Post on 30-Jul-2018
Introduction to the Standard Model
• Origins of the Electroweak Theory
• Gauge Theories
• The Standard Model
References: 2008 TASI lectures: arXiv:0901.0241 [hep-ph] and The Standard Model and Beyond, CRC Press
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
The Weak Interactions
• Radioactivity (Becquerel, 1896)
• β decay appeared to violate energy(Meitner, Hahn; 1911)
• Neutrino hypothesis (Pauli, 1930)
– νe (Reines, Cowan; 1953)
– νµ (Lederman, Schwartz, Steinberger;1962)
– ντ (DONUT, 2000) (τ , 1975)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Fermi theory (1933)
– Loosely like QED, but zero range (non-renormalizable) and non-diagonal (charged current)
pe!
!e
n
J†µ Jµ
e! !e
!e e!
Jµ J†µ e! !e
!e e!
!e e!
"W !
pe!
!e
n
g g "W +
e! !e
!e e!
g g
– Typeset by FoilTEX – 1
H ∼ GFJ†µJµ
J†µ ∼ pγµn+νeγµe− [n→ p, e−→ νe]
Jµ ∼ nγµp+eγµνe [p→ n, νe→ e− ( × → e−νe)]
GF ' 1.17×10−5 GeV−2 [Fermi constant]
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Fermi theory modified to include
– parity violation (V −A) (Lee, Yang; Wu; Feynman-Gell-Mann)
– µ, τ decay
– strangeness (Cabibbo)
– quark model
– heavy quarks and CP violation (CKM)
– ν mass and mixing
• Fermi theory correctly describes (at tree level)
– Nuclear/neutron β decay/inverse (n→ pe−νe; e−p→ νen)
– µ, τ decays (µ− → e−νeνµ; τ− → µ−νµντ , ντπ−, · · · )
– π, K decays (π+ → µ+νµ, π0e+νe; K+ → µ+νµ, π
0e+νe, π+π0)
– hyperon decays (Λ→ pπ−; Σ− → nπ−; Σ+ → Λe+νe)
– heavy quark decays (c→ se+νe; b→ cµ−νµ, cπ−)
– ν scattering (νµe− → µ−νe; νµn→ µ
−p︸ ︷︷ ︸
“elastic′′
; νµN → µ−X︸ ︷︷ ︸
deep−inelastic
)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Fermi theory violates unitarity at high energy (non-renormalizable)
pe!
!e
n
J†µ Jµ
e! !e
!e e!
Jµ J†µ e! !e
!e e!
!e e!
"W !
pe!
!e
n
g g "W +
e! !e
!e e!
g g
– Typeset by FoilTEX – 1
– σ(νee−→ e−νe)→
G2F s
π(s ≡ E2
CM)
– pure S-wave unitarity: σ < 16πs
– fails for ECM2≥√
πGF∼ 500 GeV
– Born not unitary; often restored by H.O.T.
– Fermi theory: divergent integrals∫d4k
( 6kk2
)( 6kk2
)p
e!
!e
n
J†µ Jµ
e! !e
!e e!
Jµ J†µ e! !e
!e e!
!e e!
"W !
pe!
!e
n
g g "W +
e! !e
!e e!
g g
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Intermediate vector boson theory (Yukawa, 1935; Schwinger, 1957)
pe!
!e
n
J†µ Jµ
e! !e
!e e!
Jµ J†µ e! !e
!e e!
!e e!
"W !
pe!
!e
n
g g "W +
e! !e
!e e!
g g
– Typeset by FoilTEX – 1
pe!
!e
n
J†µ Jµ
e! !e
!e e!
Jµ J†µ e! !e
!e e!
!e e!
"W !
pe!
