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FYS3500 - spring 2020
Weak Interactions and Electroweak Unification*
Alex ReadUniversity Of OsloDepartment of Physics
*Martin and Shaw, Nuclear and Particle Physics, 3rd Ed., Chapter 6 (Last update 01.04.2020 16:39)
Part II Electroweak unification and the Higgs boson
2
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak interactions and gauge invariance
❖ Gauge invariance and spontaneous breaking of gauge invariance is at the heart of electroweak unification and the BEH mechanism.
3
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak interactions and gauge invariance
❖ Gauge invariance and spontaneous breaking of gauge invariance is at the heart of electroweak unification and the BEH mechanism.
❖ Gauge principle: Propose a gauge (phase) transformation of the wavefunction and add an interaction so that the gauge remains unobservable.
3
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance and EM❖ Example, fields in electromagnetism:
B = ∇ × A , E = − ∇ ϕ −1c
∂ A∂t
4
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance and EM❖ Example, fields in electromagnetism:
B = ∇ × A , E = − ∇ ϕ −1c
∂ A∂t
❖ Gauge transformation of potential and vector-potential : ϕ A
4
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance and EM❖ Example, fields in electromagnetism:
B = ∇ × A , E = − ∇ ϕ −1c
∂ A∂t
❖ Gauge transformation of potential and vector-potential : ϕ A
❖(ϕ, A ) → (ϕ, A )′ = (ϕ −
1c
∂α∂t
, A + ∇ α)
4
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance and EM❖ Example, fields in electromagnetism:
B = ∇ × A , E = − ∇ ϕ −1c
∂ A∂t
❖ Gauge transformation of potential and vector-potential : ϕ A
❖(ϕ, A ) → (ϕ, A )′ = (ϕ −
1c
∂α∂t
, A + ∇ α)❖ where is an arbitrary doubly-differentiable scalar
functionα(t, x )
4
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance
❖ B ′ = ∇ × A ′ = ∇ × ( A + ∇ α) = ∇ × A + ∇ × ∇ α
5
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance
❖ B ′ = ∇ × A ′ = ∇ × ( A + ∇ α) = ∇ × A + ∇ × ∇ α
❖ ∇ × ∇ α ≡ 0 ⟹ B ′ = ∇ × A = B
5
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance
❖ B ′ = ∇ × A ′ = ∇ × ( A + ∇ α) = ∇ × A + ∇ × ∇ α
❖ ∇ × ∇ α ≡ 0 ⟹ B ′ = ∇ × A = B
❖E ′ = − ∇ (ϕ −
1c
∂α∂t ) −
1c
∂∂t
( A + ∇ α) = − ∇ ϕ −1c
∂ A∂t
+1c ( ∇
∂α∂t
−∂∂t
∇ α)
5
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance
❖ B ′ = ∇ × A ′ = ∇ × ( A + ∇ α) = ∇ × A + ∇ × ∇ α
❖ ∇ × ∇ α ≡ 0 ⟹ B ′ = ∇ × A = B
❖E ′ = − ∇ (ϕ −
1c
∂α∂t ) −
1c
∂∂t
( A + ∇ α) = − ∇ ϕ −1c
∂ A∂t
+1c ( ∇
∂α∂t
−∂∂t
∇ α)❖
∇∂α∂t
−∂∂t
∇ α = 0 ⟹ E ′ = = − ∇ ϕ −1c
∂ A∂t
= E
5
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Gauge invariance
❖ B ′ = ∇ × A ′ = ∇ × ( A + ∇ α) = ∇ × A + ∇ × ∇ α
❖ ∇ × ∇ α ≡ 0 ⟹ B ′ = ∇ × A = B
❖E ′ = − ∇ (ϕ −
1c
∂α∂t ) −
1c
∂∂t
( A + ∇ α) = − ∇ ϕ −1c
∂ A∂t
+1c ( ∇
∂α∂t
−∂∂t
∇ α)❖
∇∂α∂t
−∂∂t
∇ α = 0 ⟹ E ′ = = − ∇ ϕ −1c
∂ A∂t
= E
❖ The electric and magnetic fields are unaffected by the gauge transformation: gauge invariance, or gauge symmetry∴
5
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Global gauge invariance❖ Consider the double-slit experiment: The intensity at the
screen is proportional to the phase difference from the slits to the screen.
