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Electroweak Theory: 4

• 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) 94

References

• Slides at http://www.sns.ias.edu/∼pgl/talks/ (subject to revision)• P. Langacker, The Standard Model and Beyond, (CRC Press, 2010)

(especially chapters 6, 7)

• P. Langacker, Introduction to the Standard Model and ElectroweakPhysics, [arXiv:0901.0241 [hep-ph]] (TASI 2008)

• E.D. Commins and P.H. Bucksbaum, Weak Interactions of Leptonsand Quarks, (Cambridge, 1983)

• P. Renton, Electroweak Interactions, (Cambridge, 1990)• Precision Tests of the Standard Electroweak Model, ed. P. Langacker

(World, 1995) (especially Fetscher and Gerber; Herczog; Deutsch and Quin)

• K. Nakamura et al. [Particle Data Group], J. Phys. G 37, 075021(2010)(electroweak and other reviews)


http://www.sns.ias.edu/~pgl/talks/http://www.crcpress.com/product/isbn/9781420079067http://arXiv.org/abs/0901.0241http://pdg.lbl.gov/

Previous Lecture

• The Standard Electroweak Model– Beyond the Fermi Theory

– Gauge Theories and the Standard Model

– The Standard Electroweak Model

– Spontaneous Symmetry Breaking and the Higgs Mechanism

– The Lagrangian after Symmetry Breaking


This Lecture

• The Z, the W , and the Weak Neutral Current– The Weak Neutral Current

– Renormalization and Radiative Corrections

– The W and Z

– The Z Pole and Beyond

– Triple Gauge Vertices

– Global Analysis of the Standard Model and Beyond


The Z, the W , and the Weak Neutral Current

LZ = −g

2 cos θWJµZZµ

JµZ =∑

r

t3rLψ̄0rγµ(1− γ5)ψ0r − 2 sin2 θW JµQ

t3uL = −t3dL = t3νL = −t3eL = 12, tan θW = g′/g

−LNCeff =GF√

2JµZJZµ

• Primary prediction and test of electroweak unification

• WNC discovered 1973 (Gargamelle at CERN, HPW at FNAL)

• W , Z discovered directly 1983 (UA1, UA2)

• 90’s: Z pole (LEP, SLD), 0.1%


νe→ νe

− Lνe = GF√2ν̄µ γ

µ(1− γ5)νµ ē γµ(gνeV − gνeA γ5)e

SM : gνeV ∼ −1

2+ 2 sin2 θW , g

νeA ∼ −

1

2

Z

νµ e−

νµ e−

W

e− νe

νe e−

Z

νe e−

νe e−

– Typeset by FoilTEX – 1


• Any gauge model (with left-handed ν) → some gνeV,A• Need SM rad. corr.• νe : gνeV,A −−→WCC g

νeV,A + 1

• Alternative models w.disjoint parameters andperturbations on SM


• Cross sectiondσνµ,νµ

dy=

G2FmeEν

2π× [(gνeV ± gνeA )2 + (gνeV ∓ gνeA )2(1− y)2

−(gνe2V − gνe2A )y me

Eν

]

where 0 ≤ y ≡ Te/Eν ≤ (1 +me/2Eν)−1

• For Eν � me

σ =G2F me Eν

2π

[(gνeV ± gνeA )2 +

1

3(gνeV ∓ gνeA )2

]

• Flux uncertainties ∼ cancel in R ≡ σνµe/σν̄µe

• Most precise: CHARM II (CERN)


-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


Deep Inelastic ν Scattering

q

p

!(k)

X

!′(k′)


• e±p→ e±X, µ±p→ µ±X,(−)νµ p→ µ∓X,

(−)νµ p→

(−)νµX

at Q2 �M2p (or p→ n,N)

• WCC: test of QCD, quark model

Q2 = −q2 > 0 −→︸︷︷︸lab

2kk′(1− cos θ)

ν =p · qMp∼ k − k′

x =Q2

2Mpνy =

ν

Ek∼ k − k

′

k


νq → νq (Mainly Deep Inelastic)

• WNC: test of electroweak standard model

− LνHadron = GF√2ν̄ γµ (1− γ5)ν

×∑

i

[�L(i) q̄i γµ(1− γ5)qi + �R(i) q̄i γµ(1 + γ5)qi

]