!e
n
g g "W +
e! !e
!e e!
g g
– Typeset by FoilTEX – 1
GF√2∼
g2
8M2W
for MW � Q
– no longer pure S-wave ⇒
– νee−→ νee
− better behaved
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
!e
W ! W +
e! e+
g g W 0
W ! W +
e! e+
g
g
Z
d s
d sK0
K0
– Typeset by FoilTEX – 2
– but, e+e− → W+W− violatesunitarity for
√s & 500 GeV
– εµ ∼ kµ/MW for longitudinalpolarization (non-renormalizable)
– introduce W 0 to cancel
– fixes W 0W+W− and e+e−W 0
vertices
– requires[J, J†
]∼ J0
(like SU(2))
– not realistic
!e
W ! W +
e! e+
g g W 0
W ! W +
e! e+
g
g
Z
d s
d sK0
K0
– Typeset by FoilTEX – 2
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Glashow model (1961) (W±, Z, γ, but no mechanism for MW,Z)
• Weinberg-Salam (1967): Higgs mechanism → MW,Z
• Renormalizable (1971) (’t Hooft, · · · )
• Flavor changing neutral currents (FCNC)
– very large K0 ↔ K0 mixing
– GIM mechanism (c quark)(1970)
– c discovered (1974)
Z
s d
d sK0
K0
K0
K0
u u
W
W
d s
s d
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Weak neutral current(1973)
• QCD (1970’s)
• W,Z (1983)
• Precision tests (1989-2000)
• CKM unitarity (∼ 1995-)
• t quark (1995)
• ν mass (1998-2002)
Measurement Fit |Omeas−Ofit|/σmeas
0 1 2 3
0 1 2 3
∆αhad(mZ)∆α(5) 0.02758 ± 0.00035 0.02768mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1875ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4957σhad [nb]σ0 41.540 ± 0.037 41.477RlRl 20.767 ± 0.025 20.744AfbA0,l 0.01714 ± 0.00095 0.01645Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1481RbRb 0.21629 ± 0.00066 0.21586RcRc 0.1721 ± 0.0030 0.1722AfbA0,b 0.0992 ± 0.0016 0.1038AfbA0,c 0.0707 ± 0.0035 0.0742AbAb 0.923 ± 0.020 0.935AcAc 0.670 ± 0.027 0.668Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1481sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.398 ± 0.025 80.374ΓW [GeV]ΓW [GeV] 2.140 ± 0.060 2.091mt [GeV]mt [GeV] 170.9 ± 1.8 171.3
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Gauge Theories
Standard Model is remarkably successful gauge theory of themicroscopic interactions
• Gauge symmetry⇒ (apparently) massless spin-1 (vector, gauge) bosons
• Interactions ⇔ group, representations, gauge coupling
• Like QED (U(1)), but gauge self interactions for non-abelian
• Application to strong (short range) ⇒ confinement
• Application to weak (short range)⇒ spontaneous symmetry breaking(Higgs or dynamical)
• Unique renormalizable field theory for spin-1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
QED
• Free electron equation,(iγµ
∂
∂xµ−m
)ψ = 0,
is invariant under U(1) (phase) transformations,(iγµ
∂
∂xµ−m
)ψ′ = 0, where ψ′ ≡ e−iβψ
• Not invariant under local (gauge) transf.,
ψ → ψ′ ≡ e−iβ(x)ψ, x ≡ (~x, t)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Introduce vector field Aµ ≡ ( ~A, φ):(iγµ
∂
∂xµ+eγµAµ −m
)ψ = 0,
(e > 0 is gauge coupling) is invariant under
ψ → e−iβ(x)ψ, Aµ→ Aµ −1
e
∂β
∂xµ
• Quantization of Aµ ⇒ massless gaugeboson
• Gauge invariance ⇒ γ, long rangeforce, prescribed (up to e) amplitudefor emission/absorption
!
e! p
e! p
e e
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Non-Abelian
• n non-interacting fermions of same mass m:(iγµ
∂
∂xµ−m
)ψa = 0, a = 1 · · ·n,
invariant under (global) SU(n) group, ψ1...ψn
→ exp(i
N∑i=1
βiLi)
ψ1...ψn
.Li are n×n generator matrices (N = n2−1); βi are real parameters
[Li, Lj] = icijkLk
(cijk are structure constants)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Gauge (local) transformation: βi→ βi(x)⇒(iγµ
∂
∂xµδab−g
N∑i=1
γµAiµLiab −mδab
)ψb = 0
• Invariant under
Φ ≡
ψ1...ψn
→ Φ′ ≡ UΦ
~Aµ · ~L → ~A′µ · ~L ≡ U ~Aµ · ~LU−1 +i
g(∂µU)U−1
U ≡ ei~β·~L
(1)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• Gauge invariance implies:
– N (apparently) massless gaugebosons Aiµ
– Specified interactions (up to gaugecoupling g, group, representations),including self interactions
Aiµ
!b
!a
!igLiab"
µ
– Typeset by FoilTEX – 1
g g2
– Typeset by FoilTEX – 1
• Generalize to other groups, representations, chiral (L 6= R)
– Chiral Projections: ψL(R) ≡ 12(1∓ γ5)ψ
(Chirality = helicity up to O(m/E))
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
The Standard Model
• Gauge group SU(3)× SU(2)× U(1); gauge couplings gs, g, g′(ud
)L
(ud
)L
(ud
)L
(νee−
)L
uR uR uR νeR(?)