6
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Global gauge invariance❖ Consider the double-slit experiment: The intensity at the
screen is proportional to the phase difference from the slits to the screen.
❖ ψ = ei( p ⋅ x −Et)
6
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Global gauge invariance❖ Consider the double-slit experiment: The intensity at the
screen is proportional to the phase difference from the slits to the screen.
❖ ψ = ei( p ⋅ x −Et)
❖ Introduce a global phase (gauge) transformation ψ′ = e−ieαψ
6
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Global gauge invariance❖ Consider the double-slit experiment: The intensity at the
screen is proportional to the phase difference from the slits to the screen.
❖ ψ = ei( p ⋅ x −Et)
❖ Introduce a global phase (gauge) transformation ψ′ = e−ieαψ
❖ Since the global phase doesn’t affect the outcome.
I ∝ ψ*′ ψ′ = ψ*ψ
6
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Local gauge invariance❖ Now try , i.e. a local phase (gauge) transformationα = α( x )
7
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Local gauge invariance❖ Now try , i.e. a local phase (gauge) transformationα = α( x )
❖ Now the phase difference would also depend on , affecting the intensity pattern, but there is no experimental support for this.
α
7
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Local gauge invariance❖ Now try , i.e. a local phase (gauge) transformationα = α( x )
❖ Now the phase difference would also depend on , affecting the intensity pattern, but there is no experimental support for this.
α
❖ ∇ (phase′ ) = ∇ (i( p ⋅ x − Et) − ieα( x )) = i p − ie ∇ α( x )
7
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Local gauge invariance❖ Now try , i.e. a local phase (gauge) transformationα = α( x )
❖ Now the phase difference would also depend on , affecting the intensity pattern, but there is no experimental support for this.
α
❖ ∇ (phase′ ) = ∇ (i( p ⋅ x − Et) − ieα( x )) = i p − ie ∇ α( x )
❖ Have to introduce something in addition to restore gauge invariance: Let p → p + e A , and make use of A → A + ∇ α( x )
7
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Local gauge invariance❖ Now try , i.e. a local phase (gauge) transformationα = α( x )
❖ Now the phase difference would also depend on , affecting the intensity pattern, but there is no experimental support for this.
α
❖ ∇ (phase′ ) = ∇ (i( p ⋅ x − Et) − ieα( x )) = i p − ie ∇ α( x )
❖ Have to introduce something in addition to restore gauge invariance: Let p → p + e A , and make use of A → A + ∇ α( x )
❖ ∇ (phase′ ) = i p + ie A − ieα( x ) = i p = ∇ (phase)
7
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Local gauge invariance❖ Now try , i.e. a local phase (gauge) transformationα = α( x )
❖ Now the phase difference would also depend on , affecting the intensity pattern, but there is no experimental support for this.
α
❖ ∇ (phase′ ) = ∇ (i( p ⋅ x − Et) − ieα( x )) = i p − ie ∇ α( x )
❖ Have to introduce something in addition to restore gauge invariance: Let p → p + e A , and make use of A → A + ∇ α( x )
❖ ∇ (phase′ ) = i p + ie A − ieα( x ) = i p = ∇ (phase)
❖ Adding the interaction with the photon field has restored the local gauge invariance.
