New physics, Observables, and Quantum Field Theory Axel Maas 13th of March 2015 Institute of High Energy Physics Vienna Austria
Overview ●
●
Setting the scene Why to wonder about seeing the W/Z and the Higgs
●
Resolving the paradox
●
Confirming the resolution
●
Implications for new Physics
●
Summary
Short version: 1502.02421
Main messages
Main messages ●
For theory ●
●
●
That perturbation theory works in the standard model is not trivial That it works can be explained using field theory It does not need to work beyond-thestandard model
Main messages ●
For theory ●
●
●
●
That perturbation theory works in the standard model is not trivial That it works can be explained using field theory It does not need to work beyond-thestandard model
For experiment ●
●
Predictions for new physics signatures may be too optimistic Theories can be better constrained/falsified
What is non-perturbative? ●
Standard statement: When couplings are small/weak enough everything is perturbative
What is non-perturbative? ●
●
Standard statement: When couplings are small/weak enough everything is perturbative Strong interactions are non-perturbative ●
Like QCD
What is non-perturbative? ●
●
Standard statement: When couplings are small/weak enough everything is perturbative Strong interactions are non-perturbative ●
●
Like QCD
But not entirely true: Weak interactions can be non-perturbative ●
●
QED is weakly interacting, but has nonperturbative features like atoms, molecules, matter with phase structure,... Bound states, phase transitions,...
What is non-perturbative? ●
●
Standard statement: When couplings are small/weak enough everything is perturbative Strong interactions are non-perturbative ●
●
But not entirely true: Weak interactions can be non-perturbative ●
●
●
Like QCD
QED is weakly interacting, but has nonperturbative features like atoms, molecules, matter with phase structure,... Bound states, phase transitions,...
Are there (relevant) non-perturbative effects at the electroweak scale?
Setting the scene
Standard model
●
Particles can be grouped according to the forces
Standard model
●
Electromagnetic sector u
c
t
d
s
b
e
Particles can be grouped according to the forces ●
Electromagnetic sector (QED)
Standard model
●
Strong sector
Electromagnetic sector g
u
c
t
d
s
b
e
Particles can be grouped according to the forces ●
Electromagnetic sector (QED)
●
Strong sector (QCD)
Standard model
●
Strong sector
Electromagnetic sector g
u
c
t
d
s
b
e
W
e
Z
Weak sector
Particles can be grouped according to the forces ●
Electromagnetic sector (QED)
●
Strong sector (QCD)
●
Weak sector
Standard model
●
Strong sector
Electromagnetic sector g
u
c
t
d
s
b
W
Z
Higgs sector h
e
e
Weak sector
Particles can be grouped according to the forces ●
Electromagnetic sector (QED)
●
Strong sector (QCD)
●
Weak sector
●
Higgs sector
Standard model
●
Strong sector
Electromagnetic sector g
u
c
t
d
s
b
W
Z
Higgs sector h
e
e
Weak sector
Particles can be grouped according to the forces ●
Electromagnetic sector (QED)
●
Strong sector (QCD)
●
Weak sector
●
Higgs sector – actually 13 different interactions
The Brout-Englert-Higgs effect
●
The Higgs is assumed to create much of the mass
The Brout-Englert-Higgs effect 100% 80% 60%
Strong Higgs
40% 20% 0%
●
u
d
s
c
b
t
W
Z Leptons
The Higgs is assumed to create much of the mass
The Brout-Englert-Higgs effect 100%
h h
80%
h h h
60%
Strong Higgs
40% 20% 0%
u
d
s
c
b
t
W
Z Leptons
●
The Higgs is assumed to create much of the mass
●
Mechanism: “Higgs condenses”
The Brout-Englert-Higgs effect 100%
h h
80%
h t h
h
60% 40% 20% 0%
●
●
Strong Higgs
u
d
s
c
b
t
W
Z Leptons
The Higgs is assumed to create much of the mass Mechanism: “Higgs condenses and the particles are slowed (gain mass)”
The Brout-Englert-Higgs effect 100%
h h
80%
h t h
h
60% 40% 20% 0%
●
●
●
Strong Higgs
u
d
s
c
b
t
W
Z Leptons
The Higgs is assumed to create much of the mass Mechanism: “Higgs condenses and the particles are slowed (gain mass)” Higgs only particle which has a static mass
The elusiveness of the Higgs
The elusiveness of the Higgs
●
Higgs couples to a particle proportional to its mass
The elusiveness of the Higgs
●
[ATLAS & CMS, '11+'12 data]
Higgs couples to a particle proportional to its mass
The elusiveness of the Higgs
[ATLAS & CMS, '11+'12 data]
h h
●
Higgs couples to a particle proportional to its mass
●
Required almost 2 years of data taking ●
But twice as many data by the end of this year
●
10 times more until 2020 (perhaps 100 times by 2025...)