dR dR dR e−R( L = left-handed, R = right-handed)
• SU(3): u ↔ u ↔ u, d ↔ d ↔ d (8 gluons)
• SU(2): uL↔ dL, νeL↔ e−L (W±); phases (W 0)
• U(1): phases (B)
• Heavy families (c, s, νµ, µ−), (t, b, ντ , τ
−)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Quantum Chromodynamics (QCD)
LSU(3) = −1
4F iµνF
iµν +∑r
qαr i 6Dβα qrβ
F 2 term leads to three and four-point gluon self-interactions.
F iµν = ∂µGiν − ∂νG
iµ − gsfijk G
jµ G
kν
is field strength tensor for the gluon fields Giµ, i = 1, · · · , 8.
gs = QCD gauge coupling constant. No gluon masses.
Structure constants fijk (i, j, k = 1, · · · , 8), defined by
[λi, λj] = 2ifijkλk
where λi are the Gell-Mann matrices.
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
λi =
(τ i 0
0 0
), i = 1, 2, 3
λ4 =
0 0 1
0 0 0
1 0 0
λ5 =
0 0 −i0 0 0
i 0 0
λ6 =
0 0 0
0 0 1
0 1 0
λ7 =
0 0 0
0 0 −i0 i 0
λ8 = 1√
3
1 0 0
0 1 0
0 0 −2
The SU(3) (Gell-Mann) matrices.
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Quark interactions given by qαr i 6Dβα qrβ
qr = rth quark flavor; α, β = 1, 2, 3 are color indices
Gauge covariant derivative
Dµβα = (Dµ)αβ = ∂µδαβ + igs G
iµ Liαβ,
for triplet representation matrices Li = λi/2.
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Quark color interactions:
Diagonal in flavor
Off diagonal in color
Purely vector (parity conserving)
Giµ
u!
u"
!igs2 #i
"!$µ
– Typeset by FoilTEX – 1
Bare quark mass allowed by QCD, but forbidden by chiral symmetryof LSU(2)×U(1) (generated by spontaneous symmetry breaking)
Additional ghost and gauge-fixing terms
Can add (unwanted) CP-violating term
Lθ =θg2s
32π2FiµνF
iµν, F iµν ≡ 12εµναβF iαβ
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
QCD now very well established
• Short distance behavior (asymptotic freedom)
• Confinement, light hadron spectrum (lattice)
– gs = O(1) (αs(MZ) = g2s/4π ∼ 0.12)
– Strength + gluon self-interactions⇒ confinement
– Yukawa model ⇒ dipole-dipole
• Approximate global SU(3)L × SU(3)R symmetry and breaking(π,K, η are pseudo-goldstone bosons)
• Unique field theory of strong interactions
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Quasi-Chiral Exotics
(J. Kang, PL, B. Nelson, in progress)
• Exotic fermions (anomaly-cancellation)
• Examples in 27-plet of E6
– DL + DR (SU(2) singlets, chiral wrt U(1)!)
–
!E0
E"
"
L
+
!E0
E"
"
R
(SU(2) doublets, chiral wrt U(1)!)