A
7
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Standard model gauge interactions❖ QED: , gives a photonψ ⟶ e−iqα( x )ψ
8
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Standard model gauge interactions❖ QED: , gives a photonψ ⟶ e−iqα( x )ψ
❖ QCD: , 8 color matrices give 8 gluons
ψ ⟶ eiαa( x )⋅Taψ Ta = (3 × 3)
8
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Standard model gauge interactions❖ QED: , gives a photonψ ⟶ e−iqα( x )ψ
❖ QCD: , 8 color matrices give 8 gluons
ψ ⟶ eiαa( x )⋅Taψ Ta = (3 × 3)
❖ Electroweak: , Pauli matrices
ψ ⟶ eig′ α( x )+ig τ⋅ Λ( x )ψ τ = 3(2 × 2)
8
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Standard model gauge interactions❖ QED: , gives a photonψ ⟶ e−iqα( x )ψ
❖ QCD: , 8 color matrices give 8 gluons
ψ ⟶ eiαa( x )⋅Taψ Ta = (3 × 3)
❖ Electroweak: , Pauli matrices
ψ ⟶ eig′ α( x )+ig τ⋅ Λ( x )ψ τ = 3(2 × 2)
❖ : coupling to weak hypercharge, i.e. a bosong′ B0
8
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Standard model gauge interactions❖ QED: , gives a photonψ ⟶ e−iqα( x )ψ
❖ QCD: , 8 color matrices give 8 gluons
ψ ⟶ eiαa( x )⋅Taψ Ta = (3 × 3)
❖ Electroweak: , Pauli matrices
ψ ⟶ eig′ α( x )+ig τ⋅ Λ( x )ψ τ = 3(2 × 2)
❖ : coupling to weak hypercharge, i.e. a bosong′ B0
❖ : coupling to weak isospin, i.e., bosonsg W±, W0
8
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Standard model gauge interactions❖ QED: , gives a photonψ ⟶ e−iqα( x )ψ
❖ QCD: , 8 color matrices give 8 gluons
ψ ⟶ eiαa( x )⋅Taψ Ta = (3 × 3)
❖ Electroweak: , Pauli matrices
ψ ⟶ eig′ α( x )+ig τ⋅ Λ( x )ψ τ = 3(2 × 2)
❖ : coupling to weak hypercharge, i.e. a bosong′ B0
❖ : coupling to weak isospin, i.e., bosonsg W±, W0
❖ Choice of symmetry determines dynamics of the system!!
8
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak unification/mixing
9
Gauge interactions
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak unification/mixing❖ Balancing act: don’t want weak neutral currents as strong
as the charged ones, and want to recover the photon (QED).
9
Gauge interactions
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak unification/mixing❖ Balancing act: don’t want weak neutral currents as strong
as the charged ones, and want to recover the photon (QED).
❖Mixing hypothesis: ( γ
Z0) = ( cos θW sin θW
−sin θW cos θW) ( B0
W0)
9
Gauge interactions Physical interactions
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak unification/mixing❖ Balancing act: don’t want weak neutral currents as strong
as the charged ones, and want to recover the photon (QED).
❖Mixing hypothesis: ( γ
Z0) = ( cos θW sin θW
−sin θW cos θW) ( B0
W0)❖ is the Weinberg angle, defined by θW
cos θW = mW /mZ
9
Gauge interactions Physical interactions
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak unification/mixing❖ Balancing act: don’t want weak neutral currents as strong
as the charged ones, and want to recover the photon (QED).
❖Mixing hypothesis: ( γ
Z0) = ( cos θW sin θW
−sin θW cos θW) ( B0
W0)❖ is the Weinberg angle, defined by θW
cos θW = mW /mZ
❖ Unification (massless photon) when e = g sin θW = g′ cos θW
9
Gauge interactions Physical interactions
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Electroweak unification/mixing❖ Balancing act: don’t want weak neutral currents as strong
as the charged ones, and want to recover the photon (QED).
