Field Theory and Standard Model
|
|
- Cassandra Charles
- 5 years ago
- Views:
Transcription
1 Field Theory and Standard Model W. HOLLIK CERN SCHOOL OF PHYSICS BAUTZEN, JUNE 2009 p.1
2 Why Quantum Field Theory? (i) Fields: space time aspects field = quantity φ( x, t), defined for all points of space x and time t physical system defined by a Lagrangian L(φ( x, t)) p.2
3 Why Quantum Field Theory? (i) Fields: space time aspects field = quantity φ( x, t), defined for all points of space x and time t physical system defined by a Lagrangian L(φ( x, t)) fields and Lagrangian formalism accommodate symmetries: space time symmetry: Lorentz invariance internal symmetries (e.g. gauge symmetries) causality local interactions p.3
4 (ii) Particles: quantum theory aspects particles are classified by mass m and spin s quantum numbers m,s, p,s 3,charge, isospin, = eigenvalues of observables particle states m,s; p,s 3, > form quantum mechanical Hilbert space p.4
5 (ii) Particles: quantum theory aspects particles are classified by mass m and spin s quantum numbers m,s, p,s 3,charge, isospin, = eigenvalues of observables particle states m,s; p,s 3, > form quantum mechanical Hilbert space merging space-time and quantum aspects: Quantum Field Theory fields are operators that create/annihilate particles p.5
6 Outline 1. Elements of Quantum Field Theory 2. Cross sections and decay rates 3. Gauge Theories 3.1. Abelian gauge theories QED 3.2. Non-Abelian gauge theories 3.3. QCD 4. Higgs mechanism 4.1. Spontaneous symmetry breaking (SSB) 4.2. SSB in gauge theories 5. Electroweak interaction and Standard Model 5. Phenomenology of W and Z bosons, precision tests 6. Higgs bosons p.6
7 Notations and Conventions µ,ν,.. = 0,1,2,3; k,l,.. = 1,2,3 x = (x µ ) = (x 0, x), x 0 = t ( h = c = 1) p = (p µ ) = (p 0, p ), p 0 = E = p 2 + m a µ = g µν a ν , (g µν ) = a 2 = a µ a µ, µ = x µ = g µν ν, = µ µ = 2 t 2 a b = a µ b µ = a 0 b 0 a b ν = x ν [ 0 = 0, k = k ] p.7
8 1. Elements of Quantum Field Theory p.8
9 Fields in the Standard Model spin 0 particles: scalar fields φ(x) spin 1 particles: vector fields A µ (x), µ = 0,...3 spin 1/2 fermions: spinor fields ψ(x) = Lagrangian: L(φ, µ φ) Lorentz invariant Action: S = d 4 x L(φ(x), ) Lorentz invariant Hamilton s principle: δ S = 0 e.o.m. Lorentz covariant free fields: L is quadratic in the fields e.o.m. are linear diff. eqs. ψ 1 ψ 2 ψ 3 ψ 4 p.9
10 equations of motions from δs = S[φ + δφ] S[φ] = 0 Euler-Lagrange equations mechanics of particles: L(q 1,...q n, q 1,... q n ) e.o.m. d dt L qi L q i = 0 field theory: q i φ(x), q i µ φ(x) e.o.m. µ L ( µ φ) L φ = 0 field eq. example: scalar field φ(x), L = 1 2 ( µφ) 2 m2 2 φ2 field equation φ + m 2 φ = 0 solution φ(x) = 1 (2π) 3/2 d 3 k 2k 0 [a(k)e ikx + a(k) e ikx ] p.10
11 p.11
12 p.12
13 p.13
14 p.14
15 p.15
16 p.16
17 p.17
18 p.18
19 p.19
20 p.20
21 p.21
22 p.22
23 p.23
24 2. Cross sections and decay widths p.24
25 amplitudes scattering process: a + b b 1 + b b n a(p a ),b(p b )>= i>, b 1 (p 1 ), b n (p n )>= f > matrix element = probability amplitude for i f: S fi =< f S i > p.25
26 amplitudes scattering process: a + b b 1 + b b n a(p a ),b(p b )>= i>, b 1 (p 1 ), b n (p n )>= f > matrix element = probability amplitude for i f: S fi =< f S i > for i f: S fi 2 = (2π) 4 δ 4 (P i P f ) M fi 2 (2π) 3(n+2) P i = p a +p b = P f = p 1 + +p n momentum conservation factors (2π) 3 from wave function normalization (plane waves) M fi from Feynman graphs and rules p.26
27 probability for scattering into phase space element dφ: dw fi = S fi 2 dφ, dφ = d3 p 1 2p 0 1 d3 p n 2p 0 n d 3 p i 2p 0 i = d 4 p i δ(p 2 i m2 i ) Lorentz invariant phase space differential cross section: dσ = (2π) 6 4 (p a p b ) 2 m 2 am 2 b }{{} dw fi flux normalization factor from initial state p.27
28 probability for scattering into phase space element dφ: dw fi = S fi 2 dφ, dφ = d3 p 1 2p 0 1 d3 p n 2p 0 n d 3 p i 2p 0 i = d 4 p i δ(p 2 i m2 i ) Lorentz invariant phase space differential cross section: dσ = (2π) 6 4 (p a p b ) 2 m 2 am 2 b }{{} dw fi flux normalization factor from initial state dσ = (2π) 4 4 (p a p b ) 2 m 2 am 2 b M fi 2 (2π) 3n δ 4 (P i P f ) d3 p 1 2p 0 1 d3 p n 2p 0 n p.28
29 decay process: a b 1 + b b n a(p a )>= i>, b 1 (p 1 ), b n (p n )>= f > S fi 2 = (2π) 4 δ 4 (p a P f ) M fi 2 (2π) 3(n+1) decay width (differential): dγ = (2π)3 2m a }{{} normalization of a> S fi 2 dφ }{{} dw fi p.29
30 decay process: a b 1 + b b n a(p a )>= i>, b 1 (p 1 ), b n (p n )>= f > S fi 2 = (2π) 4 δ 4 (p a P f ) M fi 2 (2π) 3(n+1) decay width (differential): dγ = (2π)3 2m a }{{} normalization of a> S fi 2 dφ }{{} dw fi dγ = (2π)4 2 m a M fi 2 (2π) 3n δ 4 (p a P f ) d3 p 1 2p 0 1 d3 p n 2p 0 n p.30