• Standard model

�L(u) ∼1

2− 2

3sin2 θW �R(u) ∼ −

2

3sin2 θW

�L(d) ∼ −1

2+

1

3sin2 θW �R(d) ∼

1

3sin2 θW


• Deep inelastic (−)νµN →(−)νµX

q

p

!(k)

X

!′(k′)


d2σNCνNdx dy

=2G2FMpEν

π× {

[|�L(u)|2 + |�R(u)|2(1− y)2](xu+ xc ξc)

+[|�L(d)|2 + |�R(d)|2(1− y)2

](xd+ xs)

+[|�R(u)|2 + |�L(u)|2(1− y)2

](xū+ xc̄ ξc)

+[|�R(d)|2 + |�L(d)|2(1− y)2

](xd̄+ xs̄)}

(�L(i)↔ �R(i) for ν̄)


• 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 + g2Rr

Rν ≡σNCνNσCCνN

∼ g2L +g2Rr

– g2L ≡ �L(u)2 + �L(d)2 ≈ 12 − sin2 θW + 59 sin4 θW– g2R ≡ �R(u)2 + �R(d)2 ≈ 59 sin4 θW– r ≡ σCCνN /σCCνN measured (r → 1/3 for q̄/q → 0)


-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


• 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 �i(u)/�i(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 − σNCν̄NσCCνN − σCCν̄N

∼ g2L − g2R ∼1

2− sin2 θW


• NuTeV (FNAL) analysis minimizes mc uncertainty

• Obtains s2W = 0.2277 ± 0.0016 (insensitive to mt,MH), 3σ abovecurrent global fit value 0.2229(3) (New Ke3 ⇒ larger)

– New Physics (e.g., Z′, ν-mixing)?– QCD effect: e.g., isospin breaking; s− s̄ asymmetry (new NuTeV

reduces effect), nuclear; NLO QCD or EW corrections?


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− → `¯̀, qq̄, bb̄(SPEAR, PEP, DORIS, TRISTAN, LEP II)

– FB asymmetries in p̄p→ e+e− (CDF, D0)


• Parity-violating e-hadron

Leq =GF√

2

∑

i

[C1i ē γµ γ

5 e q̄i γµ qi + C2i ē γµ e q̄i 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


• 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


-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)


-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

0 25 50 75 100 125 150 175 200

e+e! " µ

+µ!

AF

B

#s [GeV]

LEP

L3

TRISTAN

AMY

TOPAZ

VENUS

PETRA

CELLO

JADE

MARK J

PLUTO

TASSO

PEP

HRS

MAC

MARK II

SPEAR

MARK I

(J. Mnich, Phys. Rep. 271, 181)10. Electroweak model and constraints on new physics 15

!"!!!# !"!!# !"!# !"# # #! #!! #!!! #!!!!

µ!"#$%&

!"$$%

!"$&

!"$&$

!"$&'

!"$&(

!"$&%

!"$'

!"$'$

!"$''

!"$'(

!"$'%

!"$)

*+,$θ '(µ)

-./0123

-./43

ν*+,-

5617#

859

:4;?,

4@AB8

CD556E

-F4

1. Electroweak model and constraints on new physics 33

Table 1.9: Values of the model-independent neutral-current parameters, comparedwith the SM predictions. There is a second gνeV,A solution, given approximately

by gνeV ↔ gνeA , which is eliminated by e+e− data under the assumption that theneutral current is dominated by the exchange of a single Z boson. The !L, as wellas the !R, are strongly correlated and non-Gaussian, so that for implementations werecommend the parametrization using g2i and θi = tan

−1[!i(u)/!i(d)], i = L or R.The analysis of more recent low energy experiments in polarized electron scatteringperformed in Ref. 123 is included by means of the two orthogonal constraints,cos γ C1d − sin γ C1u = 0.342 ± 0.063 and sin γ C1d + cos γ C1u = −0.0285 ± 0.0043,where tan γ ≈ 0.445. In the SM predictions, the uncertainty is from MZ , MH , mt,mb, mc, α̂(MZ), and αs.

