgs-gauge
unification, composite Higgs, Higgsless, …
Warped gravity with SM fermions and
gauge bosons in bulk and Higgs on brane
Technicolor-like theory with slowly-running couplings in 4 dim
28
What screens the Higgs mass?
What screens the Higgs mass?
€
→ + a
no m2φ2
boson
Spont. broken global symm.
€
ψ → e iaγ 5ψ
no mψ ψ
fermion
Chiral symmetry
€
Aμ → Aμ + ∂μ a
no m2Aμ Aμ
vector
Gauge symmetry
mH
Dynamical EW breaking
Delayed unitarity violat.
Fundamental scale at TeV
• Very fertile field of research• Different proposals not mutually excluded
LITTLE HIGGS SUPERSYMMETRY HIGGS-GAUGE UNIF.
TECHNICOLOR HIGGSLESS EXTRA DIMENSIONS
Symmetry
Dynamics
29
Cancellation of Existence of
positron
charmtop
10-3 eV??CAVEAT EMPTOR
electron self-energyπ+-π0 mass differenceKL-KS
mass differencegauge anomaly
cosmological constant
€
Necessary tuning MZ
2
Λ2→
MZ2
MGUT2
≈10−28
Qu
ickTim
e™
and
aTIF
F (U
nco
mp
resse
d) d
eco
mp
resso
rare
nee
de
d to
see th
is pic
ture
.
n
It is a problem of naturalness, not of consistency!
30
HIGGS AS PSEUDOGOLDSTONE BOSON
€
Φ= + f
2e iθ / f Φ = f Φ → e iaΦ :
ρ → ρ
θ →θ + a
⎧ ⎨ ⎩
Non - linearly realized symmetry h → h + a forbids m2h2
Gauge, Yukawa and self-interaction are non-derivative couplings Violate global symmetry and introduce quadratic divergences
Top sector ●●
➤
➤
No fine-tuning
If the scale of New Physics is so low, why do LEP data work so well?
31A less ambitious programme: solving the little hierarchy
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strong dynamics
new physics
energy 1 TeV 10 TeV
Little Higgs Composite Higgs
Higgsless
LEP
€
H +τ aHWμνa Bμν 10 9.7
H +Dμ H2
5.6 4.6
iH +Dμ H L γ μ L 9.2 7.3
e γ μe l γ μl 6.1 4.5
e γ μγ 5eb γ μγ 5b 4.3 3.2
1
2q Lλ uλ u
+γ μq( )2 6.4 5.0
H +d R λ d λ uλ u+σ μν qLF μν 9.3 12.4
LEP1
LEP2
MFV
-- +
€
L = ±1
Λ2O
Bounds on [TeV]
32
Explain only little hierarchy
At SM new physics cancels one-loop power divergences
LITTLE HIGGS
LH
224
4
22
222
2
TeV10 loops Two
TeV loop One
≈≈≈⇒=
≈<⇒=
SMFSM
FH
FSMSMSM
FH
mGm
Gm
Gm
Gm
ππ
ππ
“Collective breaking”: many (approximate) global symmetries preserve massless Goldstone bosonℒ1ℒ
2
H2
222
44=
ππ Hm
ℒ1 ℒ2
33
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 Φ doublets such that V(Φ
ΦΦΦ) and
Φ spontaneously break SU2
Turning off gauge coupling to Φ
Local SU2(Φ2) × global SU2(Φ) both spont. broken
HG /
21 GGG ×⊃
21SM GG ×⊂
( )loops two
42
4
42 Λ≈
πδ
gmH
34
Realistic models are rather elaborate
Effectively, new particles at the scale f cancel (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 ?)