31 special case: 2-particle phase space a + b b 1 + b 2, a b 1 + b 2 cross section in the CMS, p a + p b = 0 = p 1 + p 2 dσ dω = 1 64π 2 s p 1 p a M fi 2 dω = dcos θ dφ, θ =<( p a, p 1 ) s = (p a + p b ) 2 = E 2 CMS decay rate for final state masses m 1 = m 2 = m dγ dω = 1 64π 2 m a 1 4m2 m 2 a M fi 2 p.31
32 3. Gauge theories p.32
33 3.1 Abelian gauge theories QED free fermion field ψ (for e ± ), described by Lagrangian L 0 = ψ (iγ µ µ m)ψ L 0 is invariant under global transformations ψ(x) ψ (x) = e iα ψ(x) group: U(1), global U(1) with α real, arbitrary global gauge symmetry L 0 is not invariant under local transformations ψ(x) ψ (x) = e iα(x) }{{} ψ(x) U(x) p.33
34 invariance is obtained by minimal substitution µ D µ = µ iea µ covariant derivative under the combined transformations ψ(x) ψ (x) = e iα(x) ψ(x) U(x)ψ(x) A µ (x) A µ(x) = A µ (x) + 1 e µα(x) local gauge transformations group: local U(1), Abelian: e iα 1 e iα 2 = e iα 2 e iα 1 basic property: D µψ = U(x)D µ ψ ( µ iea µ) }{{}} U(x)ψ(x) {{} = U(x) ( µ iea µ )ψ }{{} D µ ψ D µ ψ p.34
35 L is invariant under local gauge transformations: L = ψ (iγ µ D µ m)ψ = ψ (iγ µ D µ m)ψ = L proof with ψ = Uψ = ψu = ψu 1 and D µψ = UD µ ψ The invariant Lagrangian contains a new vector field A µ which couples to the electromagnetic current: L = ψ (iγ µ D µ m)ψ = L 0 + e ψγ µ ψ A µ = L 0 + L int local gauge invariance determines the interaction A µ not yet a dynamical field add L A (invariant!) L A = 1 4 F µνf µν (+L fix ) free photon field L QED = L 0 + L A + L int p.35
36 QED as a gauge theory: main steps start with L 0 (ψ, µ ψ)) for free fermion field ψ symmetric under global gauge transformations p.36
37 QED as a gauge theory: main steps start with L 0 (ψ, µ ψ)) for free fermion field ψ symmetric under global gauge transformations perform minimal substitution L 0 (ψ,d µ ψ) µ D µ = µ iea µ invariance under local gauge transformations involves additional vector field A µ induces interaction between A µ and ψ e ψγ µ ψ A µ e j µ A µ p.37
38 QED as a gauge theory: main steps start with L 0 (ψ, µ ψ)) for free fermion field ψ symmetric under global gauge transformations perform minimal substitution L 0 (ψ,d µ ψ) µ D µ = µ iea µ invariance under local gauge transformations involves additional vector field A µ induces interaction between A µ and ψ e ψγ µ ψ A µ e j µ A µ make A µ a dynamical field by adding L A = 1 4 F µν F µν (+L fix ) p.38
39 3.2 Non-Abelian gauge theories Generalization: phase transformations that do not commute ψ ψ = Uψ with U 1 U 2 U 1 U 1 requires matrices, i.e. ψ is a multiplet ψ = ψ 1 ψ 2 : ψ n, each ψ k = ψ k (x) is a Dirac spinor U = n n -matrix p.39
40 (i) global symmetry starting point: L 0 = ψ iγ µ µ ψ where ψ = (ψ 1,,ψ n ) consider unitary matrices: U = U 1 ψ = Uψ ψ = ψ U = ψ U 1 ψ ψ = ψψ, ψ γ µ µ ψ = ψγ µ µ ψ if U does not depend on x L 0 is invariant under ψ Uψ U: global gauge transformation p.40
41 similar for scalar fields: φ ψ = Uφ, φ = φ 1 φ 2 : φ n each φ k = φ k (x) is a scalar field, φ = (φ 1,,φ n) terms φ φ, ( µ φ) ( µ φ) are invariant L 0 = ( µ φ) ( µ φ) is invariant p.41
42 relevant in physics: the special unitary n n-matrices with det=1 group SU(n) examples: ( ) ( ) SU(2) : ψ = ψ 1 ψ 2 e.g. ψ = ψ ν ψ e isospin SU(3) : ψ = ψ 1 ψ 2 e.g. ψ = ψ r ψ g colour ψ 3 ψ b p.42
43 SU(n) matrices U can be written as exponentials U(θ 1,,θ N ) = e iθ at a sum over a = 1, n θ 1, θ N : real parameters T 1, T N : n n-matrices, generators, T a = T a infinitesimal θ : U = 1 + iθ a T a (+O(θ 2 )) N-dimensional Lie Group det=1 and unitarity N = n 2 1 n = 2 : N = 3, n = 3 : N = 8 p.43
44 commutators [T a,t b ] 0 non-abelian [T a,t b ] = if abc T c Lie Algebra f abc : real numbers, structure constants f abc = f bac = antisymmetric p.44
45 commutators [T a,t b ] 0 non-abelian [T a,t b ] = if abc T c Lie Algebra f abc : real numbers, structure constants f abc = f bac = antisymmetric SU(2) f abc = ǫ abc (like angular momentum) T a = 1 2 σ a, σ a : Pauli matrices (a=1,2,3) p.45
46 commutators [T a,t b ] 0 non-abelian [T a,t b ] = f abc T c Lie Algebra f abc : real numbers, structure constants f abc = f bac = antisymmetric SU(2) f abc = ǫ abc (like angular momentum) T a = 1 2 σ a, σ a : Pauli matrices (a=1,2,3) SU(3) T a = 1 2 λ a, λ a : Gell-Mann matrices (a=1,...8) λ 1 = 1 0 0, p.46
47 p.47
48 p.48
49 p.49
50 p.50
51 p.51
52 p.52
53 p.53
54 p.54
55 p.55
56 3.3. Quantum Chromodynamics (QCD) each quark field q = u,d,... appears in 3 colours q ψ = q, ψ = (q,q,q) q T a = 1 2 λ a (a = 1,...8) generators W a µ G a µ 8 gluon fields G a µν = µ G a ν ν G a µ + g s f abc G b µg c ν field strength D µ = µ ig s T a G a µ covariant derivative g s coupling constant of strong interaction, α s = g2 s 4π p.56
57 p.57
58 p.58
59 p.59
60 4. Higgs mechanism p.60