Quantity Value SM Correlation

!L(u) 0.338 ± 0.016 0.3461(1)!L(d) −0.434 ± 0.012 −0.4292(1) non-!R(u) −0.174 +0.013−0.004 −0.1549(1) Gaussian!R(d) −0.023 +0.071−0.047 0.0775

g2L 0.3025 ± 0.0014 0.3040(2) −0.18 −0.21 −0.02g2R 0.0309 ± 0.0010 0.0300 −0.03 −0.07θL 2.48 ± 0.036 2.4630(1) 0.24θR 4.58

+0.41−0.28 5.1765

gνeV −0.040 ± 0.015 −0.0398(3) −0.05gνeA −0.507 ± 0.014 −0.5064(1)

C1u + C1d 0.1537 ± 0.0011 0.1528(1) 0.64 −0.18 −0.01C1u − C1d −0.516 ± 0.014 −0.5300(3) −0.27 −0.02C2u + C2d −0.21 ± 0.57 −0.0089 −0.30C2u − C2d −0.077 ± 0.044 −0.0625(5)

QW (e) = −2 C2e −0.0403 ± 0.0053 −0.0473(5)

defined in Eqs. (1.11)–(1.14) are given in Table 1.9 along with the predictions of theSM. The agreement is very good. (The ν-hadron results without the NuTeV data can befound in the 1998 edition of this Review, and the fits using the original NuTeV data in the2006 edition.) The off Z pole e+e− results are difficult to present in a model-independent

May 5, 2010 19:41


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; radiativecorrections)

– strong coupling αs (enters radiative corrections)

• Trade g, g′, ν for precisely known quantities– GF =

1√2ν2

from τµ (GF ∼ 1.166364(5)× 10−5 GeV−2 )

– α = 1/137.035999084(51) (but must extrapolate to MZ)

– MZ (or sin2 θW )


Definitions of sin2 θW

• Several equivalent expressions for sin2 θW at tree-level

sin2 θW = 1−M2WM2Z

⇒ on− shell

sin2 θW cos2 θW =

πα√2GFM

2Z

⇒ 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 (othersrelated by calculable, mt −MH dependent, corrections of O(α))


Radiative Corrections

γ

γ

γ


• 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


• Electroweak at multiloop level (include W , Z, γ)

self-energy vertex box


• (quadratic) mt and (logarithmic) MH dependence fromWW, ZZ, Zγ self-energies (SU(2)-breaking); mt from Zbb̄ vertex

t(b)

t(b)

Z(γ) Z

t

b

W W

H H


t

W

t

b b

Z

W

t

W

b b

Z



G


• αs from QCD vertices andmixed QCD-EW

• Mixed QCD-EW (e.g., self-energiesand vertices, fermion masses)

– Awkward in on-shell

t(b)

t(b)

Z(γ) Z

t

b

W W

H

H

H

G

mixed



The W and Z Masses and Decays

• On-shell scheme, s2W ≡ 1−M2W/M2Z

MW =A0

sW (1−∆r)1/2MZ =

MW

cW

c2W = 1− s2W , A0 = (πα/√

2GF )1/2 = 37.28061(8) GeV

∆r → rad. corrections relating α, α(MZ), GF , MW , and MZ

∆r ∼ 1− αα̂(MZ)︸︷︷︸

0.06655(11)

− ρttan2 θW︸︷︷︸

artificially large

+ small

ρt ≡3

8

GFm2t√

2π2= 0.00939

(mt

173.1 GeV

)2


• Modified minimal subtraction (MS) scheme

MW =A0

ŝZ(1−∆r̂W )1/2MZ =

MW

ρ̂1/2ĉZ

∆r̂W ∼ 1−α

α̂(MZ)︸︷︷︸0.06655(11)

+ small

ρ̂ ∼ 1 + 38

GFm2t√

2π2︸︷︷︸ρt∼0.00939

+ small


• The W decay width

Γ(W+ → e+νe) =GFM

3W

6√

2π≈ 226.31± 0.07 MeV

Γ(W+ → uid̄j) =CGFM

3W

6√

2π|Vij|2 ≈ (706.18± 0.22) |Vij|2 MeV

C =

1, leptons

3︸︷︷︸color

(1 + αs(MW )

π+ 1.409

α2sπ2− 12.77α3s

π3− 80.0α4s

π4

), quarks

– Also, QED, mass; g2MW/4√

2→ GFM3W absorbs running α– ΓW ∼ 2.0910± 0.0007 GeV (SM)– Experiment (LEP,CDF, D0): ΓW = 2.085± 0.042 GeV


The Z pole

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


The LEP/SLC Era

• Z Pole: e+e−→ Z → `+`−, qq̄, νν̄– 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−∗ qq̄, cc̄, bb̄, ss̄∗ νν̄ ⇒ Nν = 2.984± 0.009 if mν < MZ/2