35
New states have naturally mass
New states cut-off quadratically divergent contributions to mH
Ex.: littlest Higgs model
Log term: analogous to effect of stop loops in supersymmetry
Severe bounds from LEP data
36
TESTING LITTLE HIGGS AT THE LHC
• Discover new states (T, W’, Z’, …)
• Verify cancellation of quadratic divergences
€
mT
f=
λ t2 + λT
2
2λT
f from heavy gauge-boson masses
mT from T pair-production
T : we cannot measure TThh vertex (only model-dependent tests possible)
37
MT from T production can be measured up to 2.5 TeV
f and gH from DY of new gauge
bosons
Production rate and BR into leptons in region favoured by LEP (gH>>gW)
➤
➤
Can be seen up to ZH mass of 3 TeV
38
Possible to test cancellation with 10% accuracy for mT < 2.5 TeV and mZ < 3 TeV
Cleanest peak from
In order to precisely extract T from measured cross section, we must control b-quark partonic density
€
Γ T → bW( ) = 2Γ T → tZ( ) = 2Γ T → th( )∝ λT2
Measure T width?
39
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 KK
Correct Higgs quantum numbers by projecting out unwanted states with orbifold
The difficulty is to generate Yukawa and quartic couplings without reintroducing quadratic divergences
NEW INGREDIENTS FROM EXTRA DIMENSIONS
40
HIGGSLESS MODELS
Breakdown of unitarity:
€
4 d ⇒ Λ ≈4π mW
g≈ TeV
5d ⇒ Λ ≈24π 3
g52
≈12π 2 mW
g2≈10 TeV
no zero modes in restricted extra-D spaces (Scherk-Schwarz mechanism)
New ways of breaking gauge symmetries:
The gauge KK modes delay unitarity violation
41
y
RScherk-Schwarz breaking
A field under a 2πR translation has to remain the same, unless there is a symmetry (the field has to be equal up
to a symmetry transformation)
€
Φ x, y + 2πR( ) = e iQ Φ x, y( )
KK expansion with orbifold boundary condition
Φ x, y( ) = eiQy
2πR einy
R
n=−∞
+∞
∑ Φ(n )(x) ⇒ mn2 = n +
Q
2π
⎛
⎝ ⎜
⎞
⎠ ⎟2
1
R2
No more zero-modes!
42
At the LHC discover KK resonances of gauge bosons and test sum rules on couplings and masses required
to improve unitarity
43
DUALITY
AdS/CFT Composite Higgs
5-D warped gravity
large-N technicolor
SM in warped extra dims strongly-int’ing 4-d theory
KK excitations “hadrons” of new strong force
Technicolor strikes back?TeV brane Planck
brane
5th dim
IR UV
RG flow
5-D gravity 4-D gauge theory
Motion in 5th dim RG flow
UV brane Planck cutoff
IR brane breaking of conformal inv.
Bulk local symmetries global symmetries
44
TC
Technicolor-like theories in new disguise
Old problems
The presence of a light Higgs helps
• Light Higgs screens IR contributions to S and T
• (f pseudo-Goldstone decay constant) Can be tuned small for strong dynamics 4πf at few TeV
€
S =N
6π
v 2
f 2
45
Structure of the theory
m mass of resonances g coupling of resonances
Communicate via gauge (ga) and (proto)-Yukawa (i)
quarks, leptons &
gauge bosons
strong sector
Strong sector characterized by
In the limit I, ga =0, strong sector contains Higgs as Goldstone bosons
Ex. H = SU(3)/SU(2)U(1) or H = SO(5)/SO(4)
σ-model with f = m / g
Take I, ga << g < 4π
46
ga , i break global symmetry Higgs mass
New theory addresses hierarchy problem reduced sensitivity of mH to short distances (below m
-1)
€
mH2 ≈
α
4πmρ
2
Ex.:
• Georgi-Kaplan: g=4π, f = v, no separation of scales
• Holographic Higgs: g= gKK, m= mKK
• Little Higgs: g, m couplings and masses of new t’, W’, Z’
47
Production of resonances at m allows to test models at the LHC
Study of Higgs properties allows a model independent test of the nature of the EW breaking sector
Is the Higgs
fundamental?
SM (with mH < 180 GeV)
supersymmetry
composite?
Holographic Higgs
Gauge-Higgs unification
Little Higgs
48
Construct the Lagrangian of the effective theory below m
€
U = e iπ aT a
Goldstones; Φ heavy fields
LSILH =mρ
4
gρ2
L(0) U,Φ,∂
mρ
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟+
gρ2
16π 2L(1) U,Φ,
∂
mρ
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟+
gρ4
16π 2( )
2 L(2) U,Φ,∂
mρ
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟+ ...
