Electroweak Physics
• Tests of the Standard Model and Beyond
• Problems With the Standard Model
(Structure Of The Standard Model, hep-ph/0304186.
Electroweak Review in W. M. Yao et al.
Particle Data Group, J. Phys. G 33, 1 (2006),
and 2008 update.)
TASI 2008 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)
TASI 2008 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))
TASI 2008 Paul Langacker (IAS)
νe→ νe
−Lνe =GF√
2νµ γ
µ(1− γ5)νµ e γµ(gνeV − gνeA γ
5)e
SM : gνeV ∼ −1
2+ 2 sin2 θW , gνeA ∼ −
1
2
• Any gauge model (with left-
handed ν) → some gνeV,A
• Need SM rad. corr.
• νe : gνeV,A −−→WCCgνeV,A + 1
• Alternative models w.disjoint parameters andperturbations on SM (Amaldi et al, PR D36, 1385 (1987))
TASI 2008 Paul Langacker (IAS)
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0gA
�
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
g V
�
ν� µ ereactorν� e e (LANL)
all
0.0
0.3
0.6
TASI 2008 Paul Langacker (IAS)
νq → νq (Mainly Deep Inelastic)
• WNC:
−LνHadron =GF√
2ν γµ (1− γ5)ν
×∑i
[εL(i) qi γµ(1− γ5)qi + εR(i) qi γµ(1 + γ5)qi
]• Standard model
εL(u) ∼1
2−
2
3sin2 θW εR(u) ∼ −
2
3sin2 θW
εL(d) ∼ −1
2+
1
3sin2 θW εR(d) ∼
1
3sin2 θW
TASI 2008 Paul Langacker (IAS)
• Deep inelastic(−)νµN →
(−)νµX
q
p
!(k)
X
!!(k!)
– Typeset by FoilTEX – 1
d2σNCνNdx dy
=2G2
FMpEν
π× {[
|εL(u)|2 + |εR(u)|2(1− y)2] (xu+ xc ξc)
+[|εL(d)|2 + |εR(d)|2(1− y)2] (xd+ xs)
+[|εR(u)|2 + |εL(u)|2(1− y)2] (xu+ xc ξc)
+[|εR(d)|2 + |εL(d)|2(1− y)2] (xd+ xs)}
(εL(i)↔ εR(i) for ν)
TASI 2008 Paul Langacker (IAS)
• WNN/WCC ratios measured to 1% or better by CDHS andCHARM (CERN) and CCFR (FNAL) (many strong interaction, ν flux,
and systematic effects cancel)
• For isoscalar targer (Np = Nn); ignoring s, c and third family sea;ignoring c threshold correction (ξc = 1)
Rν ≡σNCνNσCCνN
∼ g2L + g2
Rr
Rν ≡σNCνNσCCνN
∼ g2L +
g2R
r
– g2L ≡ εL(u)2 + εL(d)2 ≈ 1
2 − sin2 θW + 59 sin4 θW
– g2R ≡ εR(u)2 + εR(d)2 ≈ 5
9 sin4 θW
– r ≡ σCCνN /σCCνN measured (r → 1/3 for q/q → 0)
TASI 2008 Paul Langacker (IAS)
-0.2 -0.1 0.0 0.1 0.2
εR(u)
-0.2
-0.1
0.0
0.1
0.2
ε R(d
)
-0.2 -0.1 0.0 0.1 0.2
εR(u)
-0.2
-0.1
0.0
0.1
0.2
ε R(u
)
-0.4 -0.2 0.0 0.2 0.4
εL(u)
-0.4
-0.2
0.0
0.2
0.4
ε L(d
)
-0.4 -0.2 0.0 0.2 0.4
εL(u)
-0.4
-0.2
0.0
0.2
0.4
ε L(u
)
0.0
0.3
0.0
0.4
0.7
1.0
TASI 2008 Paul Langacker (IAS)
• Most precise sin2 θW before LEP/SLD: s2W ∼ 0.233 ±
0.003 (exp)± 0.005 (mc)
• Must correct for Nn 6= Np; s(x), c(x), ξc, QCD, third familymixing, W/Z propagators, radiative corrections, experimental cuts
• Can separate εi(u)/εi(d) by p and n targets, e.g., bubble chamber(less precise)
• Error dominated by charm threshold (mc in ξc)
• Can reduce sensitivity using Paschos-Wolfenstein ratio
R− =σNCνN − σNCνNσCCνN − σCCνN
∼ g2L − g
2R ∼
1
2− sin2 θW
TASI 2008 Paul Langacker (IAS)
• Recent NuTeV (FNAL) analysis minimizes mc uncertainty
• Obtains s2W = 0.2277 ± 0.0016 (insensitive to mt,MH), 3σ above
current global fit value 0.2231(3)
– New Physics (e.g., Z′, ν-mixing)?
– QCD effect, e.g., isospin breaking; s− s asymmetry (new NuTeV
reduces effect); NLO QCD or EW corrections?