Questions to the standard model ●
Why does the Higgs has the mass it has? ●
Could have any mass
Questions to the standard model ●
Why does the Higgs has the mass it has? ●
●
Could have any mass
Why does it interact the way it does? ●
Why are the masses of the matter particles so different?
Questions to the standard model ●
Why does the Higgs has the mass it has? ●
●
Why does it interact the way it does? ●
●
Could have any mass Why are the masses of the matter particles so different?
Why is there the Brout-Englert-Higgs effect? ●
No intrinsic reason
Questions to the standard model ●
Why does the Higgs has the mass it has? ●
●
Why does it interact the way it does? ●
●
No intrinsic reason
Why have electrons the same charge as protons? ●
●
Why are the masses of the matter particles so different?
Why is there the Brout-Englert-Higgs effect? ●
●
Could have any mass
...
Could have any rational ratio
The Higgs – a touchstone ●
Why do we observe the Higgs at all? ●
From a theoretical point of view, this is not obvious
Why to wonder
Coordinates
●
Space-time
Coordinates
●
Space-time is a set of points
Coordinates
●
Space-time is a set of points ●
Coordinate systems are used to describe them
Coordinates
●
Space-time is a set of points ●
●
Coordinate systems are used to describe them
Coordinates must not be the usual cartesian ones ●
E.g. spherical coordinates
Coordinate transformations
●
Coordinates systems are made by humans ●
Points do not care about them
Coordinate transformations
= ●
Coordinates systems are made by humans ●
Points do not care about them
●
Physics must be independent of coordinates
●
Or: Physics is the same in any coordinate system
Coordinate transformations
= ●
Coordinates systems are made by humans ●
Points do not care about them
●
Physics must be independent of coordinates
●
Or: Physics is the same in any coordinate system
●
There is a transformation between them ●
Coordinate transformation
Redundant coordinates
●
Coordinates are not always independent ●
●
Some coordinates may be redundant
Something moving in the plane, but described also by height
Redundant coordinates
●
Coordinates are not always independent ●
●
Some coordinates may be redundant
Something moving in the plane, but described also by height
Redundant coordinates
●
Coordinates are not always independent ●
●
●
Some coordinates may be redundant
Something moving in the plane, but described also by height One can eliminate the additional coordinates ●
Can be technically helpful
Redundant coordinates
●
Coordinates are not always independent ●
●
●
Something moving in the plane, but described also by height One can eliminate the additional coordinates ●
●
Some coordinates may be redundant
Can be technically helpful
But this is not necessary
External space-time
Space ●
Particle physics takes place in space-time
Time
External space-time
Time
Space ●
●
Particle physics takes place in space-time Space-time is then just the arena where particle physics happens
External space-time
Time
Space ●
●
Particle physics takes place in space-time Space-time is then just the arena where particle physics happens
External space-time
Time
Space ●
●
Particle physics takes place in space-time Space-time is then just the arena where particle physics happens
External space-time
Time
Space ●
●
●
Particle physics takes place in space-time Space-time is then just the arena where particle physics happens Space-time is therefore called the external space
Internal space
●
Space-time
Particles have more properties than just position and speed
Internal space
Space-time e Spin
●
●
Particles have more properties than just position and speed Example: Spin (internal angular momentum) ●
Electrons have spin ½
●
This spin has a direction
●
That is an additional information
●
This requires one more coordinate
Internal space
Space-time e Spin
●
●
●
Particles have more properties than just position and speed Example: Spin (internal angular momentum) ●
Electrons have spin ½
●
This spin has a direction
●
That is an additional information
●
This requires one more coordinate
It is thus internal: It belongs to the electron, not to space-time
Internal space
●
There are much more possibilities
Internal space p ●
There are much more possibilities ●
E.g.: Proton and neutron
n
Internal space p ●
N
n
There are much more possibilities ●
E.g.: Proton and neutron
●
The Strong nuclear force cannot distinguish them
●
Behaves like a single particle: Nucleon
Internal space
-
+
p ●
N
Isospin
n
There are much more possibilities ●
E.g.: Proton and neutron
●
The Strong nuclear force cannot distinguish them
●
Behaves like a single particle: Nucleon
●
Can be described by an internal space: Isospin
●
Isospin + is a proton, Isospin – is a neutron
Internal space
-
+
p ●
N
Isospin
n
There are much more possibilities ●
E.g.: Proton and neutron
●
The Strong nuclear force cannot distinguish them
●
Behaves like a single particle: Nucleon
●
Can be described by an internal space: Isospin
●
Isospin + is a proton, Isospin – is a neutron
●
Other forces can distinguish
Internal space
-
+
p ●
●
N
Isospin
n
There are much more possibilities ●
E.g.: Proton and neutron
●
The Strong nuclear force cannot distinguish them
●
Behaves like a single particle: Nucleon
●
Can be described by an internal space: Isospin
●
Isospin + is a proton, Isospin – is a neutron
●
Other forces can distinguish
To be proton or neutron is an internal (discrete) coordinate
Internal space
-
+
p
●
N
Isospin
n
Where is then the difference, if one neglects everything but the strong nuclear force?