• Pair produce D + D by QCD processes (smaller rate for exotic leptons)
• Lightest may decay by mixing; by diquark or leptoquark coupling;or be quasi-stable
22nd Henry Primako! Lecture Paul Langacker (3/1/2006)
Quantum Chromodynamics (QCD)
Modern theory of the strong interactions
NYS APS (October 15, 2004) Paul Langacker (Penn)
9. Quantum chromodynamics 7
0.1 0.12 0.14
Average
Hadronic Jets
Polarized DIS
Deep Inelastic Scattering (DIS)
! decays
Z width
Fragmentation
Spectroscopy (Lattice)
ep event shapes
Photo-production
" decay
e+e
- rates
#s(M
Z)
Figure 9.1: Summary of the value of !s(MZ) from various processes. The valuesshown indicate the process and the measured value of !s extrapolated to µ = MZ .The error shown is the total error including theoretical uncertainties. The averagequoted in this report which comes from these measurements is also shown. See textfor discussion of errors.
theoretical estimates. If the nonperturbative terms are omitted from the fit, the extractedvalue of !s(m! ) decreases by ! 0.02.
For !s(m! ) = 0.35 the perturbative series for R! is R! ! 3.058(1+0.112+0.064+0.036).The size (estimated error) of the nonperturbative term is 20% (7%) of the size of theorder !3
s term. The perturbation series is not very well convergent; if the order !3s term
is omitted, the extracted value of !s(m! ) increases by 0.05. The order !4s term has been
estimated [47] and attempts made to resum the entire series [48,49]. These estimates canbe used to obtain an estimate of the errors due to these unknown terms [50,51]. Anotherapproach to estimating this !4
s term gives a contribution that is slightly larger than the!3
s term [52].R! can be extracted from the semi-leptonic branching ratio from the relation
R! = 1/(B(" " e##) # 1.97256); where B(" " e##) is measured directly or extractedfrom the lifetime, the muon mass, and the muon lifetime assuming universality of lepton
December 20, 2005 11:23
18 9. Quantum chromodynamics
0
0.1
0.2
0.3
1 10 102
µ GeV!
s(µ
)
Figure 9.2: Summary of the values of !s(µ) at the values of µ where they aremeasured. The lines show the central values and the ±1" limits of our average.The figure clearly shows the decrease in !s(µ) with increasing µ. The data are,in increasing order of µ, # width, $ decays, deep inelastic scattering, e+e! eventshapes at 22 GeV from the JADE data, shapes at TRISTAN at 58 GeV, Z width,and e+e! event shapes at 135 and 189 GeV.
The value of !s at any scale corresponding to our average can be obtainedfrom http://www-theory.lbl.gov/!ianh/alpha/alpha.html which uses Eq. (9.5) tointerpolate.
References:1. R.K. Ellis et al., “QCD and Collider Physics” (Cambridge 1996).2. For reviews see, for example, A.S. Kronfeld and P.B. Mackenzie, Ann. Rev. Nucl.
and Part. Sci. 43, 793 (1993);H. Wittig, Int. J. Mod. Phys. A12, 4477 (1997).
3. For example see, P. Gambino, International Conference on Lepton PhotonInteractions, Fermilab, USA, (2003); J. Butterworth International Conference onLepton Photon Interactions, Upsala, Sweden, (2005).
December 20, 2005 11:23
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
The Electroweak Sector
LSU(2)×U(1) = Lgauge + Lϕ + Lf + LYukawa
Gauge part
Lgauge = −1
4F iµνF
µνi −1
4BµνB
µν
Field strength tensors
Bµν = ∂µBν − ∂νBµF iµν = ∂µW
iν − ∂νW
iµ − gεijkW
jµW
kν , i = 1 · · · 3
g(g′) is SU(2) (U(1)) gauge coupling; εijk is totally antisymmetric symbol
Three and four-point self-interactions for the Wi
B and W3 will mix to form γ, Z
g g2
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
U(1): Φj → exp(ig′yjβ)Φj, yj = qj − t3j = weak hypercharge
Scalar part
Lϕ = (Dµϕ)†Dµϕ− V (ϕ)
where ϕ =
(ϕ+
ϕ0
)is the (complex) Higgs doublet with yϕ = 1/2.
Gauge covariant derivative:
Dµϕ =
(∂µ + ig
τ i
2W iµ +
ig′
2Bµ
)ϕ
where τ i are the Pauli matrices
Three and four-point interactionsbetween gauge and scalar fields g g2
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Higgs potential
V (ϕ) = +µ2ϕ†ϕ+ λ(ϕ†ϕ)2
Allowed by renormalizability and gaugeinvariance
Spontaneous symmetry breaking for µ2 < 0
Vacuum stability: λ > 0.