❖Mixing hypothesis: ( γ
Z0) = ( cos θW sin θW
−sin θW cos θW) ( B0
W0)❖ is the Weinberg angle, defined by θW
cos θW = mW /mZ
❖ Unification (massless photon) when e = g sin θW = g′ cos θW
❖or , where
e2 2ϵ0
= gW sin θW = gZ cos θW
gW ≡g
2 2ϵ0, gZ ≡
g′
2 2ϵ0
9
Gauge interactions Physical interactions
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Aside: Gauge symmetry removes divergences
❖ This diagram alone is divergent but after adding the and contributions of the same order the cross
section is finite.γ Z0
10
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Aside: Gauge symmetry removes divergences
❖ This diagram alone is divergent but after adding the and contributions of the same order the cross
section is finite.γ Z0
❖ Showing the electroweak theory is as “renormalizable” (divergence free) as QED was worthy of a Nobel Prize ('t Hooft and Veltman, 1999)
10
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Aside: Gauge symmetry removes divergences
❖ This diagram alone is divergent but after adding the and contributions of the same order the cross
section is finite.γ Z0
❖ Showing the electroweak theory is as “renormalizable” (divergence free) as QED was worthy of a Nobel Prize ('t Hooft and Veltman, 1999)
10
Question: Can you draw the additional and diagrams of the same order?
γZ0
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Theory free of “anomalies” relates lepton and quark charges : l a
∑l
Ql + 3∑a
Qa = 0
11
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Theory free of “anomalies” relates lepton and quark charges : l a
∑l
Ql + 3∑a
Qa = 0
❖ Partial explanation for complete generations (so far zero evidence of a 4’th).
11
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Theory free of “anomalies” relates lepton and quark charges : l a
∑l
Ql + 3∑a
Qa = 0
❖ Partial explanation for complete generations (so far zero evidence of a 4’th).
❖Low energy couplings: GW ≡ GF =
(ℏc)2 2g2W
m2Wc4
, GZ =(ℏc)2 2g2
Z
m2Zc4
11
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Theory free of “anomalies” relates lepton and quark charges : l a
∑l
Ql + 3∑a
Qa = 0
❖ Partial explanation for complete generations (so far zero evidence of a 4’th).
❖Low energy couplings: GW ≡ GF =
(ℏc)2 2g2W
m2Wc4
, GZ =(ℏc)2 2g2
Z
m2Zc4
❖, measured to in low-energy
neutrino scattering
GZ
GF=
g2Z
g2W
m2W
m2Z
= sin2 θW sin2 θW = 0.227 ± 0.014
11
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Theory free of “anomalies” relates lepton and quark charges : l a
∑l
Ql + 3∑a
Qa = 0
❖ Partial explanation for complete generations (so far zero evidence of a 4’th).
❖Low energy couplings: GW ≡ GF =
(ℏc)2 2g2W
m2Wc4
, GZ =(ℏc)2 2g2
Z
m2Zc4
❖, measured to in low-energy
neutrino scattering
GZ
GF=
g2Z
g2W
m2W
m2Z
= sin2 θW sin2 θW = 0.227 ± 0.014
❖ Remember that it was challenging to discover neutral currents - this is partly why.
11
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Combined with measurements such as muon lifetime, and
taking into account higher-order diagrams, the masses of the and bosons were predicted (ca. 80 and 91 GeV/c2).W Z
12
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Combined with measurements such as muon lifetime, and
taking into account higher-order diagrams, the masses of the and bosons were predicted (ca. 80 and 91 GeV/c2).W Z
❖ and bosons were discovered by the UA1 and UA2 experiments at CERN in 1983 (not 1993 as M&S write, e.g. on page 230).
W± Z
12
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Other predictions❖ Combined with measurements such as muon lifetime, and
taking into account higher-order diagrams, the masses of the and bosons were predicted (ca. 80 and 91 GeV/c2).W Z
❖ and bosons were discovered by the UA1 and UA2 experiments at CERN in 1983 (not 1993 as M&S write, e.g. on page 230).