61 problem: weak interaction, gauge bosons are massive mass terms M 2 W a µw a, µ spoil local gauge invariance bad high energy behaviour of amplitudes and cross sections, conflict with unitarity reason: longitudinal polarization ǫ µ kµ M kµ bad divergence of higher orders with loop diagrams reason: propagators contain g µν + k µk ν M 2 additional powers of momenta in loop integration spoil renormalizability renormalizable theory: divergences can be absorbed into the parameters gauge invariant theories are renormalizable p.61
62 4.1 Spontaneous symmetry breaking (SSB) physical system: ground state: has a symmetry not symmetric p.62
63 consider complex scalar field φ φ Lagrangian with interaction V (potential), minimum at φ 0 = v L = µ φ 2 V (φ) V(φ) ϕ 1 φ V = V ( φ ) : L symmetric under φ e iα φ, U(1) v 0 : φ 0 = eiα v φ 0 not symmetric ϕ 2 V = V ( φ 0 ) = V ( φ 0 ) : vacuum is degenerate p.63
64 p.64
65 p.65
66 p.66
67 p.67
68 two different gauges properties φ field A µ field symmetry manifest H, θ 2 polarizations (transverse) physics manifest H 3 polarizations (2 transverse + 1 longitudinal) θ longitudinal polarization of A µ p.68
69 5. Electroweak interaction and Standard Model p.69
70 preliminaries Dirac matrices: γ µ (µ = 0, 1, 2, 3), γ µ γ ν + γ ν γ µ = 2g µν Γ = γ 0 (Γ) γ 0, Γ any Dirac matrix oder product of matrices further Dirac matrix: γ 5 = γ 0 γ 1 γ 2 γ 3 = γ 5 γ µ + γ µ γ 5 = 0, γ 5 = γ 5, γ 2 5 = 1 chiral fermions: ψ L = 1 γ 5 2 ψ left-handed spinor, L-chiral spinor ψ R = 1+γ 5 2 ψ right-handed spinor, R-chiral spinor ( projectors on left/right chirality: ω ± = 1±γ 5 2, (ω ± ) 2 = ω ± ) p.70
71 chiral currents: ψ L γ µ ψ L = ψ γ µ 1 γ 5 2 ψ J µ L left-handed current ψ R γ µ ψ R = ψ γ µ 1+γ 5 2 ψ J µ R right-handed current J µ V = ψγµ ψ = J µ L + Jµ R J µ A = ψγµ γ 5 ψ = J µ L + Jµ R vector current axialvector current mass term: mψψ = m (ψ L ψ R + ψ R ψ L ) connects L and R! p.71
72 symmetry group: SU(2) I U(1) Y SU(2) I : weak isospin, generators T a I = 1 2 σa for L, = 0 for R U(1) Y : weak hypercharge, generator Y L T 3 I + Y/2 = Q Fermion content of the SM: (ignoring possible right-handed neutrinos) TI 3 Q ν L «leptons: Ψ L e ν L «µ ν L «τ L = e L, µ L, τ L, 1 quarks: (Each quark exists in 3 colours!) 1 2 ψl R = e R, µ R, τ R, 0 1 u L «c L «t L « Ψ L 2 3 Q =,,, d L s L b L ψ R u = u R, c R, t R, ψ R d = d R, s R, b R, p.72
73 gauge boson content SU(2) I : generators T 1 I, T 2 I, T 3 I gauge fields W 1 µ, W 2 µ, W 3 µ also: W ± µ = 1 2 ( W 1 µ ± iw 2 µ), W 3 µ U(1) Y : generator Y gauge field B µ p.73
74 Free Lagrangian of (still massless) fermions: L 0,ferm = iψ f / ψ f = iψ L L / ΨL L + iψ L Q / ΨL Q + iψ R l / ψr l + iψ R u / ψ R u + iψ R d / ψr d Minimal substitution: µ D µ = µ ig 2 TI a Wµ a 1 + ig 1 Y B 2 µ = Dµω L + Dµ R ω +, Dµ L = µ ig 2 0 W + «µ 2 Wµ i g2 Wµ 3 g 1 Y L B µ g 2 Wµ 3 g 1 Y L B µ D R µ = µ + ig Y R B µ «, Photon identification: ««Zµ cw s W W 3 «µ c W = cosθ W, s W =sin θ W, rotation : =, A µ s W c W B µ θ W = mixing angle Dµ L = i Aµ 2 A g2 s W g 1 c W Y L ««0! Q1 0 µ 0 g 2 s W g 1 c W Y L = iea µ 0 Q 2 charged difference in doublet Q 1 Q 2 = 1 g 2 = e normalize Y L/R such that g 1 = e c W Y fixed by Gell-Mann Nishijima relation : Q = T 3 I + Y 2 s W p.74
75 Fermion gauge-boson interaction: L ferm,ym = e 0 /W + Ψ L F 2sW /W 0 «Ψ L F + e 2c W s W Ψ L F σ3 /ZΨ L F e s W c W Q f ψ f /Zψ f eq f ψ f /Aψ f (f=all fermions, F = all doublets) Feynman rules: f f W µ ie 2sW γ µ ω f f A µ iq f eγ µ f f Z µ ieγ µ (g + f ω + + g f ω ) = ieγ µ (v f a f γ 5 ) with g + f = s W c W Q f, g f = s W c W Q f + T 3 I,f c W s W, v f = s W c W Q f + T 3 I,f 2c W s W, a f = T 3 I,f 2c W s W p.75
76 gauge field Lagrangian (Yang-Mills Lagrangian) Field-strength tensors: L YM = 1 4 W a µνw a,µν 1 4 B µνb µν W a µν = µ W a ν ν W a µ + g 2 ǫ abc W b µw c ν, B µν = µ B ν ν B µ Lagrangian in terms of physical fields: L YM = 1 2 ( µw + ν ν W + µ )( µ W,ν ν W,µ ) 1 4 ( µz ν ν Z µ )( µ Z ν ν Z µ ) 1 4 ( µa ν ν A µ )( µ A ν ν A µ ) + (trilinear interaction terms involving AW + W, ZW + W ) + (quadrilinear interaction terms involving AAW + W, AZW + W, ZZW + W, W + W W + W ) p.76
77 Feynman rules for gauge-boson self-interactions: (fields and momenta incoming) W + µ W ν V ρ iec WWV h g µν (k + k ) ρ + g νρ (k k V ) µ + g ρµ (k V k + ) ν i with C WWγ = 1, C WWZ = c W s W W + µ W ν V ρ V σ ie 2 C WWV V h2g µν g ρσ g µρ g σν g µσ g νρ i with C WWγγ = 1, C WWγZ = c W s W, C WWZZ = c2 W, C s 2 WWWW = 1 W s 2 W p.77
78 Higgs mechanism masses of W and Z bosons spontaneous breaking SU(2) I U(1) Y U(1) Q unbroken em. gauge symmetry, massless photon GSW model: Minimal scalar sector with complex scalar doublet Φ = Scalar self-interaction via Higgs potential: V (Φ) = µ 2 Φ Φ + λ 4 (Φ Φ) 2, µ 2, λ > 0, φ + φ 0 «, Y Φ = 1 V = SU(2) I U(1) Y symmetric r 2µ 2 Re(φ 0 ) V (Φ) = minimal for Φ = λ v > 0 2 Im(φ 0 ) ground state Φ 0 (=vacuum «expectation value of Φ) not unique 0 specific choice Φ 0 = v not gauge invariant spontaneous symmetry breaking 2 «1 0 elmg. gauge invariance unbroken, since QΦ 0 = Φ 0 = p.78