Quartic self-interactions!+
!0
!!
!0
"
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Fermion part
LF =
F∑m=1
(q0mLi 6Dq
0mL + l0mLi 6Dl
0mL
+ u0mRi 6Du
0mR + d0
mRi 6Dd0mR + e0
mRi 6De0mR+ν0
mRi 6Dν0mR
)L-doublets
q0mL =
(u0m
d0m
)L
l0mL =
(ν0m
e−0m
)L
R-singlets
u0mR, d
0mR, e
−0mR, ν
0mR(?)
(F ≥ 3 families; m = 1 · · ·F = family index;0 = weak eigenstates (definite SU(2) rep.), mixtures of mass eigenstates (flavors);
quark color indices α = r, g, b suppressed (e.g., u0mαL). )
Can add gauge singlet ν0mR for Dirac neutrino mass term
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Different (chiral) L and R representations lead to parity and chargeconjugation violation (maximal for SU(2))
Fermion mass terms forbidden by chiral symmetry
Triangle anomalies absent for chosen hypercharges (quark-leptoncancellations)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Gauge covariant derivatives
Dµq0mL =
(∂µ +
ig
2τ iW i
µ + ig′
6Bµ
)q0mL
Dµl0mL =
(∂µ +
ig
2τ iW i
µ − ig′
2Bµ
)l0mL
Dµu0mR =
(∂µ + i
2
3g′Bµ
)u0mR
Dµd0mR =
(∂µ − i
g′
3Bµ
)d0mR
Dµe0mR = (∂µ − ig′Bµ) e0
mR
Read off W and Bcouplings to fermions W i
µ
!ig2! i"µ
“1!"5
2
”
Bµ!ig"y"µ
“1#"5
2
”
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Spontaneous Symmetry Breaking (Higgs mechanism)
Higgs covariant kinetic energy terms:
(Dµϕ)†Dµϕ =1
2(0 ν)
[g
2τ iW i
µ +g′
2Bµ
]2(0ν
)+H terms
→ M2WW
+µW−µ +M2Z
2ZµZµ
+ H kinetic energy and gauge interaction terms
W
W
!
!
g2
eR
eL
!he
– Typeset by FoilTEX – 1
MW =gν
2
me =heν√
2W
W
!
!
g2
eR
eL
!he
– Typeset by FoilTEX – 1
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Mass eigenstate bosons: W, Z, and A (photon)
W± =1√
2(W 1 ∓ iW 2)
Z = − sin θWB + cos θWW3
A = cos θWB + sin θWW3
Weak angle: tan θW ≡ g′/g
Masses:
MW =gν
2, MZ =
√g2 + g′2
ν
2=
MW
cos θW, MA = 0
(Goldstone scalars “eaten”→ longitudinal components of W±, Z )
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Will show: Fermi constant GF/√
2 ∼ g2/8M2W
(GF = 1.166367(5)× 10−5 GeV −2 from muon lifetime)
Electroweak scale:
ν = 2MW/g ' (√
2GF )−1/2 ' 246 GeV
Will show: g = e/ sin θW (α = e2/4π ∼ 1/137.036) ⇒
MW = MZ cos θW =gν
2∼
(πα/√
2GF )1/2
sin θW
Weak neutral current: sin2 θW ∼ 0.23 ⇒ MW ∼ 78 GeV , andMZ ∼ 89 GeV (increased by ∼ 2 GeV by loop corrections)
Discovered at CERN: UA1 and UA2, 1983
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
The Weak Charged Current
Fermi Theory incorporated in SM and made renormalizable
W -fermion interaction
L = −g
2√
2
(JµWW
−µ + Jµ†WW
+µ
)
Charge-raising current (ignoring ν masses)
Jµ†W =
F∑m=1
[ν0mγ
µ(1− γ5)e0m + u0
mγµ(1− γ5)d0
m
]= (νeνµντ)γ
µ(1− γ5)
e−
µ−
τ−
+ (u c t)γµ(1− γ5)V
dsb
.23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Ignore ν masses for now
Pure V − A ⇒ maximal P and C violation; CP conserved exceptfor phases in V
V = Au†L AdL is F × F unitary Cabibbo-Kobayashi-Maskawa (CKM)
matrix from mismatch between weak and Yukawa interactions
Cabibbo matrix for F = 2
V =
(cos θc sin θc− sin θc cos θc