W± Z
❖ Precision measurements of and at TeVatron (USA) and LEP (CERN) in the 1990’s are consistent with the electroweak theory.
mW mZ
12
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
13
a = quark
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
13
e, gZ
gZ
eqa, gZa = quark
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
❖ Assume that couples to Z0 uu, cc, tt, d′ d′ , s′ s′ , b′ b′
13
e, gZ
gZ
eqa, gZa = quark
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
❖ Assume that couples to Z0 uu, cc, tt, d′ d′ , s′ s′ , b′ b′
13
e, gZ
gZ
eqa, gZa = quark
(a, b, c)T ≡ (abc)
(AB)† ≡ (A*B*)T = B*T A*T = B†A†
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
❖ Assume that couples to Z0 uu, cc, tt, d′ d′ , s′ s′ , b′ b′
❖
d′ d′ + s′ s′ + b′ b′ = [Vi,j(d, s, b)T]†Vi,j(d, s, b)T
= (d, s, b)V†i,jVi,j(d, s, b)T
= (d, s, b)(d, s, b)T = dd + ss + bb
13
e, gZ
gZ
eqa, gZa = quark
(a, b, c)T ≡ (abc)
(AB)† ≡ (A*B*)T = B*T A*T = B†A†
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
❖ Assume that couples to Z0 uu, cc, tt, d′ d′ , s′ s′ , b′ b′
❖
d′ d′ + s′ s′ + b′ b′ = [Vi,j(d, s, b)T]†Vi,j(d, s, b)T
= (d, s, b)V†i,jVi,j(d, s, b)T
= (d, s, b)(d, s, b)T = dd + ss + bb
❖ We can use the strong quark eigenstates for both and interactions
γ Z0
13
e, gZ
gZ
eqa, gZa = quark
(a, b, c)T ≡ (abc)
(AB)† ≡ (A*B*)T = B*T A*T = B†A†
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
❖ Assume that couples to Z0 uu, cc, tt, d′ d′ , s′ s′ , b′ b′
❖
d′ d′ + s′ s′ + b′ b′ = [Vi,j(d, s, b)T]†Vi,j(d, s, b)T
= (d, s, b)V†i,jVi,j(d, s, b)T
= (d, s, b)(d, s, b)T = dd + ss + bb
❖ We can use the strong quark eigenstates for both and interactions
γ Z0
❖ In principle in any diagram where there is a there is a similar corresponding diagram with a , i.e. we could always write .
γZ0 γ/Z0
13
e, gZ
gZ
eqa, gZa = quark
(a, b, c)T ≡ (abc)
(AB)† ≡ (A*B*)T = B*T A*T = B†A†
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Basic vertices
❖ Assume that couples to Z0 uu, cc, tt, d′ d′ , s′ s′ , b′ b′
❖
d′ d′ + s′ s′ + b′ b′ = [Vi,j(d, s, b)T]†Vi,j(d, s, b)T
= (d, s, b)V†i,jVi,j(d, s, b)T
= (d, s, b)(d, s, b)T = dd + ss + bb
❖ We can use the strong quark eigenstates for both and interactions
γ Z0
❖ In principle in any diagram where there is a there is a similar corresponding diagram with a , i.e. we could always write .
γZ0 γ/Z0
❖ Sometimes (in 2 slides) it is practical to keep them separate.