TASI 2008 Paul Langacker (IAS)
Weak-Electromagnetic Interference
• Low energy: Z exchange much smaller than Coulomb, but observeV −A (parity-violating) and A−A (parity conserving) effects
• High energy: γ and Z may be comparable (propagator effects)
• Observables
– Polarization (charge) asymmetries in eD → eX (SLAC), µC →µX (CERN); e−e− Møller (SLAC); low energy elastic or quasi-elastic (Mainz, Bates, CEBAF)
– Atomic parity violation in Cs (Boulder, Paris) and other atoms
– Cross sections and FB asymmetries in e+e− → `¯, qq, bb(SPEAR, PEP, DORIS, TRISTAN, LEP II)
– FB asymmetries in pp→ e+e− (CDF, D0)
TASI 2008 Paul Langacker (IAS)
• Parity-violating e-hadron
Leq =GF√
2
∑i
[C1i e γµ γ
5 e qi γµ qi + C2i e γµ e qi γ
µ γ5 qi]
• Standard model
C1u ∼ −1
2+
4
3sin2 θW C2u ∼ −
1
2+ 2 sin2 θW
C1d ∼1
2−
2
3sin2 θW C2d ∼
1
2− 2 sin2 θW
TASI 2008 Paul Langacker (IAS)
• Atomic parity violation
– Axial e−, vector nucleon currents lead to potential
V (~re) ∼GF
4√
2QWδ
3(~re)~σe · ~vec
+ HC
– Weak charge
QW = −2 [C1u (2Z +N) + C1d(Z + 2N)]
≈ Z(1− 4 sin2 θW )−N
– Measure in 6S − 7S transition (S − P wave mixing)
– Cs is very simple atom; radiative corrections now under control
TASI 2008 Paul Langacker (IAS)
-0.8 -0.7 -0.6 -0.5 -0.4C1 u-C1 d
0.1
0.12
0.14
0.16
0.18
C1
u+C
1 d
SLAC: D DIS Mainz: Be
Bates: C
APV Tl
APV Cs
PVES
-0.8 -0.7 -0.6 -0.5 -0.4C1 u-C1 d
0.1
0.12
0.14
0.16
0.18
C1
u+C
1 d
(Young et al, 0704.2618)
TASI 2008 Paul Langacker (IAS)
0.001 0.01 0.1 1 10 100 1000Q [GeV]
0.225
0.230
0.235
0.240
0.245
0.250
sin2
θ W^(Q
)
APV
Qweak
APV
ν-DISAFB
Z-pole
currentfutureSM
(Running s2Z in MS scheme)
• SLAC E158 PolarizedMøller Asymmetry
– e−e− asymmetry,P ∼ 90%
– sin2 θeffW (Q) =0.2397 ± 0.0013at Q2 = 0.026GeV2
• Future: QWEAK
(CEBAF): polarizedep, ∆s2 ∼ 0.0006;NuSOnG proposal
((−)νµe,
(−)νµN
NC,CC)
TASI 2008 Paul Langacker (IAS)
Input Parameters for Weak Neutral Current and Z-Pole
• Basic inputs
– SU(2) and U(1) gauge couplings g and g′
– ν =√
2〈0|ϕ0|0〉 (vacuum of theory)
– Higgs mass MH (value unknown) (enters radiative corrections)
– Heavy fermion masses, mt, mb, · · · (phase space; radiative
corrections)
– strong coupling αs (enters radiative corrections)
• Trade g, g′, ν for precisely known quantities
– GF = 1√2ν2 from τµ (GF ∼ 1.166367(5)× 10−5 GeV−2 )
– α = 1/137.035999679(94) (but must extrapolate to MZ)
– MZ (or sin2 θW )
TASI 2008 Paul Langacker (IAS)
Definitions of sin2 θW
• Several equivalent expressions for sin2 θW at tree-level
sin2 θW = 1−M2W
M2Z
⇒ on− shell
sin2 θW cos2 θW =πα
√2GFM2
Z
⇒ Z −mass
sin2 θW =g′2
g2 + g′2⇒ MS
gZe+e−
V = −1
2+ 2 sin2 θW ⇒ effective
• Each can be basis of definition of renormalized sin2 θW (others
related by calculable, mt −MH dependent, corrections of O(α))
TASI 2008 Paul Langacker (IAS)
Radiative Corrections
!
!
!
– Typeset by FoilTEX – 1
• QED corrections to W or Z exchange
– No vacuum polarization or box diagrams
– Finite and gauge invariant
– Depend on kinematic variables and cuts →calculate for each experiment
TASI 2008 Paul Langacker (IAS)
• Electroweak at multiloop level (include W , Z, γ)
self-energy vertex box
– Typeset by FoilTEX – 1
• (quadratic) mt and (logarithmic) MH dependence fromWW, ZZ, Zγ self-energies (SU(2)-breaking). Also, mt from Zbbvertex.