– asymmetries: FB, polarization, Pτ , mixed

– lepton family universality


10-1

1

10

100 150!s" [GeV]

#ha

dron

SM: !s"´/"s" > 0.10SM: !s"´/"s" > 0.85

Combined LEP

TOPAZ


The Z Lineshape

Basic Observables: e+e−→ ff̄ (f = e, µ, τ, s, b, c, hadrons)(s = E2CM)

σf(s) ∼ σfsΓ2Z

(s−M2Z)2

+s2Γ2ZM2Z

(plus initial state rad. corrections)

MZ and ΓZ: from peak position and width

Peak Cross Section:

σf =12π

M2Z

Γ(e+e−)Γ(ff̄)

Γ2Z

(Z model independent; γ and γ − Z int. removed, (usually) assuming S.M.)


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 effects yields the dashed curves, whichdefine the Z parameters described in the text.

33

(LEPEWWG, hep-ex/0509008)


• The Z width and partial widths

Γ(ff̄) ∼ CfGFM3Z

6√

2πρ̂︸︷︷︸

only MS

[|ḡV f |2 + |ḡAf |2]

(plus fermion mass, QED (2 loop), QCD (3 loop), mixed QED-QCD(2 loop) corrections; C` = 1, Cq = 3)

ḡAf =√ρft

f3L ḡV f =

√ρf

(tf3L − 2s̄2fqf

)

s̄2f = κfs2W = κ̂f ŝ

2Z

• Standard model (mt = 173.2(1.3) GeV, MH = 117 GeV)

Γ(ff̄) ∼

300.20± 0.06 MeV(uū), 167.21± 0.02 MeV(νν̄)382.98± 0.06 MeV(dd̄), 83.99± 0.01 MeV(e+e−)375.94∓ 0.04 MeV(bb̄)


• Conventional (weakly correlated) observables: MZ,ΓZ, σhad, R`, Rb, Rc

σhad ≡12π

M2Z

Γ(e+e−)Γ(Z → hadrons)Γ2Z

Rqi ≡Γ(qiq̄i)

Γ(had), qi = (b, c)

Rì ≡Γ(had)

Γ(ì ¯̀i), ì = (e, µ, τ )

(lepton universality test: Re = Rµ = Rτ → R`)

• Derived

Γ(inv) = ΓZ − Γ(had)−∑

i

Γ(ì ¯̀i) ≡ NνΓ(νν̄)

(counts anything invisible in detector)


0.01

0.014

0.018

0.022

20.6 20.7 20.8 20.9R0l=!had/!ll

A0,l fb

68% CL

l+l"e+e"µ+µ"

#+#"

$s

mt

mH

%$

Rl

MH

[G

eV]

Ratio of Hadronic to Leptonic Width

Mt = 172.7±2.9 GeV

linearly added to!S = 0.118±0.003

Experiment Rl = "had / "lALEPH 20.729 ± 0.039

DELPHI 20.730 ± 0.060

L3 20.809 ± 0.060

OPAL 20.822 ± 0.044

#2 / dof = 3.5 / 3

LEP 20.767 ± 0.025

common error 0.007

10

10 2

10 3

20.65 20.75 20.85


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. Grünewald and the LEP Electroweak Working Group, 2003)

• Nν = 3 + ∆Nν = 2.984±0.009

• ∆Nν = 1 for fourth family ν withmν . MZ/2

• ∆Nν = 12, light ν̃ in super-symmetry

• ∆Nν = 2, Majoron + scalarin triplet model of mν withspontaneous L violation


Z-Pole Asymmetries

• Effective axial and vector couplings of Z to fermion f

ḡAf =√ρft3f

ḡV f =√ρf

[t3f − 2s̄2fqf

]

where s̄2f the effective weak angle,

s̄2f = κfs2W (on− shell)

= κ̂f ŝ2Z ∼ ŝ2Z + 0.00029 (f = e) (MS),

ρf , κf , and κ̂f are electroweak corrections, qf = electric charge,t3f = weak isospin


• A0 = Born asymmetry (after removing γ, off-pole, box (small), Pe−)

forward− backward : A0fFB =3

4AeAf

(A0eFB = A0µFB = A

0τFB ≡ A0`FB ⇒ universality)