)
sin θc ' 0.22 ≡ Cabibbo angle
Good zeroth-order description since third family almost decouples
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
CKM matrix for F = 3 involves 3 angles and 1 CP -violating phase(after removing unobservable qL phases) (new interations involving qR
could make observable)
V =
Vud Vus VubVcd Vcs VcbVtd Vtd Vtd
Extensive studies, especially in B decays, to test unitarity of V as
probe of new physics and test origin of CP violation
Need additional source of CP breaking for baryogenesis
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Effective zero- range 4-fermi interaction (Fermi theory)
For |Q| � MW ,neglect Q2 in Wpropagator
−Lcceff =
(g
2√
2
)2
JµW
( −gµνQ2 −M2
W
)J†νW ∼
g2
8M2W
JµWJ†Wµ
Fermi constant: GF√2' g2
8M2W
= 12ν2
Muon lifetime: τ−1 =G2Fm
5µ
192π3 ⇒ GF = 1.17× 10−5 GeV−2
Weak scale: ν =√
2〈0|ϕ0|0〉 ' 246 GeV
Excellent description of β, K, hyperon, heavy quark, µ, and τdecays, νµe→ µ−νe, νµn→ µ−p, νµN → µ−X
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Full theory probed:
e±p→(−)ν e X at high energy (HERA)
Electroweak radiative corrections (loop level)(Very important. Only calculable in full theory.)
MKS −MKL, kaon CP violation, B ↔ B mixing (loop level)
-1.5
-1
-0.5
0
0.5
1
1.5
-1 -0.5 0 0.5 1 1.5 2
sin 2!
sol. w/ cos 2! < 0(excl. at CL > 0.95)
excluded at CL > 0.95
"
"
#
#
$md
$ms & $md
%K
%K
|Vub/Vcb|
sin 2!
sol. w/ cos 2! < 0(excl. at CL > 0.95)
excluded at CL > 0.95
#
!"
&
'
excluded area has CL > 0.95
C K Mf i t t e r
EPS 2005
(CKMFITTER group:
http://ckmfitter.in2p3.fr/)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Quantum Electrodynamics (QED)
Incorporated into standard model
Lagrangian:
L = −gg′√g2 + g′2
JµQ(cos θWBµ + sin θWW3µ)
Photon field:
Aµ = cos θWBµ + sin θWW3µ
Positron electric charge: e = g sin θW , where tan θW ≡ g′/g
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Electromagnetic current:
JµQ =
F∑m=1
[2
3u0mγ
µu0m −
1
3d0mγ
µd0m − e
0mγ
µe0m
]
=
F∑m=1
[2
3umγ
µum −1
3dmγ
µdm − emγµem]
Electric charge: Q = T 3 + Y , where Y = weak hypercharge(coefficient of ig′Bµ in covariant derivatives)
Flavor diagonal: Same form in weak and mass bases because fieldswhich mix have same charge
Purely vector (parity conserving): L and R fields have same charge(qi = t3i + yi is the same for L and R fields, even though t3i and yi are not)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Experiment Value of α−1 Precision ∆e
ae = (ge − 2)/2 137.035 999 683 (94) [6.9× 10−10] –
h/m (Rb, Cs) 137.035 999 35 (69) [5.0× 10−9] 0.33± 0.69
Quantum Hall 137.036 003 0 (25) [1.8× 10−8] −3.3± 2.5
h/m (neutron) 137.036 007 7 (28) [2.1× 10−8] −8.0± 2.8
γp,3He
(J. J.) 137.035 987 5 (43) [3.1× 10−8] 12.2± 4.3
µ+e− hyperfine 137.036 001 7 (80) [5.8× 10−8] −2.0± 8.0
Spectacularly successful:
Most precise: e anomalous magnetic moment → α
Many low energy tests to few ×10−8
mγ < 6× 10−17 eV, qγ < 5× 10−30|e|Running α(Q2) observed
Muon g − 2 sensitive to new physics. Anomaly?