t(b)
t(b)
Z(!) Z
t
b
W W
H
H
H
G
mixed
– Typeset by FoilTEX – 1
t
W
t
b b
Z
W
t
W
b b
Z
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
G
– Typeset by FoilTEX – 1
• αs from QCD vertices andmixed QCD-EW
• Mixed QCD-EW (e.g., self-energies
and vertices, fermion masses)
– Awkward in on-shell
t(b)
t(b)
Z(!) Z
t
b
W W
H
H
H
G
mixed
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
The W and Z Masses and Decays
• On-shell scheme, s2W ≡ 1−M2
W/M2Z
MW =A0
sW (1−∆r)1/2MZ =
MW
cW
c2W = 1− s2
W , A0 = (πα/√
2GF )1/2 = 37.28057(8) GeV∆r → rad. corrections relating α, α(MZ), GF , MW , and MZ
∆r ∼ 1−α
α(MZ)︸ ︷︷ ︸0.06649(12)
−ρt
tan2 θW︸ ︷︷ ︸artificially large
+ small
ρt ≡3
8
GFm2t√
2π2= 0.00915
(mt
170.9 GeV
)2
TASI 2008 Paul Langacker (IAS)
• Modified minimal subtraction (MS ) scheme
MW =A0
sZ(1−∆rW )1/2MZ =
MW
ρ1/2cZ
∆rW ∼ 1−α
α(MZ)︸ ︷︷ ︸0.06649(12)
+ small
ρ ∼ 1 +3
8
GFm2t√
2π2︸ ︷︷ ︸ρt∼0.00915
+ small
TASI 2008 Paul Langacker (IAS)
• The W decay width
Γ(W+ → e+νe) =GFM
3W
6√
2π≈ 226.20± 0.10 MeV
Γ(W+ → uidj) =CGFM
3W
6√
2π|Vij|2 ≈ (705.97± 0.31) |Vij|2 MeV
C =
1, leptons
3︸︷︷︸color
(1 + αs(MW )
π+ 1.409α
2sπ2 − 12.77α
3sπ3
), quarks
– Also, QED, mass; g2MW/4√
2→ GFM3W absorbs running α
– ΓW ∼ 2.0902± 0.0009 GeV (SM)
– Experiment (LEP,CDF, D0): ΓW = 2.141±0.041 GeV; pp uses
σ(pp→ W → `ν`)
σ(pp→ Z → `¯)=σ(pp→ W )
σ(pp→ Z)︸ ︷︷ ︸theory
Γ(W → `ν`)︸ ︷︷ ︸theory
1
B(Z → `¯)︸ ︷︷ ︸LEP
1
ΓW
TASI 2008 Paul Langacker (IAS)
The Z pole
√s [GeV]
σ [n
b]
Z
PEPPETRA
TRISTAN
LEP ISLC
LEP 1.5
LEP II
e+e−→qq−
10-2
10-1
1
10
10 2
50 100 150 200
e+e− → hadrons(γ)
Monte Carlo 161 GeV
√s' [GeV]
even
ts
0
1000
2000
3000
4000
50 75 100 125 150
TASI 2008 Paul Langacker (IAS)
The LEP/SLC Era
• Z Pole: e+e−→ Z → `+`−, qq, νν
– LEP (CERN), 2×107 Z′s, unpolarized (ALEPH, DELPHI, L3, OPAL);SLC (SLAC), 5× 105, Pe− ∼ 75 % (SLD)
• Z pole observables
– lineshape: MZ,ΓZ, σ– branching ratios∗ e+e−, µ+µ−, τ+τ−
∗ qq, cc, bb, ss∗ νν ⇒ Nν = 2.985± 0.009 if mν < MZ/2
– asymmetries: FB, polarization, Pτ , mixed
– lepton family universality
TASI 2008 Paul Langacker (IAS)
10-1
1
10
100 150!s" [GeV]
#ha
dron
SM: !s"´/"s" > 0.10SM: !s"´/"s" > 0.85
Combined LEP
TOPAZ
TASI 2008 Paul Langacker (IAS)
The Z Lineshape
Basic Observables: e+e−→ ff (f = e, µ, τ, s, b, c, hadrons)(s = E2
CM)
σf(s) ∼ σfsΓ2
Z
(s−M2Z)2 + s2Γ2
Z
M2Z
(plus initial state rad. corrections)
MZ and ΓZ: from peak position and width
Peak Cross Section:
σf =12π
M2Z
Γ(e+e−)Γ(ff)
Γ2Z
(Z model independent; γ and γ − Z int. removed, (usually) assuming S.M.)
TASI 2008 Paul Langacker (IAS)
Ecm [GeV]
σha
d [nb]
σ from fitQED corrected
measurements (error barsincreased by factor 10)
ALEPHDELPHIL3OPAL
σ0
ΓZ
MZ
10
20
30
40
86 88 90 92 94
Ecm [GeV]
AFB
(µ)
AFB from fit
QED correctedaverage measurements
ALEPHDELPHIL3OPAL
MZ
AFB0
-0.4
-0.2
0
0.2
0.4
88 90 92 94
Figure 1.12: Average over measurements of the hadronic cross-sections (top) and of the muonforward-backward asymmetry (bottom) by the four experiments, as a function of centre-of-massenergy. The full line represents the results of model-independent fits to the measurements, asoutlined in Section 1.5. Correcting for QED photonic e!ects yields the dashed curves, whichdefine the Z parameters described in the text.