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
From the kinetic term, we obtain the definition of f = m / g
Each extra H insertion gives operators suppressed by 1 / f
• Each extra derivative “ “ 1 / m
€
g2
mW2 − q2
=4
v 21+
q2
mW2
+ ... ⎛
⎝ ⎜
⎞
⎠ ⎟
f: symmetry-breaking scale m: new-physics mass threshold
• Operators that violate Goldstone symmetry are suppressed by corresponding (weak) coupling
49
Operators testing the strong self coupling of the Higgs (determined by the structure of the σ model)
€
cH
2 f 2∂ μ H +H( )∂μ H +H( ) −
c6λ
f 2H +H( )
3+
cy y f
f 2H +Hf LHfR + h.c.
⎛
⎝ ⎜
⎞
⎠ ⎟
and yf are SM couplings; ci model-dependent coefficients
Form factors sensitive to the scale m
€
icW g
2mρ2
H +σ it D μ H( )D
ν Wμνi +
icB ′ g
2mρ2
H +t D μ H( )∂
ν Bμν
cγ ′ g 2g2
16π 2mρ2
H +HBμν Bμν +cggS
2y t2
16π 2mρ2
H +HGμνa Gaμν
€
ic HW g
16π 2 f 2Dμ H( )
+σ i Dν H( )Wμν
i +ic HB ′ g
16π 2 f 2Dμ H( )
+Dν H( )Bμν
Loop-suppressed strong dynamics
€
1
f 2
€
1
mρ2
€
gρ2
16π 2
1
mρ2
50€
cH → L =1
21+ cH
v 2
f 2 1+h
v
⎛
⎝ ⎜
⎞
⎠ ⎟2 ⎡
⎣ ⎢
⎤
⎦ ⎥∂ μ h∂μ h All Higgs couplings
rescaled by
€
1
1+ cH
v 2
f 2
≈1−cH
2
v 2
f 2
€
cy → L = −mψ
v1− cy
v 2
f 2
⎛
⎝ ⎜
⎞
⎠ ⎟ψ ψ h Modified Higgs couplings to matter
€
v 2
f 2=
1
4
Effects in Higgs production and decay
51
Dührssen 2003
SLHC Report 2002
52
LHC can measure cHv2/f2 and cyv2/f2 up to 20-40%
SLHC can improve it to about 10%
A sizeable deviation from SM in the absence of new light states would be indirect evidence for the composite nature of the Higgs
ILC can test v2/f2 up to the % level
ECFA/DESY LC Report 2001
ILC can explore the Higgs compositeness scale 4πf up to 30 TeV
53
• Effective-theory approach is half-way between model-dependent and operator analyses
• Dominant effects come from strong self-Higgs interactions characterized by
• From operator analyses, Higgs processes loop-suppressed in SM are often considered most important for searches
• However, operators h and hgg are suppressed 1/(16π2m
2)
• Since h is charge and color neutral, gauging SU(3)cU(1)Q does not break the generator under which h shifts (Covariant derivative acting on h does not contain or g)
• Not the case for hZ (loop, but not 1/g suppressed)
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gρ
mρ
=1
f
54
Higgs decay rates
55
Genuine signal of Higgs compositeness at high energies
In spite of light Higgs, longitudinal gauge-boson scattering amplitude violate unitarity at high energies
hWL
WL
WL
WLModified coupling
LHC with 200 fb-1 sensitive up to cH 0.3
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Higgs is viewed as pseudoGoldstone boson: its properties are related to those of the exact
(eaten) Goldstones: O(4) symmetry
Can bbbb at high invariant mass be separated from background? h WW leptons is more promising
Sum rule (with cuts and s<M2)
Strong gauge-boson scattering strong Higgs production
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In many realizations, the top quark belongs to the strongly-coupled sector
At leading order in 1/f2
Modified top-quark couplings to h and Z
At ILC ghtt up to 5% with s=800 GeV and L=1000 fb-1
From gZtt, cR ~ 0.04 with s=500 GeV and L=300 fb-1
FCNC effects