79 Field excitations in Φ: Φ(x) = φ + (x) 1 2 v + H(x) + iχ(x)! Gauge-invariant Lagrangian of Higgs sector: (φ = (φ + ) ) L H = (D µ Φ) (D µ Φ) V (Φ) with D µ = µ ig 2 σ a 2 W a µ + i g 1 2 B µ = ( µ φ + )( µ φ ) iev (W µ + µ φ Wµ µ φ + )+ e2 v 2 W 2s W 4s 2 µ + W,µ W ( χ)2 + ev Z µ µ χ+ e2 v 2 Z c W s W 4c 2 Ws 2 W 2 ( H)2 µ 2 H 2 + (trilinear SSS, SSV, SV V interactions) + (quadrilinear SSSS, SSV V interactions) Implications: gauge-boson masses: M W = ev, M Z = ev = M W, M γ = 0 2s W 2c W s W c W physical Higgs boson H: M H = p 2µ 2 = free parameter would-be Goldstone bosons φ ±, χ: unphysical degrees of freedom p.79
80 Fermion masses fermions in chiral representations of gauge symmetry ) ( νe e L, e R mass term m e (e L e R + e R e L ) = m e ee not gauge invariant solution of the SM: introduce Yukawa interaction = new interaction of fermions with the Higgs field gauge invariant interaction, g = Yukawa coupling constant L Yuk = g [ψ L Φe R + e R Φ ψ L ] p.80
81 most transparent in unitary gauge ( ) ( 1 2 Φ = φ + φ 0 0 v + H apply to the first lepton generation ψ L = g 2 [ (ν L,e L ) ( 0 v + H ) e R + e R (0,v + H) ( ( ) ν L e L ν L e L ) ) ], e R : = g v 2 }{{} [e L e R + e R e L ] + g 2 H [e L e R + e R e L ] m e = m e ee + m e v H ee p.81
82 3 generations of leptons and quarks Lagrangian for Yukawa couplings: L Yuk = Ψ L L G lψl R Φ Ψ L Q G uψu R Φ Ψ L Q G dψd R Φ + h.c. G l, G u,g d = 3 3 matrices in 3-dim. space of generations (ν masses ignored) φ 0 «Φ = iσ 2 Φ = φ = charge conjugate Higgs doublet, Y Φ = 1 Fermion mass terms: mass terms = bilinear terms in L Yuk, obtained by setting Φ Φ 0 : L mf = v ψl LG lψl R v ψug L u ψu R v ψd LG dψd R + h.c diagonalization by unitary field transformations (f = l, u, d) ˆψ L/R f U L/R f ψ L/R f such that v 2 U L f G f (U R f ) = diag(m f ) standard form: L mf = m f ˆψL f ˆψR f + h.c. = m f ˆψf ˆψf p.82
83 Quark mixing: ψ f correspond to eigenstates of the gauge interaction ˆψf correspond to mass eigenstates, for massless neutrinos define ˆψL ν U L l ψ L ν no lepton-flavour changing Yukawa and gauge interactions in terms of mass eigenstates: 2ml L Yuk = φ + ˆψL v νl ˆψR l + φ 2mu ˆψRl ˆψL νl + φ + ˆψR v u V ˆψ d L + φ ˆψLd V ˆψR u 2md φ + ˆψL u V v ˆψ d R + φ ˆψRd V ˆψL u m f v isgn(t I,f)χ 3 ˆψ f γ 5 ˆψf L ferm,ym = m f v (v + H) ˆψ f ˆψf, e 0 /W + ˆΨL L 2sW /W 0 + «ˆψ L L + e 0 V /W + «ˆΨL Q 2sW V /W 0 e 2c W s W ˆΨL F σ 3 /Z ˆΨ L F e s W c W Q f ˆψf /Z ˆψ f eq f ˆψf /A ˆψ f only charged-current coupling of quarks modified by V = U L u (U L d ) = unitary ˆψ L Q Higgs fermion coupling strength = m f v (Cabibbo Kobayashi Maskawa (CKM) matrix) p.83
84 Features of the CKM mixing: V = 3-dim. generalization of Cabibbo matrix U C V is parametrized by 4 free parameters: 3 real angles, 1 complex phase complex phase is the only source of CP violation in SM counting: #real d.o.f. in V «#unitarity relations ««#phase diffs. of u-type quarks = = 4 no flavour-changing neutral currents in lowest order, «#phase diffs. of d-type quarks «#phase diff. between u- and d-type quarks flavour-changing suppressed by factors G µ (m 2 q 1 m 2 q 2 ) in higher orders ( Glashow Iliopoulos Maiani mechanism ) p.84
Standard Model. Ansgar Denner, Würzburg. 44. Herbstschule für Hochenergiephysik, Maria Laach September 2012
Standard Model Ansgar Denner, Würzburg 44. Herbstschule für Hochenergiephysik, Maria Laach 04. - 14. September 01 Lecture 1: Formulation of the Standard Model Lecture : Precision tests of the Standard
More informationQED and the Standard Model Autumn 2014
QED and the Standard Model Autumn 2014 Joel Goldstein University of Bristol Joel.Goldstein@bristol.ac.uk These lectures are designed to give an introduction to the gauge theories of the standard model
More informationAula/Lecture 18 Non-Abelian Gauge theories The Higgs Mechanism The Standard Model: Part I
Física de Partículas Aula/Lecture 18 Non-Abelian Gauge theories The The : Part I Jorge C. Romão Instituto Superior Técnico, Departamento de Física & CFTP A. Rovisco Pais 1, 1049-001 Lisboa, Portugal 2016
More informationPARTICLE PHYSICS Major Option
PATICE PHYSICS Major Option Michaelmas Term 00 ichard Batley Handout No 8 QED Maxwell s equations are invariant under the gauge transformation A A A χ where A ( φ, A) and χ χ ( t, x) is the 4-vector potential
More informationElectroweak physics and the LHC an introduction to the Standard Model
Electroweak physics and the LHC an introduction to the Standard Model Paolo Gambino INFN Torino LHC School Martignano 12-18 June 2006 Outline Prologue on weak interactions Express review of gauge theories
More informationGauge Symmetry in QED