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
The Weak Neutral Current
Prediction of SU(2)× U(1)
L = −√g2 + g′2
2JµZ
(− sin θWBµ + cos θWW
3µ
)= −
g
2 cos θWJµZZµ
Neutral current process and effective 4-fermi interaction for|Q| �MZ
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Neutral current:
JµZ =∑m
[u0mLγ
µu0mL − d
0mLγ
µd0mL + ν0
mLγµν0mL − e
0mLγ
µe0mL
]−2 sin2 θWJ
µQ
=∑m
[umLγ
µumL − dmLγµdmL + νmLγµνmL − emLγµemL
]−2 sin2 θWJ
µQ
Flavor diagonal: Same form in weak and mass bases because fieldswhich mix have same charge
GIM mechanism: c quark predicted so that sL could be in doubletto avoid unwanted flavor changing neutral currents (FCNC) attree and loop level
Parity and charge conjugation violated but not maximally: first termis pure V −A, second is V
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
Effective 4-fermi interaction for |Q2| �M2Z:
−LNCeff =GF√
2JµZJZµ
Coefficient same as WCC because
GF√2
=g2
8M2W
=g2 + g′2
8M2Z
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
10
10 2
10 3
10 4
10 5
0 20 40 60 80 100 120 140 160 180 200 220
Centre-of-mass energy (GeV)
Cro
ss-s
ecti
on (
pb)
CESRDORIS
PEP
PETRATRISTAN
KEKBPEP-II
SLC
LEP I LEP II
Z
W+W-
e+e−→hadrons
0.0001 0.001 0.01 0.1 1 10 100 1000 10000µ [GeV]
0.228
0.23
0.232
0.234
0.236
0.238
0.24
0.242
0.244
0.246
0.248
0.25
sin2 !
W(µ
)
QW(APV)QW(e)
"-DIS
LEP 1SLC
Tevatron
e-DIS
MOLLER
Qweak
0
10
20
30
160 180 200
!s (GeV)
"W
W (
pb
)
YFSWW/RacoonWW
no ZWW vertex (Gentle)
only #e exchange (Gentle)
LEPPRELIMINARY
17/02/2005
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
The Z, the W , and the Weak Neutral Current
• Primary prediction and test of electroweak unification
• WNC discovered 1973 (Gargamelle at CERN, HPW at FNAL)
• 70’s, 80’s: weak neutral current experiments (few %)
– Pure weak: νN , νe scattering
– Weak-elm interference in eD, e+e−, atomic parity violation
– Model independent analyses (νe, νq, eq)
– SU(2)× U(1) group/representations; t and ντ exist; mt limit;hint for SUSY unification; limits on TeV scale physics
• W , Z discovered directly 1983 (UA1, UA2)
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• 90’s: Z pole (LEP, SLD), 0.1%; lineshape, modes, asymmetries
• LEP 2: MW , Higgs search , gauge self-interactions
• Tevatron: mt, MW , Higgs search
• 4th generation weak neutral current experiments (atomic parity
(Boulder); νe; νN (NuTeV); polarized Møller asymmetry (SLAC))
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)
• SM correct and unique to zerothapprox. (gauge principle, group,representations)
• SM correct at loop level (renormgauge theory; mt, αs, MH)
• TeV physics severely constrained(unification vs compositeness)
• Consistent with light elementaryHiggs
• Precise gauge couplings (SUSYgauge unification)
Measurement Fit |Omeas−Ofit|/σmeas
0 1 2 3
0 1 2 3
∆αhad(mZ)∆α(5) 0.02758 ± 0.00035 0.02768mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4959σhad [nb]σ0 41.540 ± 0.037 41.478RlRl 20.767 ± 0.025 20.742AfbA0,l 0.01714 ± 0.00095 0.01645Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1481RbRb 0.21629 ± 0.00066 0.21579RcRc 0.1721 ± 0.0030 0.1723AfbA0,b 0.0992 ± 0.0016 0.1038AfbA0,c 0.0707 ± 0.0035 0.0742AbAb 0.923 ± 0.020 0.935AcAc 0.670 ± 0.027 0.668Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1481sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.399 ± 0.023 80.379ΓW [GeV]ΓW [GeV] 2.098 ± 0.048 2.092mt [GeV]mt [GeV] 173.1 ± 1.3 173.2
August 2009
23rd Spring School, Tainan (March 31-April 3, 2010) Paul Langacker (IAS)