Internal space
-
+
p
●
●
N
Isospin
n
Where is then the difference, if one neglects everything but the strong nuclear force? None
Internal space
-
+
p
●
●
●
N
Isospin
n
Where is then the difference, if one neglects everything but the strong nuclear force? None The system does not care whether the thing is a proton or neutron
Internal space
-
+
p
●
●
●
N
Isospin
n
Where is then the difference, if one neglects everything but the strong nuclear force? None The system does not care whether the thing is a proton or neutron
●
Can be changed, and the physics remains unchanged
●
What is called proton or neutron does not matter
●
Just a coordinate system
Internal space
-
+
p
●
●
●
N
Isospin
n
Where is then the difference, if one neglects everything but the strong nuclear force? None The system does not care whether the thing is a proton or neutron
●
Can be changed, and the physics remains unchanged
●
What is called proton or neutron does not matter
●
Just a coordinate system
●
Physics must be independent of this
Classical electrodynamics ●
Triumph of classical physics in the 19th century
Classical electrodynamics ●
Triumph of classical physics in the 19th century
●
Formulated as the Maxwell equations ●
Vacuum:
∇ E=0 ∇×B=∂t E
∇ B=0 ∇×E=−∂t B
Classical electrodynamics ●
Triumph of classical physics in the 19th century
●
Formulated as the Maxwell equations ●
●
Vacuum:
∇ E=0 ∇×B=∂t E
∇ B=0 ∇×E=−∂t B
Rewriting with the vector potential (ϕ , A)
B=∇ × A
E=−∇ ϕ−∂ t A
Classical electrodynamics ●
Triumph of classical physics in the 19th century
●
Formulated as the Maxwell equations ●
●
Vacuum:
∇ E=0 ∇×B=∂t E
Rewriting with the vector potential (ϕ , A)
B=∇ × A ●
∇ B=0 ∇×E=−∂t B
E=−∇ ϕ−∂ t A
Invariant under so-called gauge transformations
A→ A+∇ Λ
ϕ→ϕ−∂t Λ
Λ arbitrary
Classical electrodynamics ●
Triumph of classical physics in the 19th century
●
Formulated as the Maxwell equations ●
●
Vacuum:
∇ E=0 ∇×B=∂t E
Rewriting with the vector potential (ϕ , A)
B=∇ × A ●
E=−∇ ϕ−∂ t A
Invariant under so-called gauge transformations
A→ A+∇ Λ ●
∇ B=0 ∇×E=−∂t B
ϕ→ϕ−∂t Λ
Λ arbitrary
Extreme case of coordinate transformations ●
Some part of the vector potential is redundant
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a μν L=− W μ ν W a 4 a a a W μ ν=∂μ W ν−∂ ν W μ
●
Ws
W
a μ
W
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a μν L=− W μ ν W a 4 a a a a b c W μ ν=∂μ W ν−∂ ν W μ + gf bc W μ W ν
●
Ws
●
Coupling g and some numbers f abc
W
a μ
W
W
W
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a μν L=− W μ ν W a 4 a a a a b c W μ ν=∂μ W ν−∂ ν W μ + gf bc W μ W ν
●
Ws
W
W
a μ
●
No QED: Ws and Zs are degenerate
●
Coupling g and some numbers f abc
h h
W
W
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a μν ij j + μ L=− W μ ν W a + ( Dμ h ) D ik h k 4 a a a a b c W μ ν =∂μ W ν−∂ ν W μ + gf bc W μ W ν D ijμ =δij ∂μ
●
●
Ws
W Higgs hi
a μ
●
No QED: Ws and Zs are degenerate
●
Coupling g and some numbers f abc
W h
W
W
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a μν ij j + μ L=− W μ ν W a + ( Dμ h ) D ik h k 4 a a a a b c W μ ν =∂μ W ν−∂ ν W μ + gf bc W μ W ν Dμij =δij ∂μ −igW μa t ija
●
●
Ws
W Higgs hi
a μ
●
No QED: Ws and Zs are degenerate
●
Coupling g and some numbers f abc and taij
W h
W
W
h W
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a μν ij j + μ a + 2 2 L=− W μ ν W a +( Dμ h ) D ik hk +λ (h ha −v ) 4 a a a a b c W μ ν =∂μ W ν −∂ ν W μ + gf bc W μ W ν W W W ij ij a ij D μ =δ ∂μ −igW μ t a
●
●
Ws
W Higgs hi
a μ
h
h W h h
●
No QED: Ws and Zs are degenerate
●
Couplings g, v, λ and some numbers f abc and taij
The Higgs sector as a gauge theory ●
The Higgs sector is a gauge theory
1 a ij j a 2 2 L=− W W a D h D ik h k h h a −v 4 a a a a b c W =∂ W −∂ W gf bc W W W W W ij ij a ij D = ∂ −igW t a
●
●
Ws
W Higgs hi
a μ
h
h W h h
●
No QED: Ws and Zs are degenerate
●
Couplings g, v, λ and some numbers f abc and taij
●
If not stated differently: Tree-level masses as in SM