Gauge Symmetry in QED The Lagrangian density for the free e.m. field is L em = 1 4 F µνf µν where F µν is the field strength tensor F µν = µ A ν ν A µ = Thus L em = 1 (E B ) 0 E x E y E z E x 0 B z B y
More informationWeek 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books
Week 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books Burgess-Moore, Chapter Weiberg, Chapter 5 Donoghue, Golowich, Holstein Chapter 1, 1 Free field Lagrangians
More informationGroup Structure of Spontaneously Broken Gauge Theories
Group Structure of SpontaneouslyBroken Gauge Theories p. 1/25 Group Structure of Spontaneously Broken Gauge Theories Laura Daniel ldaniel@ucsc.edu Physics Department University of California, Santa Cruz
More informationThe Standar Model of Particle Physics Lecture I
The Standar Model of Particle Physics Lecture I Aspects and properties of the fundamental theory of particle interactions at the electroweak scale Laura Reina Maria Laach School, Bautzen, September 011
More informationIntroduction to particle physics Lecture 6
Introduction to particle physics Lecture 6 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Fermi s theory, once more 2 From effective to full theory: Weak gauge bosons 3 Massive gauge bosons:
More informationHunting New Physics in the Higgs Sector
HS Hunting New Physics in the Higgs Sector SM Higgs Sector - Test of the Higgs Mechanism Oleg Kaikov KIT, Seminar WS 2015/16 Prof. Dr. M. Margarete Mühlleitner, Dr. Roger Wolf, Dr. Hendrik Mantler Advisor:
More informationStandard Model & Beyond
XI SERC School on Experimental High-Energy Physics National Institute of Science Education and Research 13 th November 2017 Standard Model & Beyond Lecture III Sreerup Raychaudhuri TIFR, Mumbai 2 Fermions
More information752 Final. April 16, Fadeev Popov Ghosts and Non-Abelian Gauge Fields. Tim Wendler BYU Physics and Astronomy. The standard model Lagrangian
752 Final April 16, 2010 Tim Wendler BYU Physics and Astronomy Fadeev Popov Ghosts and Non-Abelian Gauge Fields The standard model Lagrangian L SM = L Y M + L W D + L Y u + L H The rst term, the Yang Mills
More informationAnomaly. Kenichi KONISHI University of Pisa. College de France, 14 February 2006
Anomaly Kenichi KONISHI University of Pisa College de France, 14 February 2006 Abstract Symmetry and quantization U A (1) anomaly and π 0 decay Origin of anomalies Chiral and nonabelian anomaly Anomally
More information3.3 Lagrangian and symmetries for a spin- 1 2 field
3.3 Lagrangian and symmetries for a spin- 1 2 field The Lagrangian for the free spin- 1 2 field is The corresponding Hamiltonian density is L = ψ(i/ µ m)ψ. (3.31) H = ψ( γ p + m)ψ. (3.32) The Lagrangian
More informationIntroduction to the SM (5)
Y. Grossman The SM (5) TES-HEP, July 12, 2015 p. 1 Introduction to the SM (5) Yuval Grossman Cornell Y. Grossman The SM (5) TES-HEP, July 12, 2015 p. 2 Yesterday... Yesterday: Symmetries Today SSB the
More informationYou may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.
MATHEMATICAL TRIPOS Part III Monday 7 June, 004 1.30 to 4.30 PAPER 48 THE STANDARD MODEL Attempt THREE questions. There are four questions in total. The questions carry equal weight. You may not start
More informationLeptons and SU(2) U(1)
Leptons and SU() U(1) Contents I. Defining the Leptonic Standard Model 1 II. L kin and the gauge symmetry 3 III. L mψ = 0 4 IV. L φ and spontaneous symmetry breaking 4 V. Back to L kin (φ): The vector
More informationModels of Neutrino Masses
Models of Neutrino Masses Fernando Romero López 13.05.2016 1 Introduction and Motivation 3 2 Dirac and Majorana Spinors 4 3 SU(2) L U(1) Y Extensions 11 4 Neutrino masses in R-Parity Violating Supersymmetry
More informationHiggs Boson Phenomenology Lecture I
iggs Boson Phenomenology Lecture I Laura Reina TASI 2011, CU-Boulder, June 2011 Outline of Lecture I Understanding the Electroweak Symmetry Breaking as a first step towards a more fundamental theory of
More informationLecture III: Higgs Mechanism
ecture III: Higgs Mechanism Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for eptons Quark Masses & Mixing III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest
More informationParticle Physics I Lecture Exam Question Sheet
Particle Physics I Lecture Exam Question Sheet Five out of these 16 questions will be given to you at the beginning of the exam. (1) (a) Which are the different fundamental interactions that exist in Nature?
More informationCHAPTER II: The QCD Lagrangian
CHAPTER II: The QCD Lagrangian.. Preparation: Gauge invariance for QED - 8 - Ã µ UA µ U i µ U U e U A µ i.5 e U µ U U Consider electrons represented by Dirac field ψx. Gauge transformation: Gauge field
More informationPAPER 305 THE STANDARD MODEL
MATHEMATICAL TRIPOS Part III Tuesday, 6 June, 017 9:00 am to 1:00 pm PAPER 305 THE STANDARD MODEL Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight.