33
(LEPEWWG, hep-ex/0509008)
TASI 2008 Paul Langacker (IAS)
• The Z width and partial widths
Γ(ff) ∼CfGFM
3Z
6√
2πρ︸︷︷︸
only MS
[|gV f |2 + |gAf |2
](plus fermion mass, QED (2 loop), QCD (3 loop), mixed QED-QCD(2 loop) corrections; C` = 1, Cq = 3)
gAf =√ρft
f3L gV f =
√ρf
(tf3L − 2s2
fqf
)s2f = κfs
2W = κf s
2Z
• Standard model (mt = 170.9(1.8)(0.6) GeV, MH = 117 GeV)
Γ(ff) ∼
300.10± 0.09 MeV(uu), 167.18± 0.02 MeV(νν)382.89± 0.08 MeV(dd), 83.97± 0.03 MeV(e+e−)376.01∓ 0.05 MeV(bb)
TASI 2008 Paul Langacker (IAS)
• Conventional (weakly correlated) observables: MZ,ΓZ, σhad, R`, Rb, Rc
σhad ≡12π
M2Z
Γ(e+e−)Γ(Z → hadrons)
Γ2Z
Rqi ≡Γ(qiqi)
Γ(had), qi = (b, c)
R`i ≡Γ(had)
Γ(`i ¯i), `i = (e, µ, τ )
(lepton universality test: Re = Rµ = Rτ → R`)
• Derived
Γ(inv) = ΓZ − Γ(had)−∑i
Γ(`i ¯i) ≡ NνΓ(νν)
(counts anything invisible in detector)
TASI 2008 Paul Langacker (IAS)
8 40. Plots of cross sections and related quantities
Annihilation Cross Section Near MZ
Figure 40.8: Combined data from the ALEPH, DELPHI, L3, and OPAL Collaborations for the cross section in e+e! annihilation intohadronic final states as a function of the center-of-mass energy near the Z pole. The curves show the predictions of the Standard Model withtwo, three, and four species of light neutrinos. The asymmetry of the curve is produced by initial-state radiation. Note that the error bars havebeen increased by a factor ten for display purposes. References:
ALEPH: R. Barate et al., Eur. Phys. J. C14, 1 (2000).DELPHI: P. Abreu et al., Eur. Phys. J. C16, 371 (2000).L3: M. Acciarri et al., Eur. Phys. J. C16, 1 (2000).OPAL: G. Abbiendi et al., Eur. Phys. J. C19, 587 (2001).Combination: The Four LEP Collaborations (ALEPH, DELPHI, L3, OPAL)
and the Lineshape Sub-group of the LEP Electroweak Working Group, hep-ph/0101027.(Courtesy of M. Grunewald and the LEP Electroweak Working Group, 2003)
• Nν = 3 + ∆Nν = 2.985±0.009
• ∆Nν = 1 for fourth family ν withmν
<∼MZ/2
• ∆Nν = 12, light ν in super-
symmetry
• ∆Nν = 2, Majoron + scalarin triplet model of mν withspontaneous L violation
TASI 2008 Paul Langacker (IAS)
Z-Pole Asymmetries
• Effective axial and vector couplings of Z to fermion f
gAf =√ρft3f
gV f =√ρf
[t3f − 2s2
fqf
]where s2
f the effective weak angle,
s2f = κfs
2W (on− shell)
= κf s2Z ∼ s
2Z + 0.00029 (f = e) (MS ),
ρf , κf , and κf are electroweak corrections, qf = electric charge,t3f = weak isospin
TASI 2008 Paul Langacker (IAS)
• A0 = Born asymmetry (after removing γ, off-pole, box (small), Pe−)
forward− backward : A0fFB =
3
4AeAf
(A0eFB = A0µ
FB = A0τFB ≡ A
0`FB → universality)
τ polarization : P 0τ = −
Aτ +Ae2z
1+z2
1 +AτAe2z
1+z2
(z = cos θ, θ = scattering angle)
e− polarization (SLD) : A0LR = Ae
mixed (SLD) : A0FBLR =
σfLF − σfLB − σ
fRF + σfRB
σfLF + σfLB + σfRF + σfRB=
3
4Af
Af ≡2gV f gAfg2V f + g2
Af
gV ` ∼ −1
2+ 2s2
` (small)
TASI 2008 Paul Langacker (IAS)
• Asymmetries depend onAf ≡
2gV f gAfg2V f
+g2Af→ little sensitivity
to mt, MH
• mt, MH enter in comparisonwith MZ and other lineshape
• ALR ∝ gV ` ∼ −12 + 2s2
` moresensitive to s2
` than A0`FB ∝ g2
V `
• A0bFB = 3
4AeAb much moresensitive to e vertex than bvertex assuming SM, but possiblediscrepancy
A0,lFB
MH
[G
eV]
Forward-Backward Pole Asymmetry
Mt = 172.7±2.9 GeV
linearly added to 0.02758±0.00035!"(5)!"had=
Experiment A0,lFB
ALEPH 0.0173 ± 0.0016
DELPHI 0.0187 ± 0.0019
L3 0.0192 ± 0.0024
OPAL 0.0145 ± 0.0017
#2 / dof = 3.9 / 3
LEP 0.0171 ± 0.0010
common error 0.0003
10
10 2
10 3
0.013 0.017 0.021
TASI 2008 Paul Langacker (IAS)
24 10. Electroweak model and constraints on new physics
Quantity Value StandardModel Pull Deviation
mt [GeV] 170.9± 1.8± 0.6 171.1± 1.9 !0.1 !0.8MW [GeV] 80.428± 0.039 80.375± 0.015 1.4 1.7
80.376± 0.033 0.0 0.5MZ [GeV] 91.1876± 0.0021 91.1874± 0.0021 0.1 !0.1!Z [GeV] 2.4952± 0.0023 2.4968± 0.0010 !0.7 !0.5!(had) [GeV] 1.7444± 0.0020 1.7434± 0.0010 — —!(inv) [MeV] 499.0± 1.5 501.59± 0.08 — —!(!+!!) [MeV] 83.984± 0.086 83.988± 0.016 — —"had [nb] 41.541± 0.037 41.466± 0.009 2.0 2.0Re 20.804± 0.050 20.758± 0.011 0.9 1.0Rµ 20.785± 0.033 20.758± 0.011 0.8 0.9R! 20.764± 0.045 20.803± 0.011 !0.9 !0.8Rb 0.21629± 0.00066 0.21584± 0.00006 0.7 0.7Rc 0.1721± 0.0030 0.17228± 0.00004 !0.1 !0.1
A(0,e)FB 0.0145± 0.0025 0.01627± 0.00023 !0.7 !0.6
A(0,µ)FB 0.0169± 0.0013 0.5 0.7
A(0,!)FB 0.0188± 0.0017 1.5 1.6
A(0,b)FB 0.0992± 0.0016 0.1033± 0.0007 !2.5 !2.0