Symmetries 1 a μν ij j + μ a + 2 2 L=− W μ ν W a + ( Dμ h ) D ik h k + λ(h ha −v ) 4 a a a a b c W μ ν =∂μ W ν −∂ ν W μ + gf bc W μ W ν Dμij =δij ∂μ −igW μa t ija
Symmetries 1 a μν ij j + μ a + 2 2 L=− W μ ν W a + ( Dμ h ) D ik h k + λ(h ha −v ) 4 a a a a b c W μ ν =∂μ W ν −∂ ν W μ + gf bc W μ W ν Dμij =δij ∂μ −igW μa t ija ●
Local SU(2) gauge symmetry ●
a
Invariant under arbitrary gauge transformations x a
a
a b
a bc
c
W W ∂ −g f W
b
ij a
a
hi hi g t h j
Symmetries 1 a μν ij j + μ a + 2 2 L=− W μ ν W a + ( Dμ h ) D ik h k + λ(h ha −v ) 4 a a a a b c W μ ν =∂μ W ν −∂ ν W μ + gf bc W μ W ν Dμij =δij ∂μ −igW μa t ija ●
Local SU(2) gauge symmetry ●
a
Invariant under arbitrary gauge transformations x a
a
a b
a bc
c
W W ∂ −g f W ●
b
ij a
a
hi hi g t h j
Global SU(2) Higgs custodial (flavor) symmetry ●
Acts as right-transformation on the Higgs field only a μ
W →W
a μ
ij
ij
∗
hi → hi + a h j + b h j
The trouble with the Higgs ●
Weak interactions are an extreme case of redundancy ●
Strong interactions also; same story, different details
The trouble with the Higgs ●
Weak interactions are an extreme case of redundancy ●
●
Strong interactions also; same story, different details
Elementary particles are auxiliary objects ● ●
Depend on a coordinate system in internal space Properties can change under coordinate transformation
The trouble with the Higgs ●
Weak interactions are an extreme case of redundancy ●
●
Elementary particles are auxiliary objects ● ●
●
Strong interactions also; same story, different details Depend on a coordinate system in internal space Properties can change under coordinate transformation
Getting a coordinate-independent object requires at least a combination (bound-state) of two h
h
Resolving the paradox
The trouble with the Higgs ●
But what is then this?
The trouble with the Higgs ●
But what is then this?
●
Field theory
The trouble with the Higgs ●
But what is then this?
●
Field theory: h
h
The trouble with the Higgs ●
But what is then this?
●
Field theory: h
h
[Fröhlich et al. PLB 80]
⟨(h
+
h)( x)(h
+
h)( y)⟩
The trouble with the Higgs ●
But what is then this?
●
Field theory: h h
h
≈
h
+
h h
h
h
+ something small
h
[Fröhlich et al. PLB 80]
⟨(h
+
h)( x)(h
+
h=v+η + 3 h)( y)⟩ ≈ const .+⟨η (x) η( y)⟩+O (η )
The trouble with the Higgs ●
But what is then this?
●
Field theory: h h
●
h
≈
h
+
h h
h
h
+ something small
h
Touchstone ●
Compare theory and experiment
●
Will require much more data
⟨(h
+
h)( x)(h
+
[Fröhlich et al. PLB 80]
h=v+η + 3 h)( y)⟩ ≈ const .+⟨η (x) η( y)⟩+O (η )
Confirming the resolution
Confirming the resolution Requires a (non-perturbative) suitable method
Confirming the resolution Requires a (non-perturbative) suitable method: Lattice gauge theory
Lattice calculations ●
Take a finite volume – usually a hypercube
L
Lattice calculations ●
●
Take a finite volume – usually a hypercube Discretize it, and get a finite, hypercubic lattice
a L
Lattice calculations ●
●
●
Take a finite volume – usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral ●
Can be done numerically
●
Uses Monte-Carlo methods
a L
Lattice calculations ●
●
●
●
Take a finite volume – usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral ●
Can be done numerically
●
Uses Monte-Carlo methods
Artifacts ●
Finite volume/discretization a L
Lattice calculations ●
●
●
●
Take a finite volume – usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral ●
Can be done numerically
●
Uses Monte-Carlo methods
Artifacts ●
Finite volume/discretization
●
Masses vs. wave-lengths
a L
Lattice calculations ●
●
●
●
Take a finite volume – usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral ●
Can be done numerically
●
Uses Monte-Carlo methods
Artifacts ●
Finite volume/discretization
●
Masses vs. wave-lengths
a L
Lattice calculations ●
●
●
●
Take a finite volume – usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral ●
Can be done numerically
●
Uses Monte-Carlo methods
Artifacts ●
Finite volume/discretization
●
Masses vs. wave-lengths
●
Euclidean formulation