More informationThe Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local Gauge Transformations Dynamics of Field Ten
Lecture 4 QCD as a Gauge Theory Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora The Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local
More informationAs usual, these notes are intended for use by class participants only, and are not for circulation. Week 8: Lectures 15, 16
As usual, these notes are intended for use by class participants only, and are not for circulation. Week 8: Lectures 15, 16 Masses for Vectors: the Higgs mechanism April 6, 2012 The momentum-space propagator
More informationOUTLINE. CHARGED LEPTONIC WEAK INTERACTION - Decay of the Muon - Decay of the Neutron - Decay of the Pion
Weak Interactions OUTLINE CHARGED LEPTONIC WEAK INTERACTION - Decay of the Muon - Decay of the Neutron - Decay of the Pion CHARGED WEAK INTERACTIONS OF QUARKS - Cabibbo-GIM Mechanism - Cabibbo-Kobayashi-Maskawa
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks Cabibbo-GIM Mechanism Cabibbo-Kobayashi-Maskawa
More informationThe Higgs Mechanism and the Higgs Particle
The Higgs Mechanism and the Higgs Particle Heavy-Ion Seminar... or the Anderson-Higgs-Brout-Englert-Guralnik-Hagen-Kibble Mechanism Philip W. Anderson Peter W. Higgs Tom W. B. Gerald Carl R. François Robert
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks Cabibbo-GIM Mechanism Cabibbo-Kobayashi-Maskawa
More informationChapter 2 The Higgs Boson in the Standard Model of Particle Physics
Chapter The Higgs Boson in the Standard Model of Particle Physics.1 The Principle of Gauge Symmetries The principle of gauge symmetries can be motivated by the Lagrangian density of the free Dirac field,
More informationQuantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University
Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1
More information12.2 Problem Set 2 Solutions
78 CHAPTER. PROBLEM SET SOLUTIONS. Problem Set Solutions. I will use a basis m, which ψ C = iγ ψ = Cγ ψ (.47) We can define left (light) handed Majorana fields as, so that ω = ψ L + (ψ L ) C (.48) χ =
More informationNon Abelian Higgs Mechanism
Non Abelian Higgs Mechanism When a local rather than global symmetry is spontaneously broken, we do not get a massless Goldstone boson. Instead, the gauge field of the broken symmetry becomes massive,
More informationQuantum Field Theory 2 nd Edition
Quantum Field Theory 2 nd Edition FRANZ MANDL and GRAHAM SHAW School of Physics & Astromony, The University of Manchester, Manchester, UK WILEY A John Wiley and Sons, Ltd., Publication Contents Preface
More informationElectroweak Theory & Neutrino Scattering
Electroweak Theory & 01.12.2005 Electroweak Theory & Contents Glashow-Weinberg-Salam-Model Electroweak Theory & Contents Glashow-Weinberg-Salam-Model Electroweak Theory & Contents Glashow-Weinberg-Salam-Model
More informationIntroduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013
Introduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013 Rogerio Rosenfeld IFT-UNESP Lecture 1: Motivation/QFT/Gauge Symmetries/QED/QCD Lecture 2: QCD tests/electroweak
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 99890701 Allowed tools: mathematical tables Some formulas can be found on p.2. 1. Concepts.
More informationMasses and the Higgs Mechanism
Chapter 8 Masses and the Higgs Mechanism The Z, like the W ± must be very heavy. This much can be inferred immediately because a massless Z boson would give rise to a peculiar parity-violating long-range
More informationDetection Prospects of Doubly Charged Higgs Bosons from the Higgs Triplet Model at the LHC
UPTEC F11 44 Examensarbete 3 hp Juni 11 Detection Prospects of Doubly Charged Higgs Bosons from the Higgs Triplet Model at the LHC Viveca Lindahl Abstract Detection Prospects of Doubly Charged Higgs Bosons
More informationTHE STANDARD MODEL. Thomas Teubner. Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, U.K.
THE STANDARD MODEL Thomas Teubner Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, U.K. Lectures presented at the School for Young High Energy Physicists, Somerville College,
More informationFlavour Physics Lecture 1
Flavour Physics Lecture 1 Chris Sachrajda School of Physics and Astronomy University of Southampton Southampton SO17 1BJ UK New Horizons in Lattice Field Theory, Natal, Rio Grande do Norte, Brazil March
More informationA model of the basic interactions between elementary particles is defined by the following three ingredients:
I. THE STANDARD MODEL A model of the basic interactions between elementary particles is defined by the following three ingredients:. The symmetries of the Lagrangian; 2. The representations of fermions
More informationAs usual, these notes are intended for use by class participants only, and are not for circulation. Week 7: Lectures 13, 14.
As usual, these notes are intended for use by class participants only, and are not for circulation. Week 7: Lectures 13, 14 Majorana spinors March 15, 2012 So far, we have only considered massless, two-component
More informationIntroduction to gauge theory
Introduction to gauge theory 2008 High energy lecture 1 장상현 연세대학교 September 24, 2008 장상현 ( 연세대학교 ) Introduction to gauge theory September 24, 2008 1 / 72 Table of Contents 1 Introduction 2 Dirac equation
More informationAn Introduction to the Standard Model of Particle Physics
An Introduction to the Standard Model of Particle Physics W. N. COTTINGHAM and D. A. GREENWOOD Ж CAMBRIDGE UNIVERSITY PRESS Contents Preface. page xiii Notation xv 1 The particle physicist's view of Nature
More informationThe Role and Discovery of the Higgs
The Role and Discovery of the Higgs David Clarke Abstract This paper summarizes the importance of the Higgs boson in QFT and outlines experiments leading up to the discovery of the Higgs boson. First we
More informationIntercollegiate post-graduate course in High Energy Physics. Paper 1: The Standard Model
Brunel University Queen Mary, University of London Royal Holloway, University of London University College London Intercollegiate post-graduate course in High Energy Physics Paper 1: The Standard Model
More informationIntroduction to the Standard Model
Introduction to the Standard Model IMPRS Elementary Particle Physics MPP, January 16-19, 2018 W. HOLLIK MAX-PLANCK-INSTITUT ÜR PHYSIK, MÜNCHEN Outline 1. Elements of Quantum ield Theory 2. Gauge Theories
More informationTheory toolbox. Chapter Chiral effective field theories
Chapter 3 Theory toolbox 3.1 Chiral effective field theories The near chiral symmetry of the QCD Lagrangian and its spontaneous breaking can be exploited to construct low-energy effective theories of QCD
More informationWeak interactions and vector bosons
Weak interactions and vector bosons What do we know now about weak interactions? Theory of weak interactions Fermi's theory of weak interactions V-A theory Current - current theory, current algebra W and
More information1 Weak Interaction. Author: Ling fong Li. 1.1 Selection Rules in Weak Interaction
Author: ing fong i 1 Weak Interaction Classification Because the strong interaction effects are diffi cult to compute reliably we distinguish processe involving hadrons from leptons in weak interactions.