τ polarization : P 0τ = −Aτ +Ae

2z1+z2

1 +AτAe2z

1+z2

(z = cos θ, θ = scattering angle)

e− polarization (SLD) : A0LR = Ae

mixed (SLD) : A0FBLR =σfLF − σfLB − σfRF + σfRBσfLF + σ

fLB + σ

fRF + σ

fRB

=3

4Af

Af ≡2ḡV f ḡAf

ḡ2V f + ḡ2Af

ḡV ` ∼ −1

2+ 2s̄2` (small)


• Asymmetries depend onAf ≡ 2ḡV f ḡAfḡ2

V f+ḡ2

Af→ little sensitivity

to mt, MH

• mt, MH enter in comparisonwith MZ and other lineshape

• ALR ∝ ḡV ` ∼ −12 + 2s̄2` moresensitive to s̄2` than A

0`FB ∝ ḡ2V `

• A0bFB = 34AeAb much moresensitive to e vertex than bvertex assuming SM, but possiblediscrepancy

A0,lFBM

H [

GeV

]

Forward-Backward Pole Asymmetry

Mt = 172.7±2.9 GeV

linearly added to 0.02758±0.00035!"(5)!"had=

Experiment A0,lFBALEPH 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


1. Electroweak model and constraints on new physics 27

Table 1.6: Principal Z pole observables and their SM predictions (cf. Table 1.5).

The first s2! (A(0,q)FB ) is the effective angle extracted from the hadronic charge

asymmetry while the second is the combined lepton asymmetry from CDF [157] andDØ [158]. The three values of Ae are (i) from ALR for hadronic final states [152];(ii) from ALR for leptonic final states and from polarized Bhabba scattering [154];and (iii) from the angular distribution of the τ polarization at LEP 1. The two Aτvalues are from SLD and the total τ polarization, respectively.

Quantity Value Standard Model Pull Dev.

MZ [GeV] 91.1876 ± 0.0021 91.1874 ± 0.0021 0.1 0.0ΓZ [GeV] 2.4952 ± 0.0023 2.4954 ± 0.0009 −0.1 0.1Γ(had) [GeV] 1.7444 ± 0.0020 1.7418 ± 0.0009 — —Γ(inv) [MeV] 499.0 ± 1.5 501.69 ± 0.07 — —Γ("+"−) [MeV] 83.984 ± 0.086 84.005 ± 0.015 — —σhad[nb] 41.541 ± 0.037 41.484 ± 0.008 1.5 1.5Re 20.804 ± 0.050 20.735 ± 0.010 1.4 1.4Rµ 20.785 ± 0.033 20.735 ± 0.010 1.5 1.6Rτ 20.764 ± 0.045 20.780 ± 0.010 −0.4 −0.3Rb 0.21629 ± 0.00066 0.21578 ± 0.00005 0.8 0.8Rc 0.1721 ± 0.0030 0.17224 ± 0.00003 0.0 0.0A

(0,e)FB 0.0145 ± 0.0025 0.01633 ± 0.00021 −0.7 −0.7

A(0,µ)FB 0.0169 ± 0.0013 0.4 0.6

A(0,τ)FB 0.0188 ± 0.0017 1.5 1.6

A(0,b)FB 0.0992 ± 0.0016 0.1034 ± 0.0007 −2.7 −2.3

A(0,c)FB 0.0707 ± 0.0035 0.0739 ± 0.0005 −0.9 −0.8

A(0,s)FB 0.0976 ± 0.0114 0.1035 ± 0.0007 −0.6 −0.4

s̄2! (A(0,q)FB ) 0.2324 ± 0.0012 0.23146 ± 0.00012 0.8 0.7

0.2316 ± 0.0018 0.1 0.0Ae 0.15138 ± 0.00216 0.1475 ± 0.0010 1.8 2.2

0.1544 ± 0.0060 1.1 1.30.1498 ± 0.0049 0.5 0.6

Aµ 0.142 ± 0.015 −0.4 −0.3Aτ 0.136 ± 0.015 −0.8 −0.7

0.1439 ± 0.0043 −0.8 −0.7Ab 0.923 ± 0.020 0.9348 ± 0.0001 −0.6 −0.6Ac 0.670 ± 0.027 0.6680 ± 0.0004 0.1 0.1As 0.895 ± 0.091 0.9357 ± 0.0001 −0.4 −0.4

May 5, 2010 19:41STIAS (January, 2011) Paul Langacker (IAS) 136

• LEP 2– e+e−→ ff̄– MW , ΓW , B (also Tevatron)

– MH limits (hint?)