A(0,c)FB 0.0707± 0.0035 0.0738± 0.0006 !0.9 !0.7
A(0,s)FB 0.0976± 0.0114 0.1034± 0.0007 !0.5 !0.4
s2" (A
(0,q)FB ) 0.2324± 0.0012 0.23149± 0.00013 0.8 0.6
0.2238± 0.0050 !1.5 !1.6Ae 0.15138± 0.00216 0.1473± 0.0011 1.9 2.4
0.1544± 0.0060 1.2 1.40.1498± 0.0049 0.5 0.7
Aµ 0.142± 0.015 !0.4 !0.3A! 0.136± 0.015 !0.8 !0.7
0.1439± 0.0043 !0.8 !0.5Ab 0.923± 0.020 0.9348± 0.0001 !0.6 !0.6Ac 0.670± 0.027 0.6679± 0.0005 0.1 0.1As 0.895± 0.091 0.9357± 0.0001 !0.4 !0.4g2L 0.3010± 0.0015 0.30386± 0.00018 !1.9 !1.8
g2R 0.0308± 0.0011 0.03001± 0.00003 0.7 0.7
g#eV !0.040± 0.015 !0.0397± 0.0003 0.0 0.0
g#eA !0.507± 0.014 !0.5064± 0.0001 0.0 0.0
APV (!1.31± 0.17)" 10!7 (!1.54± 0.02)" 10!7 1.3 1.2QW (Cs) !72.62± 0.46 !73.16± 0.03 1.2 1.2QW (Tl) !116.4± 3.6 !116.76± 0.04 0.1 0.1!(b"s$)
!(b"Xe#)
!3.55+0.53
!0.46
"" 10!3 (3.19± 0.08)" 10!3 0.8 0.7
12 (gµ ! 2! %
& ) 4511.07(74)" 10!9 4509.08(10)" 10!9 2.7 2.7#! [fs] 290.93± 0.48 291.80± 1.76 !0.4 !0.4
January 25, 2008 12:02
TASI 2008 Paul Langacker (IAS)
• LEP 2
– e+e−→ ff
– MW , ΓW , B (also Tevatron)
– MH limits (hint?)
– WW production (triple gaugevertex)
– Quartic vertex
– SUSY/exotics searches
TASI 2008 Paul Langacker (IAS)
Gauge Self-Interactions
Three and four-point interactions predicted by gauge invariance
Indirectly verified by radiative corrections, αs running in QCD, etc.
Strong cancellations in high energy amplitudes would be upset byanomalous couplings
Tree-level diagrams contributing to e+e−→W+W−
TASI 2008 Paul Langacker (IAS)
TASI 2008 Paul Langacker (IAS)
Non-Z Pole Experiments
• Atomic parity (Boulder, Paris); νe; νN (NuTeV); polarized Møllerasymmetry (SLAC E158); MW , mt (Tevatron)
• Non-Z pole WNC experiments less precise but still extremelyimportant
– Z-pole is blind to new physics that doesn’t directly affect Z orits couplings to fermions (e.g., new box-diagrams, four-Fermi operators)
TASI 2008 Paul Langacker (IAS)
32 10. Electroweak model and constraints on new physics
Table 10.8: Values of the model-independent neutral-current parameters, comparedwith the SM predictions. There is a second g!e
V,A solution, given approximately byg!eV ! g!e
A , which is eliminated by e+e! data under the assumption that the neutralcurrent is dominated by the exchange of a single Z boson. The !L, as well as the !R,are strongly correlated and non-Gaussian, so that for implementations we recommendthe parametrization using g2
i and "i = tan!1[!i(u)/!i(d)], i = L or R. The analysisof more recent low-energy experiments in polarized electron scattering performed inRef. 112 is included by means of an additional constraint on the linear combination,7C1u + 3C1d = "0.254 ± 0.034, which reproduces the results [112] on C1u and C1d(including their correlation) almost exactly. In the SM predictions, the uncertainty isfrom MZ , MH , mt, mb, mc, !#(MZ), and #s.
ExperimentalQuantity Value SM Correlation
!L(u) 0.328 ±0.015 0.3460(1)!L(d) "0.440 ±0.011 "0.4291(1) non-!R(u) "0.175 +0.013
!0.004 "0.1549(1) Gaussian!R(d) "0.023 +0.072
!0.048 0.0775
g2L 0.3012±0.0013 0.3039(2) "0.12 "0.22 "0.01
g2R 0.0310±0.0010 0.0300 "0.02 "0.03
"L 2.50 ±0.033 2.4630(1) 0.26"R 4.58 +0.41
!0.28 5.1765
g!eV "0.040 ±0.015 "0.0397(3) "0.05
g!eA "0.507 ±0.014 "0.5064(1)
C1u + C1d 0.1526 ±0.0013 0.1528(1) 0.49 "0.14 "0.01C1u " C1d "0.514 ±0.015 "0.5298(3) "0.27 "0.02C2u + C2d "0.23 ±0.57 "0.0095 "0.30C2u " C2d "0.077 ±0.044 "0.0623(5)
where the lower limit on MH is the direct search bound. (If the direct limit is ignored oneobtains MH = 76+111
! 38 GeV and $0 = 1.0000+0.0011!0.0007.) The error bar in Eq. (10.53) is highly
asymmetric: at the 2 % level one has $0 = 1.0004+0.0027!0.0007 with no meaningful bound on
MH . The result in Eq. (10.53) is slightly above but consistent with the SM expectation,$0 = 1. It can be used to constrain higher-dimensional Higgs representations to havevacuum expectation values of less than a few percent of those of the doublets. Indeed, therelation between MW and MZ is modified if there are Higgs multiplets with weak isospin> 1/2 with significant vacuum expectation values. In order to calculate to higher orders
January 25, 2008 12:02
TASI 2008 Paul Langacker (IAS)
The Anomalous Magnetic Moment of the Muon
• Muon aµ ≡ gµ−22 sensitive to new physics ( usually ∼ (mµ/MX)2)
aSMµ = aQED
µ + aHadµ + aEW
µ
• aQEDµ known to four loops (3 analytic); leading logs to five
µ µ
!