13
e, gZ
gZ
eqa, gZa = quark
(a, b, c)T ≡ (abc)
(AB)† ≡ (A*B*)T = B*T A*T = B†A†
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Lepton-quark symmetry almost as straightforward as for
-interactionsW
14
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Lepton-quark symmetry almost as straightforward as for
-interactionsW
14
https://en.wikipedia.org/wiki/W_and_Z_bosons
x ≡ sin2 θw
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Lepton-quark symmetry almost as straightforward as for
-interactionsW
14
https://en.wikipedia.org/wiki/W_and_Z_bosons
x ≡ sin2 θw
14.3
14.34.84.84.8
71.4
14.3
14.3
l-q symmetry
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0
❖ Lepton-quark symmetry almost as straightforward as for
-interactionsW
❖ Remember that and are mixtures of
γZ0
B0(g′ ) and W0(g′ /tan θ)
14
https://en.wikipedia.org/wiki/W_and_Z_bosons
x ≡ sin2 θw
14.3
14.34.84.84.8
71.4
14.3
14.3
l-q symmetry
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0/γ❖ Consider at low energy
( )e+e− → μ+μ−
E ≪ mZc2
15
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0/γ❖ Consider at low energy
( )e+e− → μ+μ−
E ≪ mZc2
❖ By dimensional arguments and
σγ ≈ α2EM(ℏc)2/E2
σZ ≈ G2ZE2/(ℏc)4
15
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0/γ❖ Consider at low energy
( )e+e− → μ+μ−
E ≪ mZc2
❖ By dimensional arguments and
σγ ≈ α2EM(ℏc)2/E2
σZ ≈ G2ZE2/(ℏc)4
❖
σZ
σγ=
G2ZE4
α2EM(ℏc)6
= ( GZ
(ℏc)3 )2 E4
α2EM
= ( 2g2Z
ℏcm2Zc4 )
2E4
α2EM
≈ ( EmZc2 )
4
≪ 1
15
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0/γ❖ Consider at low energy
( )e+e− → μ+μ−
E ≪ mZc2
❖ By dimensional arguments and
σγ ≈ α2EM(ℏc)2/E2
σZ ≈ G2ZE2/(ℏc)4
❖
σZ
σγ=
G2ZE4
α2EM(ℏc)6
= ( GZ
(ℏc)3 )2 E4
α2EM
= ( 2g2Z
ℏcm2Zc4 )
2E4
α2EM
≈ ( EmZc2 )
4
≪ 1
15mzc2
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
InteractionsZ0/γ❖ Consider at low energy
( )e+e− → μ+μ−
E ≪ mZc2
❖ By dimensional arguments and
σγ ≈ α2EM(ℏc)2/E2
σZ ≈ G2ZE2/(ℏc)4
❖
σZ
σγ=
G2ZE4
α2EM(ℏc)6
= ( GZ
(ℏc)3 )2 E4
α2EM
= ( 2g2Z
ℏcm2Zc4 )
2E4
α2EM
≈ ( EmZc2 )
4
≪ 1
❖ M&S 6.65b ( ) is for high-energy interactions ( ) !!
σZ /σγ ≈ 1/cos4 θW ≈ 1E ≫ mZc2
15mzc2
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism*
16
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism*❖ (*) Sometimes still called the Higgs Mechanism
16
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism*❖ (*) Sometimes still called the Higgs Mechanism
❖ No parity violation (more in Chap. 7) together with and masses and gauge symmetry
W± Z0
16
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism*❖ (*) Sometimes still called the Higgs Mechanism
❖ No parity violation (more in Chap. 7) together with and masses and gauge symmetry
W± Z0
❖ Don’t abandon gauge principle - introduce a scalar field that has a non-zero value in the vacuum.
16
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism*❖ (*) Sometimes still called the Higgs Mechanism
❖ No parity violation (more in Chap. 7) together with and masses and gauge symmetry
W± Z0
❖ Don’t abandon gauge principle - introduce a scalar field that has a non-zero value in the vacuum.
❖ This is well-known in superconductivity, but here there is clearly a physical medium. Old-school physicists told the young people proposing this (4 different groups had more or less the same ideas in the early 1960’s) that they didn’t understand physics!
16
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism*❖ (*) Sometimes still called the Higgs Mechanism
❖ No parity violation (more in Chap. 7) together with and masses and gauge symmetry
W± Z0
❖ Don’t abandon gauge principle - introduce a scalar field that has a non-zero value in the vacuum.
❖ This is well-known in superconductivity, but here there is clearly a physical medium. Old-school physicists told the young people proposing this (4 different groups had more or less the same ideas in the early 1960’s) that they didn’t understand physics!