a L
Masses from Euclidean propagators
Masses from Euclidean propagators
D( p)=〈O
●
+
( p)O(− p)〉
Masses can be inferred from propagators
Masses from Euclidean propagators
D( p)=〈O
●
+
1 ( p)O(− p)〉∼ 2 2 p +m
Masses can be inferred from propagators
Masses from Euclidean propagators
1 D( p)=〈O ( p)O(−p)〉∼ 2 2 p +m + C (t )=〈O ( x)O( y )〉∼exp(−m Δ t ) +
●
Masses can be inferred from propagators
Masses from Euclidean propagators
D( p)=〈O
+
( p)O(− p)〉∼∑
ai 2
2 i
p +m + C (t )=〈O (x)O( y )〉∼∑ ai exp(−mi Δ t) ∑ ai=1∧m0< m1< ... ●
Masses can be inferred from propagators
●
Long-time behavior relevant ●
No exact results on time-like momenta
Masses from Euclidean propagators
●
Masses can be inferred from propagators
●
Long-time behavior relevant ●
No exact results on time-like momenta
Masses from Euclidean propagators
●
Masses can be inferred from propagators
●
Long-time behavior relevant ●
No exact results on time-like momenta
Masses from Euclidean propagators
●
Masses can be inferred from propagators
●
Long-time behavior relevant ●
No exact results on time-like momenta
Higgsonium
h
●
+
h
Simpelst 0 bound state h + ( x)h( x)
Higgsonium
h
●
h
+
Simpelst 0 bound state h + ( x)h( x) ●
Same quantum numbers as the Higgs ●
No weak or flavor charge
Higgsonium
[Maas et al. '13]
h
●
h
+
Simpelst 0 bound state h + ( x)h( x) ●
Same quantum numbers as the Higgs ●
No weak or flavor charge
Higgsonium
[Maas et al. '13]
Influence of heavier states
h
h
Finite-volume effects
●
Finite-volume effects
+
Simpelst 0 bound state h + ( x)h( x) ●
Same quantum numbers as the Higgs ●
No weak or flavor charge
Higgsonium
[Maas et al. '13]
h
h
Finite-volume effects
●
+
Simpelst 0 bound state h + ( x)h( x) ●
Same quantum numbers as the Higgs ●
●
No weak or flavor charge
Mass is about 120 GeV
Higgsonium
[Maas et al. '13]
h
h
Finite-volume effects
●
Finite-volume effects
+
Simpelst 0 bound state h + ( x)h( x) ●
Same quantum numbers as the Higgs ●
●
No weak or flavor charge
Mass is about 120 GeV
Higgsonium
[Maas et al. '13]
Influence of heavier states
h
h
Finite-volume effects
●
Finite-volume effects
+
Simpelst 0 bound state h + ( x)h( x) ●
Same quantum numbers as the Higgs ●
●
No weak or flavor charge
Mass is about 120 GeV
Mass relation - Higgs ●
[Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13]
Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV ●
Scheme exists to shift Higgs mass always to 120 GeV
Mass relation - Higgs ●
Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV ●
●
[Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13]
Scheme exists to shift Higgs mass always to 120 GeV
Demonstrates the relation ●
Duality between elementary states and bound states [Fröhlich et al. PLB 80]
⟨(h
+
h)( x)(h
+
h=v+η + 3 h)( y)⟩ ≈ const .+⟨η (x) η( y)⟩+O (η )
●
Same poles to leading order
●
Fröhlich-Morchio-Strocchi (FMS) mechanism
Mass relation - Higgs ●
Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV ●
●
Scheme exists to shift Higgs mass always to 120 GeV
Demonstrates the relation ●
Duality between elementary states and bound states [Fröhlich et al. PLB 80]
⟨(h
●
[Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13]
+
h)( x)(h
+
h=v+η + 3 h)( y)⟩ ≈ const .+⟨η (x) η( y)⟩+O (η )
●
Same poles to leading order
●
Fröhlich-Morchio-Strocchi (FMS) mechanism
Deeply-bound relativistic state ●
Mass defect~constituent mass
●
Cannot describe with quantum mechanics
●
Very different from QCD bound states
Isovector-vector state
W
●
h h
Vector state 1- with operator
+
h a h tr t Dμ + √h h √h + h
●
Only in a Higgs phase close to a simple particle
●
Higgs-flavor triplet, instead of gauge triplet
Isovector-vector state
W
●
[Maas et al. '13]
h h
Vector state 1- with operator
+
h a h tr t Dμ + √h h √h + h
●
Only in a Higgs phase close to a simple particle
●
Higgs-flavor triplet, instead of gauge triplet
Isovector-vector state
W
●
[Maas et al. '13]
h h
Vector state 1- with operator
+
h a h tr t Dμ + √h h √h + h
●
Only in a Higgs phase close to a simple particle