µ µ
!
eµ µ
!
µ µ
!
had vacµ µ
!
had ll
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
aQEDµ =
α
2π+ 0.765857376(27)
(α
π
)2
+24.05050898(44)(α
π
)3
+ 126.07(41)(α
π
)4
+930(170)(α
π
)5
= 1165847.06(3)× 10−9
• aEWµ = 1.52(3) × 10−9 (goal of experiments) includes leading 2 and
3 loops (cancellation)
µ
Z
µ
µ µ
!
W
"
W
µ µ
!
µ
h
µ
µ µ
!
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
• Biggest uncertainty: aHadµ = hadronic vacuum polarization (2 loop)
and hadronic light by light (3 loop)
aHad vacµ =
1
3
(α
π
)2 ∫ ∞4m2
π
ds
sK(s)︸ ︷︷ ︸
fnc of m2µ/s
σ(e+e−→ had)
σ(e+e−→ µ+µ−)µ µ
!
µ µ
!
eµ µ
!
µ µ
!
had vacµ µ
!
had ll
– Typeset by FoilTEX – 1
– aHad vacµ : discrepancy between e+e−and τ decay (isospin violation?)
– aHad l.l.µ sign now settled down. Small but non-negligible
• aexpµ = 1165920.80(63)× 10−9 (dominated by BNL 821)
TASI 2008 Paul Langacker (IAS)
39
140 150 160 170 180 190 200 210
aµ – 11 659 000 (10–10)
BNL-E821 04
DEHZ 03 (e+e–-based)
DEHZ 03 (τ-based)
HMNT 03 (e+e–-based)
J 03 (e+e–-based)
TY 04 (e+e–-based)
DEHZ 04 (e+e–-based)
BNL-E821 04
180.9 ± 8.0
195.6 ± 6.8
176.3 ± 7.4
179.4 ± 9.3 (preliminary)
180.6 ± 5.9 (preliminary)
182.8 ± 7.2 (preliminary)
208 ± 5.8
FIG. 20 Comparison of the result (72) (Hocker, 2004) labelled DEHZ 04 with the BNL measurement (Muon (g ! 2)Coll., 2004). Also given are the previous estimate (Davier et al., 2003b), where the triangle with the dotted errorbar indicates the ! -based result, as well as the estimates from (Hagiwara et al., 2004; Jegerlehner, 2003; Troconiz andYndurain, 2004), not yet including the KLOE data.
F. Comparing aµ between theory and experiment
Summing the results from the previous sections on aQEDµ , aEW
µ , ahad,LOµ , ahad,NLO
µ , and ahad,LBLµ , one obtains
the SM prediction for aµ. The newest e+e!-based result reads (Hocker, 2004)
aSMµ = (11 659 182.8± 6.3had,LO+NLO ± 3.5had,LBL ± 0.3QED+EW) ! 10!10 . (72)
This value can be compared to the present measurement (61); adding all errors in quadrature, the di!erencebetween experiment and theory is
aexpµ " aSM
µ = (25.2 ± 9.2) ! 10!10 , (73)
which corresponds to 2.7 “standard deviations” (to be interpreted with care due to the dominance of exper-imental and theoretical systematic errors in the SM prediction). A graphical comparison of the result (72)with previous evaluations (also those containing ! data) and the experimental value is given in Fig. 20.
Whereas the evaluation based on the e+e! data only disagrees with the measurement, the evaluationincluding the tau data is consistent with it. The dominant contribution to the discrepancy between the twoevaluations stems from the "" channel with a di!erence of ("11.9±6.4exp±2.4rad±2.6SU(2) (±7.3total))!10!10,and a more significant energy-dependent deviation10. As a consequence, during the previous evaluations ofahad,LO
µ , the results using respectively the ! and e+e! data were quoted individually, but on the same footingsince the e+e!-based evaluation was dominated by the data from a single experiment (CMD-2).
The seeming confirmation of the e+e! data by KLOE could lead to the conclusion that the ! -based resultbe discredited for the use in the dispersion integral (Hocker, 2004). However, the newest SND data (SND-2Coll., 2005) alter this picture in favor of the ! data, along with prompting doubts on the validity of theKLOE results (see discussion in Section V.C). Comparing the SND and CMD-2 data in the overlappingenergy region between 0.61 GeV and 0.96 GeV, the SND-based evaluation of ahad,NLO
µ is found to be larger by(9.1±6.3)!10!10. However, once these two experiments are averaged using the trapezoidal rule, the increase
10 The systematic problem between ! and e+e! data is more noticeable when comparing the !! ! "!"0#! branching frac-tion with the prediction obtained from integrating the corresponding isospin-breaking-corrected e+e! spectral function (cf.Section V).
• e+e− data: 3.3σ discrepancy
• τ decay data: no discrepancy(0.9σ)
• Supersymmetry: central value(e+e−) for mSUSY ∼ 72
√tanβ
GeV
µ
!0
µ
µ µ
"
!!
#
!!