❖ In EM a heated ferromagnet has no net magnetic field. As it is cooled below the critical (Curie) temperature, small domains will be spontaneously magnetized in some random direction. At high temperature the symmetry of EM is manifest, but it appears to be broken at low temperature.
16
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism❖ Have 4 vector bosons and want to give mass to 3 of them.
17
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism❖ Have 4 vector bosons and want to give mass to 3 of them.
❖ Introduce scalar field with 4 components
17
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism❖ Have 4 vector bosons and want to give mass to 3 of them.
❖ Introduce scalar field with 4 components
❖ 3 are absorbed by the and , allowing them to have 3 degrees of polarization (the photon has only 2) and mass.
W± Z0
17
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism❖ Have 4 vector bosons and want to give mass to 3 of them.
❖ Introduce scalar field with 4 components
❖ 3 are absorbed by the and , allowing them to have 3 degrees of polarization (the photon has only 2) and mass.
W± Z0
❖ The Higgs boson is a quantum excitation of the remaining component of the scalar field; the potential is postulated to have a Mexican hat form.
17
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
BEH Mechanism❖ Have 4 vector bosons and want to give mass to 3 of them.
❖ Introduce scalar field with 4 components
❖ 3 are absorbed by the and , allowing them to have 3 degrees of polarization (the photon has only 2) and mass.
W± Z0
❖ The Higgs boson is a quantum excitation of the remaining component of the scalar field; the potential is postulated to have a Mexican hat form.
❖ The direction is determined spontaneously, breaking/hiding the original symmetry seen from the top of the hat.
17
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Bonus from BEH for fermions
18
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Bonus from BEH for fermions❖ The fermions couple to the Higgs field with a strength proportional to
their mass: .gHff = 2gWmf
mW
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FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Bonus from BEH for fermions❖ The fermions couple to the Higgs field with a strength proportional to
their mass: .gHff = 2gWmf
mW
❖ So the fermion masses are not predicted, but since we have measured the masses we can test whether the coupling is related to like this.mf
18
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Bonus from BEH for fermions❖ The fermions couple to the Higgs field with a strength proportional to
their mass: .gHff = 2gWmf
mW
❖ So the fermion masses are not predicted, but since we have measured the masses we can test whether the coupling is related to like this.mf
❖ We still have not predicted the masses, but at least we have predicted how the fermions get mass.
18
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Bonus from BEH for fermions❖ The fermions couple to the Higgs field with a strength proportional to
their mass: .gHff = 2gWmf
mW
❖ So the fermion masses are not predicted, but since we have measured the masses we can test whether the coupling is related to like this.mf
❖ We still have not predicted the masses, but at least we have predicted how the fermions get mass.
❖ …apart from the neutrino masses: They are so incredibly much smaller that it seems unlikely to be the same mechanism, and anyway it not possible to give them masses the same way due again to parity violation (more on this in Chap. 7).
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FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
P.S.
❖ By the way, until Weinberg and Salaam applied BEH to electroweak interactions a few years later, the BEH mechanism was being explored as a way to understand the strong interaction in hadrons (massive vector bosons like the )!ρ±,0
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FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs boson decays
20
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs boson decays
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FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs boson decays
20
First order Second order
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs boson decays
❖ One of the in
decays must be virtual
V = Z0, W±
H → VV
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First order Second order
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs boson decays
❖ One of the in
decays must be virtual
V = Z0, W±
H → VV
❖ (M&S write for )H → VV *
ff V
20
First order Second order
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201321
Higgs production @ LHC
Compiled by LHCXSWG
t
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201321
Higgs production @ LHC
Compiled by LHCXSWG
t
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201321
Higgs production @ LHC
Compiled by LHCXSWG
t
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201321
Higgs production @ LHC
Compiled by LHCXSWG
VBF
t
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201321
Higgs production @ LHC
Compiled by LHCXSWG
VBF
t
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201321
Higgs production @ LHC
Compiled by LHCXSWG
VBF
t
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs production at LHC
22
❖ Modest increases in yield for increasing in pp-collisions
s ≡ Ecm
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs production at LHC
22
❖ Modest increases in yield for increasing in pp-collisions
s ≡ Ecm
❖ We have data at TeVs = 7,8,13
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.2013
Candidate H ! ��
23
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.2013
CandidateH ! ZZ
⇤ ! (e+e�)(µ+µ�)
24
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.2013
Candidate H ! W+W�(⇤) ! e+�eµ��µ
25
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201326
July, 2012
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.2013
A new boson, “Higgs-like”
27
Combination of all channels and data available at the time
2 experiments with 5σ at ~same mass
The most sensitive channels making the impact
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.2013
A new boson, “Higgs-like”
27
Combination of all channels and data available at the time
2 experiments with 5σ at ~same mass
The most sensitive channels making the impact
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201328
Rest of 2012: The signals grew...