●
Higgs-flavor triplet, instead of gauge triplet
●
Mass about 80 GeV
Mass relation - W ●
Vector state: 80 GeV
●
W at tree-level: 80 GeV ●
W not scale or scheme dependent
[Fröhlich et al. PLB 80 Maas'12]
Mass relation - W ●
Vector state: 80 GeV
●
W at tree-level: 80 GeV ●
●
W not scale or scheme dependent
Same mechanism 〈(h
+
Dμ h)( x)(h
+
Dμ h)( y)〉
[Fröhlich et al. PLB 80 Maas'12]
Mass relation - W
[Fröhlich et al. PLB 80 Maas'12]
●
Vector state: 80 GeV
●
W at tree-level: 80 GeV ●
●
W not scale or scheme dependent
Same mechanism +
+
〈(h D μ h)( x)(h Dμ h)( y)〉 h=v+ η 3 ≈ const.+ 〈W μ ( x)W μ ( y)〉+ O (η ) ∂ v=0
Mass relation - W
[Fröhlich et al. PLB 80 Maas'12]
●
Vector state: 80 GeV
●
W at tree-level: 80 GeV ●
●
W not scale or scheme dependent
Same mechanism +
●
+
〈(h D μ h)( x)(h Dμ h)( y)〉 h=v+ η 3 ≈ const.+ 〈W μ ( x)W μ ( y)〉+ O (η ) ∂ v=0 Same poles at leading order ●
At least for a light Higgs
Mass relation - W
[Fröhlich et al. PLB 80 Maas'12]
●
Vector state: 80 GeV
●
W at tree-level: 80 GeV ●
●
W not scale or scheme dependent
Same mechanism +
●
+
⟨(h Dμ h)( x)(h Dμ h)( y)⟩ h=v + η 3 ≈ const .+⟨W μ ( x)W μ ( y)⟩+O (η ) ∂ v=0 Same poles at leading order ●
At least for a light Higgs
●
Remains true beyond leading order
What about the rest?
What about the rest? ●
Quarks and gluons ●
Anyhow bound by confinement in bound states ●
Top subtle, but same principle
What about the rest? ●
Quarks and gluons ●
Anyhow bound by confinement in bound states ●
●
Top subtle, but same principle
Leptons ●
Actually Higgs-lepton bound-states ●
Enormous mass defects
●
Requires confirmation
●
Except for right-handed (Dirac) neutrino
What about the rest? ●
Quarks and gluons ●
Anyhow bound by confinement in bound states ●
●
Leptons ●
Actually Higgs-lepton bound-states ●
●
Top subtle, but same principle
Enormous mass defects
●
Requires confirmation
●
Except for right-handed (Dirac) neutrino
Photons ●
QED similar but simpler
How events looks like (LEP/ILC) e--H bound state
μ --H bound state
Z-H-H bound state e+-H bound state ●
Collision of bound states
μ+-H bound state
How events looks like (LEP/ILC) e--H bound state
μ --H bound state
Z-H-H bound state e+-H bound state ●
Collision of bound states
●
'Constituent' particles
μ+-H bound state
How events looks like (LEP/ILC) e--H bound state
μ --H bound state
Z-H-H bound state e+-H bound state ●
Collision of bound states
●
'Constituent' particles
●
Higgs partners just spectators ●
Similar to pp collisions
μ+-H bound state
How events looks like (LEP/ILC) e--H bound state
μ --H bound state
Z-H-H bound state e+-H bound state ●
Collision of bound states
●
'Constituent' particles
●
Higgs partners just spectators ●
●
Similar to pp collisions
Sub-leading contributions
μ+-H bound state
How events looks like (LEP/ILC) e--H bound state
μ --H bound state
Z-H-H bound state e+-H bound state ●
Collision of bound states
●
'Constituent' particles
●
Higgs partners just spectators ●
●
Similar to pp collisions
Sub-leading contributions ●
Ordinary ones: Large and detected
μ+-H bound state
How events looks like (LEP/ILC) e--H bound state
μ --H bound state
Z-H-H bound state
μ+-H bound state
e+-H bound state ●
Collision of bound states
●
'Constituent' particles
●
Higgs partners just spectators ●
●
Similar to pp collisions
Sub-leading contributions ●
Ordinary ones: Large and detected
●
New ones: Small, require more sensitivity
Implications
Ground states ●
For W and Higgs exist gauge-invariant composite/bound states of the same mass ●
Play the role of the experimental signatures
●
“True” physical states
●
Reason for the applicability of perturbation theory for electroweak physics
Ground states ●
For W and Higgs exist gauge-invariant composite/bound states of the same mass ●
Play the role of the experimental signatures
●
“True” physical states
●
●
Reason for the applicability of perturbation theory for electroweak physics
Is this always true? ●
Full standard model: Probably
●
Other parameters?