µ µ
"
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
Global Electroweak Fits
• much more information than individual experiments
• caveat: experimental/theoretical systematics, correlations
• PDG ’06 review + ’07 update (J. Erler and PL)
• Complete Z-pole and WNC (important beyond SM)
• MS radiative correction program (Erler)
– GAPP: Global Analysis of Particle Properties (J. Erler, hep-
ph/0005084)
– Fully MS (ZFITTER on-shell)
• Good agreement with LEPEWWG up to well-understood effects(WNC, HOT, ∆αhad) despite different renormalization schemes
TASI 2008 Paul Langacker (IAS)
Global Standard Model Fit Results
• PDG 2008 (11/07) (Erler,
PL)
– χ2/df = 49.4/42
– Fully MS
– Good agreement withLEPEWWG up to knowneffects
MH = 77+28−22 GeV,
mt = 171.1± 1.9 GeV
αs = 0.1217± 0.0017
α(MZ)−1 = 127.909± 0.019
s2Z = 0.23119± 0.00014
s2` = 0.23149± 0.00013
s2W = 0.22308± 0.00030
∆α(5)had(MZ) = 0.02799± 0.00014
TASI 2008 Paul Langacker (IAS)
• mt = 171.1± 1.9 GeV
– 174.7+10.0−7.8 GeV from indirect (loops) only (direct: 170.9± 1.9)
t(b)
t(b)
Z(!) Z
t
b
W W
H
H
H
G
mixed
– Typeset by FoilTEX – 1
– Fit actually uses MS mass mt(mt) (∼ 10 GeV lower) and convertsto pole mass at end
– Significant change from previous analysis due to lower mt fromRun II
TASI 2008 Paul Langacker (IAS)
• αs= 0.1217± 0.0017
– Higher than αs = 0.1176(20)(PDG: 2006), because of τlifetime
– Z-pole alone: αs = 0.1198(28)
– insensitive to oblique new physics
– very sensitive to non-universalnew physics (e.g., Zbb vertex)
G
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
• Higgs mass MH= 77+28−22 GeV
– LEPEWWG: 76+33−24
– direct limit (LEP 2): MH>∼ 114.4 (95%) GeV
– SM: 115 (vac. stab.) <∼MH<∼ 750 (triviality)
– MSSM: MH<∼ 130 GeV (150 in extensions)
– indirect: lnMH but significant
∗ affected by new physics (S < 0, T > 0)
∗ strong AFB(b) effect
∗ MH < 167 GeV at 95%, including direct
t(b)
t(b)
Z(!) Z
t
b
W W
H
H
H
H
G
mixed
– Typeset by FoilTEX – 1
TASI 2008 Paul Langacker (IAS)
140 150 160 170 180 190mt [GeV]
1000
500
200
100
50
20
10
MH [G
eV]
excluded
all data (90% CL)
ΓΖ, σhad
, Rl, R
q
asymmetriesMW
low-energymt
TASI 2008 Paul Langacker (IAS)
155 160 165 170 175 180 185
mt [GeV]
80.30
80.35
80.40
80.45M
W [G
eV]
M H = 117 G
eV
M H = 200 G
eV
M H = 300 G
eV
M H = 500 G
eV
direct (1σ)indirect (1σ)all data (90%)
TASI 2008 Paul Langacker (IAS)
0
1
2
3
4
5
6
10030 300
mH [GeV]
∆χ2
Excluded Preliminary
∆αhad =∆α(5)
0.02758±0.000350.02749±0.00012incl. low Q2 data
Theory uncertaintymLimit = 144 GeV
TASI 2008 Paul Langacker (IAS)
Beyond the standard model
• Oblique corrections: new particles which affect W ,Z, γ propagators but not the fermion vertices!
" "
t had
– Typeset by FoilTEX – 1
• ρ0 = 11−αT : physics which affects WNC/WCC and MW/MZ
– Splittings between non-degenerate fermion or scalar doublets(like t, b)
ρ0 − 1 =3GF
8√
2π2
∑i
Ci
3∆m2
i (Ci = color factor)
∆m2 ≡ m21 +m2
2 −4m2
1m22
m21 −m2
2lnm1
m2≥ (m1 −m2)2
– Higgs triplets with non-zero VEVs
TASI 2008 Paul Langacker (IAS)
• S affects Z propagator, relation between WNC and MZ
– Chiral (parity-violating) fermion doublets, even if degenerate(e.g., fourth family, mirror family, technifamilies)
S =C
3π
∑i
(t3L(i)− t3R(i))2 →{ 2
3π (family)
1.62 (QCD-like techni-generation)
• U similarly affects W propagator, usually small
• S, T, U have coefficient of α
• Varying conventions. PDG: ρ0 ≡ 1, S = T = U = 0 in SM(SM rad corrections treated separately)
TASI 2008 Paul Langacker (IAS)
• ρ0; S, T, U : Higgs triplets, nondegenerate fermions or scalars;chiral families (ETC)
S = −0.04± 0.09 (−0.07)
T = 0.02± 0.09 (+0.09)
for MH = 117 (300) GeV and U = 0
– ρ0 ' 1 + αT = 1.0004+0.0008−0.0004 and 114.4 GeV < MH < 215
GeV (for S = U = 0) →∑iCi∆m
2i/3 < (98 GeV)2 (95% cl)
– Can evade Higgs mass limit for S < 0, T > 0 (Higgs doublet/triplet
loops, Majorana fermions)
– Degenerate heavy family excluded at 6σ
TASI 2008 Paul Langacker (IAS)
-1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25
S
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00T
all: MH = 117 GeVall: MH = 340 GeVall: MH = 1000 GeV
ΓZ, σ
had, R
l, R
q
asymmetriesMWν scatteringQW
E 158
TASI 2008 Paul Langacker (IAS)
• Supersymmetry
– decoupling limit (Mnew>∼
200 − 300 GeV): onlyprecision effect is light SM-like Higgs
– little improvement on SM fit
– Supersymmetry parametersconstrained
TASI 2008 Paul Langacker (IAS)
• A TeV scale Z′?
