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)
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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)
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)