Phase diagram (Lattice-regularized) phase diagram
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
g(Classical gauge coupling)
Phase diagram (Lattice-regularized) phase diagram
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
Higgs “phase”
g(Classical gauge coupling)
Phase diagram (Lattice-regularized) phase diagram
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
Higgs “phase”
Confinement “phase” g(Classical gauge coupling)
Phase diagram (Lattice-regularized) phase diagram
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
Higgs “phase”
Confinement “phase” g(Classical gauge coupling)
Phase diagram (Lattice-regularized) phase diagram continuous
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
Crossover
Higgs “phase”
1st order
Confinement “phase” g(Classical gauge coupling)
Phase diagram (Lattice-regularized) phase diagram continuous ●
Separation only in fixed gauges
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
Crossover
Higgs “phase” Coulomb gauge
Landau gauge
1st order
Confinement “phase” g(Classical gauge coupling)
Phase diagram (Lattice-regularized) phase diagram continuous ●
●
●
Separation only in fixed gauges
f(Classical Higgs mass)
●
[Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07]
Crossover
Same asymptotic states in confinement and Higgs pseudo-phases
Higgs “phase”
1st order
Confinement “phase” g(Classical gauge coupling)
Same asymptotic states irrespective of coupling strengths
Typical spectra
●
[Maas, Mufti '13,'14, Evertz et al.'86, Langguth et al.'85,'86]
Generically different low-lying spectra
Typical spectra
●
[Maas, Mufti '13,'14, Evertz et al.'86, Langguth et al.'85,'86]
Generically different low-lying spectra ●
0+ lighter in QCD-like region
●
1- lighter in Higgs-like region
Typical spectra
[Maas, Mufti '13,'14, Evertz et al.'86, Langguth et al.'85,'86]
“Higgs”
●
●
Generically different low-lying spectra ●
0+ lighter in QCD-like region
●
1- lighter in Higgs-like region
Use as operational definition of phase
“QCD”
Phase diagram
“QCD”
[Maas, Mufti,'14]
“Higgs”
●
Complicated phase diagram
●
QCD-like behavior even for negative bare mass
●
Similar bare couplings for both physics types
Development in the Higgs channel [Maas, Mufti'14]
Unstable Physical
●
QCD-like
Three distinct regions
Development in the Higgs channel [Maas, Mufti'14]
● ●
Base-line Lowest state as expected above threshold: 2 almost non-interacting ”Ws”
Development in the Higgs channel [Maas, Mufti'14]
●
●
Next state within errors essentially trivial throughout No discernible resonances
Development in the Higgs channel [Maas, Mufti'14]
●
Next state within errors essentially trivial throughout
●
No discernible resonances
●
Also true for the next level
●
Different from perturbation theory
Implications for Higgsed theories [Maas,'15]
●
Higgsed theories appear a lot in BSM ●
GUTs, 2HDM, (some) SUSY models,...
Implications for Higgsed theories [Maas,'15]
●
Higgsed theories appear a lot in BSM ●
●
GUTs, 2HDM, (some) SUSY models,...
Structure observed here is not generic ●
●
Mass relation of elementary states and observable states only possible for light but not too light Higgs Global symmetries determines observable state spectrum ●
SM Higgs sector is special because custodial and gauge group are the same
Implications for Higgsed theories [Maas,'15]
●
Higgsed theories appear a lot in BSM ●
●
GUTs, 2HDM, (some) SUSY models,...
Structure observed here is not generic ●
●
Mass relation of elementary states and observable states only possible for light but not too light Higgs Global symmetries determines observable state spectrum ●
●
SM Higgs sector is special because custodial and gauge group are the same
Each case may be different
Implications for 2HDM [Maas,'15]
●
Simple example: Additional Higgs doublet a
Implications for 2HDM [Maas,'15]
●
●
Simple example: Additional Higgs doublet a Standard scenario: Both Higgs condense ● ●
SM condensate is a mixture All additional Higgs particles are states, but heavier than the SM Higgs
Implications for 2HDM [Maas,'15]
●
●
Simple example: Additional Higgs doublet a Standard scenario: Both Higgs condense ● ●
●
SM condensate is a mixture All additional Higgs particles are states, but heavier than the SM Higgs
Perturbatively, the state space has just four more (heavier) Higgs
Implications for 2HDM [Maas,'15]
●
●
Simple example: Additional Higgs doublet a Standard scenario: Both Higgs condense ● ●
●
●
SM condensate is a mixture All additional Higgs particles are states, but heavier than the SM Higgs
Perturbatively, the state space has just four more (heavier) Higgs Non-perturbative?