– Expected in many string theories, grand unification, dynamicalsymmetry breaking, little Higgs, large extra dimensions
– Natural solution to µ problem
– Implications (review: arXiv:0801.1345 [hep-ph])
∗ Extended Higgs/neutralino sectors
∗ Exotics (anomaly-cancellation)
∗ Constraints on neutrino mass generation
∗ Z′ decays into sparticles/exotics
∗ Enhanced possibility of EW baryogenesis
∗ Possible Z′ mediation of supersymmetry breaking
∗ FCNC (especially in string models)
– Typically MZ′ > 600 − 900 GeV (Tevatron, LEP 2, WNC),|θZ−Z′| < few × 10−3 (Z-pole)
TASI 2008 Paul Langacker (IAS)
−0.01 −0.005 0 0.005 0.010
500
1000
1500
2000
2500
sin θ
X
MZ [GeV]
05
CDF excluded
Zχ
1oo
TASI 2008 Paul Langacker (IAS)
• Other
– Exotic fermion mixings
– Large extra dimensions
– New four-fermi operator
– Leptoquark bosons
– Little Higgs
TASI 2008 Paul Langacker (IAS)
• Gauge unification: GUTs, stringtheories
– α+ s2Z → αs = 0.130±0.010
(MSSM) (non-SUSY: 0.073(1))
– MG ∼ 3× 1016 GeV
– Perturbative string: ∼ 5×1017
GeV (10% in lnMG). Exotics:O(1) corrections.
• Gauge unification: GUTs, stringtheories
– !+ s2Z ! !s = 0.130±0.010
(MSSM) (non-SUSY: 0.073(1))
– MG " 3 # 1016 GeV
– Perturbative string: " 5#1017
GeV (10% in ln MG). Exotics:O(1) corrections.
0
10
20
30
40
50
60
105
1010
1015
1 µ (GeV)
!i-1
(µ)
SMWorld Average!
1
!2
!3
!S(M
Z)=0.117±0.005
sin2"
MS__=0.2317±0.0004
0
10
20
30
40
50
60
105
1010
1015
1 µ (GeV)
!i-1
(µ)
MSSMWorld Average68%
CL
U.A.W.d.BH.F.
!1
!2
!3
FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 40TASI 2008 Paul Langacker (IAS)
Problems with the Standard Model
Lagrangian after symmetry breaking:
L = Lgauge + LHiggs +∑i
ψi
(i 6∂ −mi −
miH
ν
)ψi
−g
2√
2
(JµWW
−µ + Jµ†WW
+µ
)− eJµQAµ −
g
2 cos θWJµZZµ
Standard model: SU(2) × U(1) (extended to include ν masses) +QCD + general relativity
Mathematically consistent, renormalizable theory
Correct to 10−16 cm
TASI 2008 Paul Langacker (IAS)
However, too much arbitrariness and fine-tuning: O(27) parameters(+ 2 for Majorana ν) and electric charges
• Gauge Problem
– complicated gauge group with 3 couplings
– charge quantization (|qe| = |qp|) unexplained
– Possible solutions: strings; grand unification; magneticmonopoles (partial); anomaly constraints (partial)
• Fermion problem
– Fermion masses, mixings, families unexplained
– Neutrino masses, nature? Probe of Planck/GUT scale?
– CP violation inadequate to explain baryon asymmetry
– Possible solutions: strings; brane worlds; family symmetries;compositeness; radiative hierarchies. New sources of CPviolation.
TASI 2008 Paul Langacker (IAS)
• Higgs/hierarchy problem
– Expect M2H = O(M2
W )– higher order corrections:δM2
H/M2W ∼ 1034
Possible solutions: supersymmetry; dynamical symmetry breaking;large extra dimensions; Little Higgs; anthropically motivated fine-tuning (split supersymmetry) (landscape)
• Strong CP problem
– Can add θ32π2g
2sF F to QCD (breaks, P, T, CP)
– dN ⇒ θ < 10−9, but δθ|weak ∼ 10−3
– Possible solutions: spontaneously broken global U(1) (Peccei-Quinn) ⇒ axion; unbroken global U(1) (massless u quark);spontaneously broken CP + other symmetries
TASI 2008 Paul Langacker (IAS)
• Graviton problem
– gravity not unified
– quantum gravity not renormalizable
– cosmological constant: ΛSSB = 8πGN〈V 〉 > 1050Λobs
(10124 for GUTs, strings)
Possible solutions:
– supergravity and Kaluza Klein unify
– strings yield finite gravity
– Λ? Anthropically motivated fine-tuning (landscape)?
TASI 2008 Paul Langacker (IAS)
• Necessary new ingredients
– Mechanism for small neutrino masses
∗ Planck/GUT scale? Small Dirac (intermediate scale)?
– Mechanism for baryon asymmetry?
∗ Electroweak transition (Z′ or extended Higgs?)
∗ Heavy Majorana neutrino decay (seesaw)?
∗ Decay of coherent field? CPT violation?
– What is the dark energy?
∗ Cosmological Constant? Quintessence?
∗ Related to inflation? Time variation of couplings?
– What is the dark matter?
∗ Lightest supersymmetric particle? Axion?
– Suppression of flavor changing neutral currents? Proton decay?Electric dipole moments?
∗ Automatic in standard model, but not in extensions
TASI 2008 Paul Langacker (IAS)
Conclusions
• The standard model is spectacularly successful, but is incomplete
• Promising theoretical ideas at Planck and TeV scale
• Eagerly anticipate guidance from LHC
TASI 2008 Paul Langacker (IAS)