Animations: https://cds.cern.ch/record/2230893?ln=en
Alex Read - Higgs boson measurements Nobel Symposium, 15.05.201328
Rest of 2012: The signals grew...
Animations: https://cds.cern.ch/record/2230893?ln=en
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
29
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
29
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
Mass measurements
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
29
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
Mass measurements Cross-section versuscenter-of-mass energy s
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
29
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
Mass measurements Cross-section versuscenter-of-mass energy s
Test of (scalar)JP = 0+
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
30
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
30
Cross-sections andBranching fractions
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
30
Cross-sections andBranching fractions
Test of coupling strength versusmass of fermion or vector boson
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
State of the art (ATLAS only)
30
Cross-sections andBranching fractions
Test of coupling strength versusmass of fermion or vector boson Coupling strengths and
limits on exotic decayshttps://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
31
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
❖ All -collision production mechanisms observed.pp
31
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
❖ All -collision production mechanisms observed.pp
❖ Coupling pattern to vector bosons and 3rd-generation fermions confirmed.
31
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
❖ All -collision production mechanisms observed.pp
❖ Coupling pattern to vector bosons and 3rd-generation fermions confirmed.
❖ Need more data to test second generation: by 2037?cc and μ+μ−
31
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
❖ All -collision production mechanisms observed.pp
❖ Coupling pattern to vector bosons and 3rd-generation fermions confirmed.
❖ Need more data to test second generation: by 2037?cc and μ+μ−
❖ Need more data to confirm (a fundamental prediction of the model): challenging but possible by 2037.
H → HH
31
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
❖ All -collision production mechanisms observed.pp
❖ Coupling pattern to vector bosons and 3rd-generation fermions confirmed.
❖ Need more data to test second generation: by 2037?cc and μ+μ−
❖ Need more data to confirm (a fundamental prediction of the model): challenging but possible by 2037.
H → HH
❖ Speculative models rely on Higgs boson as a “portal” to dark matter - no signs yet.
31
FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Higgs summary❖ So far all observations consistent with simplest possible model of the BEH mechanism.
❖ All -collision production mechanisms observed.pp
❖ Coupling pattern to vector bosons and 3rd-generation fermions confirmed.
❖ Need more data to test second generation: by 2037?cc and μ+μ−
❖ Need more data to confirm (a fundamental prediction of the model): challenging but possible by 2037.
H → HH
❖ Speculative models rely on Higgs boson as a “portal” to dark matter - no signs yet.
❖ Most fanatic proponents of supersymmetry (see Chap. 10) interpret as indirect evidence of supersymmetry.mH ≈ 125 GeV ∼ mZ
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FYS3500 Spring 2020 Alex Read, U. Oslo, Dept. Physics
Lists of concepts
❖ Gauge invariance
❖ Gauge symmetry
❖ Gauge principle
❖ Electroweak unification
❖ Weak mixing angle
❖ Weinberg angle
❖ BEH mechanism
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❖ BEH Mechanism
❖ Vector boson masses
❖ Higgs boson
❖ Fermion masses
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