Implications for 2HDM [Maas,'15]
●
FMS states
Implications for 2HDM [Maas,'15]
●
FMS states: ●
Higgs 1:
⟨(h
+
h)(x)(h
+
+ h
3 h
h)( y )⟩ ≈ const .+⟨ η (x )ηh ( y )⟩+O(η )
Implications for 2HDM [Maas,'15]
●
FMS states: ●
Higgs 1:
⟨(h ●
+
h)(x)(h
+ h
3 h
+
3
+
h)( y )⟩ ≈ const .+⟨ η (x )ηh ( y )⟩+O(η )
+
a)( y )⟩ ≈ const .+⟨ ηa (x)ηa ( y)⟩+O(ηa )
Higgs 2:
⟨(a
+
a)(x)(a
Implications for 2HDM [Maas,'15]
●
FMS states: ●
Higgs 1:
⟨(h ●
h)(x)(h
+ h
3 h
+
3
+
h)( y )⟩ ≈ const .+⟨ η (x )ηh ( y )⟩+O(η )
+
a)( y )⟩ ≈ const .+⟨ ηa (x)ηa ( y)⟩+O(ηa )
Higgs 2:
⟨(a ●
+
+
a)(x)(a
W 1: ⟨(h + Dμ h)(x )(h + D μ h)( y)⟩ ≈ const .+⟨W μ ( x)W μ ( y)⟩+O(η3h )
Implications for 2HDM [Maas,'15]
●
FMS states: ●
Higgs 1:
⟨(h ●
h)(x)(h
+ h
3 h
+
3
+
h)( y )⟩ ≈ const .+⟨ η (x )ηh ( y )⟩+O(η )
+
a)( y )⟩ ≈ const .+⟨ ηa (x)ηa ( y)⟩+O(ηa )
Higgs 2:
⟨(a ●
+
+
a)(x)(a
W 1: ⟨(h + Dμ h)(x )(h + D μ h)( y)⟩ ≈ const .+⟨W μ ( x)W μ ( y)⟩+O(η3h )
●
W 2:
⟨(a + Dμ a)(x)(a + D μ a)( y )⟩ ≈ const .+⟨W μ ( x)W μ ( y )⟩+O(η3a )
Implications for 2HDM [Maas,'15]
●
FMS states: ●
Higgs 1:
⟨(h ●
h)(x)(h
+ h
3 h
+
3
+
h)( y )⟩ ≈ const .+⟨ η (x )ηh ( y )⟩+O(η )
+
a)( y )⟩ ≈ const .+⟨ ηa (x)ηa ( y)⟩+O(ηa )
Higgs 2:
⟨(a ●
+
+
a)(x)(a
W 1: ⟨(h + Dμ h)(x )(h + D μ h)( y)⟩ ≈ const .+⟨W μ ( x)W μ ( y)⟩+O(η3h )
●
W 2:
⟨(a + Dμ a)(x)(a + D μ a)( y )⟩ ≈ const .+⟨W μ ( x)W μ ( y )⟩+O(η3a ) ●
Twice as many W ●
Beyond expansion: Lattice is running
Implications for other BSM scenarios [Maas,'15]
●
Grand-unified theories ●
All gauge interactions from a single one at a high scale (>1015 GeV)
●
Broken by a second BEH effect
●
Explains relations of electric charges
●
Explains gauge coupling unification
●
Explains intrafamily relations ●
●
Anomaly-freeness of the standard model
Most prominent signature: Proton decay
Implications for other BSM scenarios [Maas,'15]
●
Grand-unified theories ●
All gauge interactions from a single one at a high scale (>1015 GeV)
●
Broken by a second BEH effect
●
Explains relations of electric charges
●
Explains gauge coupling unification
●
Explains intrafamily relations ●
Anomaly-freeness of the standard model
●
Most prominent signature: Proton decay
●
Impact: Structure restricted
Implications for other BSM scenarios [Maas,'15]
●
Technicolor ●
Higgs replaced by new fermions (techniquarks) and new gauge interaction (technicolor)
Implications for other BSM scenarios [Maas,'15]
●
Technicolor ●
●
Higgs replaced by new fermions (techniquarks) and new gauge interaction (technicolor) FMS mechanism cannot work
Implications for other BSM scenarios [Maas,'15]
●
Technicolor ●
● ●
Higgs replaced by new fermions (techniquarks) and new gauge interaction (technicolor) FMS mechanism cannot work Observable states must still be gaugeinvariant
Implications for other BSM scenarios [Maas,'15]
●
Technicolor ●
● ●
●
Higgs replaced by new fermions (techniquarks) and new gauge interaction (technicolor) FMS mechanism cannot work Observable states must still be gaugeinvariant Needs to create signals by bound states: W/Z and Higgs Has not been adressed so far ● Only effective theories ●
Summary ●
●
Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality ●
Highly relativistic bound states
Summary ●
●
Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality ●
●
●
Highly relativistic bound states
Permits physical interpretation of resonances in cross sections Generalizations to other BSM theories with Higgs effect possible ●
Required to understand observable spectrum
●
Differences to perturbative one possible
Summary ●
●
Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality ●
●
●
Highly relativistic bound states
Permits physical interpretation of resonances in cross sections Generalizations to other BSM theories with Higgs effect possible ●
Required to understand observable spectrum
●
Differences to perturbative one possible
●
New restrictions and opportunities for falsification
●
Could qualitatively alter experimental signatures