More informationTHE STANDARD MODEL. II. Lagrangians 7 A. Scalars 9 B. Fermions 10 C. Fermions and scalars 10
THE STANDARD MODEL Contents I. Introduction to the Standard Model 2 A. Interactions and particles 2 B. Problems of the Standard Model 4 C. The Scale of New Physics 5 II. Lagrangians 7 A. Scalars 9 B. Fermions
More informationMay 7, Physics Beyond the Standard Model. Francesco Fucito. Introduction. Standard. Model- Boson Sector. Standard. Model- Fermion Sector
- Boson - May 7, 2017 - Boson - The standard model of particle physics is the state of the art in quantum field theory All the knowledge we have developed so far in this field enters in its definition:
More informationPhysics 129 LECTURE 6 January 23, Particle Physics Symmetries (Perkins Chapter 3)
Physics 129 LECTURE 6 January 23, 2014 Particle Physics Symmetries (Perkins Chapter 3) n Lagrangian Deductions n Rotations n Parity n Charge Conjugation Gauge Invariance and Charge Conservation The Higgs
More informationThe Strong Interaction and LHC phenomenology
The Strong Interaction and LHC phenomenology Juan Rojo STFC Rutherford Fellow University of Oxford Theoretical Physics Graduate School course Lecture 2: The QCD Lagrangian, Symmetries and Feynman Rules
More informationLecture 6 The Super-Higgs Mechanism
Lecture 6 The Super-Higgs Mechanism Introduction: moduli space. Outline Explicit computation of moduli space for SUSY QCD with F < N and F N. The Higgs mechanism. The super-higgs mechanism. Reading: Terning
More information2.4 Parity transformation
2.4 Parity transformation An extremely simple group is one that has only two elements: {e, P }. Obviously, P 1 = P, so P 2 = e, with e represented by the unit n n matrix in an n- dimensional representation.
More informationParticle Physics. Dr Victoria Martin, Spring Semester 2013 Lecture 17: Electroweak and Higgs
Particle Physics Dr Victoria Martin, Spring Semester 013 Lecture 17: Electroweak and Higgs Weak Isospin and Weak Hypercharge Weak Isospin and Weak Hypercharge currents γ W ± Z 0 bosons Spontaneous Symmetry
More informationInvariant Mass Distributions of SUSY Cascade Decays
Invariant Mass Distributions of SUSY Cascade Decays Anders Kvellestad Department of Physics and Technology University of Bergen Master s Thesis in Theoretical Particle Physics June 0 ii Acknowledgements
More informationPHY 396 K. Problem set #11, the last set this semester! Due December 1, 2016.
PHY 396 K. Problem set #11, the last set this semester! Due December 1, 2016. In my notations, the A µ and their components A a µ are the canonically normalized vector fields, while the A µ = ga µ and
More informationQFT Dimensional Analysis
QFT Dimensional Analysis In the h = c = 1 units, all quantities are measured in units of energy to some power. For example m = p µ = E +1 while x µ = E 1 where m stands for the dimensionality of the mass
More informationFundamental Physics: Quantum Field Theory
Mobolaji Williams (mwilliams@physics.harvard.edu x) First Version: June 1, 216 Fundamental Physics: Quantum Field Theory What is the topic? Quantum field theory refers to the quantum theory of fields in
More informationPhysics 582, Problem Set 1 Solutions
Physics 582, Problem Set 1 Solutions TAs: Hart Goldman and Ramanjit Sohal Fall 2018 1. THE DIRAC EQUATION [20 PTS] Consider a four-component fermion Ψ(x) in 3+1D, L[ Ψ, Ψ] = Ψ(i/ m)ψ, (1.1) where we use
More informationLectures on Chiral Perturbation Theory
Lectures on Chiral Perturbation Theory I. Foundations II. Lattice Applications III. Baryons IV. Convergence Brian Tiburzi RIKEN BNL Research Center Chiral Perturbation Theory I. Foundations Low-energy
More informationThe Higgs discovery - a portal to new physics
The Higgs discovery - a portal to new physics Department of astronomy and theoretical physics, 2012-10-17 1 / 1 The Higgs discovery 2 / 1 July 4th 2012 - a historic day in many ways... 3 / 1 July 4th 2012
More informationSymmetry Groups conservation law quantum numbers Gauge symmetries local bosons mediate the interaction Group Abelian Product of Groups simple
Symmetry Groups Symmetry plays an essential role in particle theory. If a theory is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. For example,
More informationFundamental Symmetries - l
National Nuclear Physics Summer School MIT, Cambridge, MA July 18-29 2016 Fundamental Symmetries - l Vincenzo Cirigliano Los Alamos National Laboratory Goal of these lectures Introduce the field of nuclear
More informationQFT Dimensional Analysis
QFT Dimensional Analysis In h = c = 1 units, all quantities are measured in units of energy to some power. For example m = p µ = E +1 while x µ = E 1 where m stands for the dimensionality of the mass rather
More informationTHE STANDARD MODEL OF PARTICLE PHYSICS
THE STANDARD MODEL OF PARTICLE PHYSICS P.J. Mulders Department of Theoretical Physics, Faculty of Sciences, Vrije Universiteit, 08 HV Amsterdam, the Netherlands E-mail: mulders@few.vu.nl Lectures given
More informationTwo Fundamental Principles of Nature s Interactions
Two Fundamental Principles of Nature s Interactions Tian Ma, Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/ fluid I. Gravity and Principle of Interaction Dynamics PID)
More informationHiggs Physics from the Lattice Lecture 1: Standard Model Higgs Physics
Higgs Physics from the Lattice Lecture 1: Standard Model Higgs Physics Julius Kuti University of California, San Diego INT Summer School on Lattice QCD and its applications Seattle, August 8-28, 2007 Julius
More informationFermions of the ElectroWeak Theory
Fermions of the ElectroWeak Theory The Quarks, The eptons, and their Masses. This is my second set of notes on the Glashow Weinberg Salam theory of weak and electromagnetic interactions. The first set
More informationElectroweak Theory: 3
Electroweak Theory: 3 Introduction QED The Fermi theory The standard model Precision tests CP violation; K and B systems Higgs physics Prospectus STIAS January, 2011 Paul Langacker IAS 55 References Slides
More informationLecture 16 V2. October 24, 2017
Lecture 16 V2 October 24, 2017 Recap: gamma matrices Recap: pion decay properties Unifying the weak and electromagnetic interactions Ø Recap: QED Lagrangian for U Q (1) gauge symmetry Ø Introduction of
More informationLecture II. QCD and its basic symmetries. Renormalisation and the running coupling constant
Lecture II QCD and its basic symmetries Renormalisation and the running coupling constant Experimental evidence for QCD based on comparison with perturbative calculations The road to QCD: SU(3) quark model
More informationThe Standard Model and beyond
The Standard Model and beyond In this chapter we overview the structure of the Standard Model (SM) of particle physics, its shortcomings, and different ideas for physics beyond the Standard Model (BSM)
More informationThis means that n or p form a doublet under isospin transformation. Isospin invariance simply means that. [T i, H s ] = 0
1 QCD 1.1 Quark Model 1. Isospin symmetry In early studies of nuclear reactions, it was found that, to a good approximation, nuclear force is independent of the electromagnetic charge carried by the nucleons
More informationEffective Field Theory
Effective Field Theory Iain Stewart MIT The 19 th Taiwan Spring School on Particles and Fields April, 2006 Physics compartmentalized Quantum Field Theory String Theory? General Relativity short distance
More informationThe Standard Model Part. II
Our Story Thus Far The Standard Model Part. II!!We started with QED (and!)!!we extended this to the Fermi theory of weak interactions! Adding G F!!Today we will extended this to Glashow-Weinberg-Salam
More informationFundamental Symmetries - 2
HUGS 2018 Jefferson Lab, Newport News, VA May 29- June 15 2018 Fundamental Symmetries - 2 Vincenzo Cirigliano Los Alamos National Laboratory Plan of the lectures Review symmetry and symmetry breaking Introduce
More informationUnified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy
Unified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy Tian Ma, Shouhong Wang Supported in part by NSF and ONR http://www.indiana.edu/ fluid 1 Outline I. Motivations II.
More informationSISSA entrance examination (2007)
SISSA Entrance Examination Theory of Elementary Particles Trieste, 18 July 2007 Four problems are given. You are expected to solve completely two of them. Please, do not try to solve more than two problems;
More informationThe Dirac Field. Physics , Quantum Field Theory. October Michael Dine Department of Physics University of California, Santa Cruz
Michael Dine Department of Physics University of California, Santa Cruz October 2013 Lorentz Transformation Properties of the Dirac Field First, rotations. In ordinary quantum mechanics, ψ σ i ψ (1) is
More informationChiral Anomaly. Kathryn Polejaeva. Seminar on Theoretical Particle Physics. Springterm 2006 Bonn University
Chiral Anomaly Kathryn Polejaeva Seminar on Theoretical Particle Physics Springterm 2006 Bonn University Outline of the Talk Introduction: What do they mean by anomaly? Main Part: QM formulation of current
More informationTheory of Elementary Particles homework VIII (June 04)
Theory of Elementary Particles homework VIII June 4) At the head of your report, please write your name, student ID number and a list of problems that you worked on in a report like II-1, II-3, IV- ).
More informationElectroweak Theory, SSB, and the Higgs: Lecture 2
1 Electroweak Theory, SSB, and the iggs: Lecture Spontaneous symmetry breaking (iggs mechanism) - Gauge invariance implies massless gauge bosons and fermions - Weak interactions short ranged spontaneous
More informationPart III The Standard Model
Part III The Standard Model Theorems Based on lectures by C. E. Thomas Notes taken by Dexter Chua Lent 2017 These notes are not endorsed by the lecturers, and I have modified them (often significantly)
More informationAdding families: GIM mechanism and CKM matrix
Particules Élémentaires, Gravitation et Cosmologie Année 2007-08 08 Le Modèle Standard et ses extensions Cours VII: 29 février f 2008 Adding families: GIM mechanism and CKM matrix 29 fevrier 2008 G. Veneziano,
More informationCurrent knowledge tells us that matter is made of fundamental particle called fermions,
Chapter 1 Particle Physics 1.1 Fundamental Particles Current knowledge tells us that matter is made of fundamental particle called fermions, which are spin 1 particles. Our world is composed of two kinds
More informationParticle Physics Status and Perspectives
Particle Physics Status and Perspectives 142.095 Claudia-Elisabeth Wulz Institute of High Energy Physics Austrian Academy of Sciences c/o CERN/PH, CH-1211 Geneva 23 Tel. 0041 22 767 6592, GSM: 0041 75
More informationQuantum Field Theory I Examination questions will be composed from those below and from questions in the textbook and previous exams
Quantum Field Theory I Examination questions will be composed from those below and from questions in the textbook and previous exams III. Quantization of constrained systems and Maxwell s theory 1. The
More informationLecture 8. September 21, General plan for construction of Standard Model theory. Choice of gauge symmetries for the Standard Model
Lecture 8 September 21, 2017 Today General plan for construction of Standard Model theory Properties of SU(n) transformations (review) Choice of gauge symmetries for the Standard Model Use of Lagrangian
More informationElectroweak Theory and Higgs Mechanism
Electroweak Theory and Higgs Mechanism Stefano Pozzorini 016 CTEQ & MCnet School, DESY Hamburg 7 July 016 Standard Model of Particle Physics Gauge interactions (3 parameters) SU(3) SU() U(1) symmetry,
More informationTHE STANDARD MODEL AND THE GENERALIZED COVARIANT DERIVATIVE
THE STANDAD MODEL AND THE GENEALIZED COVAIANT DEIVATIVE arxiv:hep-ph/9907480v Jul 999 M. Chaves and H. Morales Escuela de Física, Universidad de Costa ica San José, Costa ica E-mails: mchaves@cariari.ucr.ac.cr,
More informationA UNITARY AND RENORMALIZABLE THEORY OF THE STANDARD MODEL IN GHOST-FREE LIGHT-CONE GAUGE 1. Prem P. Srivastava a,b,c 2. Stanley J.
SLAC-PUB-9137 FERMILAB-Pub-0/00-T February 00 A UNITARY AND RENORMALIZABLE THEORY OF THE STANDARD MODEL IN GHOST-FREE LIGHT-CONE GAUGE 1 Prem P. Srivastava a,b,c and Stanley J. Brodsky c 3 a Instituto
More informationAxions Theory SLAC Summer Institute 2007
Axions Theory p. 1/? Axions Theory SLAC Summer Institute 2007 Helen Quinn Stanford Linear Accelerator Center Axions Theory p. 2/? Lectures from an Axion Workshop Strong CP Problem and Axions Roberto Peccei
More informationMeasurement of electroweak W + Jets Production and Search for anomalous Triple Gauge Boson Couplings with the ATLAS Experiment at s = 8 TeV
Bergische Universität Wuppertal Fakultät 4 - Mathematik und Naturwissenschaften Measurement of electroweak W + Jets Production and Search for anomalous Triple Gauge Boson Couplings with the ATLAS Experiment
More informationInteractions... + similar terms for µ and τ Feynman rule: gauge-boson propagator: ig 2 2 γ λ(1 γ 5 ) = i(g µν k µ k ν /M 2 W ) k 2 M 2 W
Interactions... L W-l = g [ νγµ (1 γ 5 )ew µ + +ēγ µ (1 γ 5 )νwµ ] + similar terms for µ and τ Feynman rule: e λ ig γ λ(1 γ 5 ) ν gauge-boson propagator: W = i(g µν k µ k ν /M W ) k M W. Chris Quigg Electroweak
More informationLectures on the Symmetries and Interactions of Particle Physics
Lectures on the Symmetries and Interactions of Particle Physics James D. Wells CERN Theory, Geneva, Switzerland, and Physics Department, University of Michigan, Ann Arbor, MI USA July 4-10, 013, CERN Summer
More information