– WW production (triple gaugevertex)

– Quartic vertex

– SUSY/exotics searches

Cµνσ(p, q, r) ≡gµν(q − p)σ+ gµσ(p− r)ν + gνσ(r − q)µ

Qµνρσ ≡2gµνgρσ − gµρgνσ − gµσgνρ

q

p r

γν

W+µ W−σ

q

p r

Zν

W+µ W−σ

W+ν

W+µ

W−σ

W−ρ

Zν

W+µ

γσ

W−ρ

Zν

W+µ

Zσ

W−ρ

γν

W+µ

γσ

W−ρ


ieCµνσ(p, q, r)

ie

tan θWCµνσ(p, q, r)

ie2

sin2 θWQµνρσ

−i e2

tan θWQµρνσ

−i e2

tan2 θWQµρνσ

−ie2Qµρνσ


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

νe

W − W +

e− e+

γ

W − W +

e− e+

Z

W − W +

e− e+


(Tree-level diagrams contributing to e+e− →W+W−)


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


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)


26 1. Electroweak model and constraints on new physics

Table 1.5: Principal non-Z pole observables, compared with the SM best fitpredictions. The first MW value is from the Tevatron [207] and the second onefrom LEP 2 [160]. The values of MW and mt differ from those in the ParticleListings when they include recent preliminary results. g2L, which has been adjusted

as discussed in Sec. 1.3, and g2R are from NuTeV [98] and have a very small(−1.7%) residual anti-correlation. e-DIS [123] and the older ν-DIS constraints fromCDHS [92], CHARM [93], and CCFR [94] are included, as well, but not shownin the Table. The world averages for gνeV,A are dominated by the CHARM II [116]

results, gνeV = −0.035 ± 0.017 and gνeA = −0.503 ± 0.017. The errors are the total(experimental plus theoretical) uncertainties. The ττ value is the τ lifetime worldaverage computed by combining the direct measurements with values derived fromthe leptonic branching ratios [5]; in this case, the theory uncertainty is included inthe SM prediction. In all other SM predictions, the uncertainty is from MZ , MH ,mt, mb, mc, α̂(MZ), and αs, and their correlations have been accounted for. Thecolumn denoted Pull gives the standard deviations for the principal fit with MHfree, while the column denoted Dev. (Deviation) is for MH = 117 GeV fixed.

Quantity Value Standard Model Pull Dev.

mt [GeV] 173.1 ± 1.3 173.2 ± 1.3 −0.1 −0.5MW [GeV] 80.420 ± 0.031 80.384 ± 0.014 1.2 1.5

80.376 ± 0.033 −0.2 0.1g2L 0.3027 ± 0.0018 0.30399 ± 0.00017 −0.7 −0.6g2R 0.0308 ± 0.0011 0.03001 ± 0.00002 0.7 0.7gνeV −0.040 ± 0.015 −0.0398 ± 0.0003 0.0 0.0gνeA −0.507 ± 0.014 −0.5064 ± 0.0001 0.0 0.0QW (e) −0.0403 ± 0.0053 −0.0473 ± 0.0005 1.3 1.2QW (Cs) −73.20 ± 0.35 −73.15 ± 0.02 −0.1 −0.1QW (Tl) −116.4 ± 3.6 −116.76 ± 0.04 0.1 0.1ττ [fs] 291.09 ± 0.48 290.02 ± 2.09 0.5 0.5Γ(b→sγ)

Γ(b→Xeν)(3.38+0.51−0.44

)× 10−3 (3.11 ± 0.07) × 10−3 0.6 0.6

12 (gµ − 2 − απ ) (4511.07 ± 0.77) × 10−9 (4509.13 ± 0.08) × 10−9 2.5 2.5

Note, however, that the uncertainty in A(0,b)FB is strongly statistics dominated. The

combined value, Ab = 0.899 ± 0.013 deviates by 2.8 σ. It would be difficult to account forthis 4.0% deviation by new physics that enters only at the level of radiative correctionssince about a 20% correction to κ̂b would be necessary to account for the central valueof Ab [211]. If this deviation is due to new physics, it is most likely of tree-level typeaffecting preferentially the third generation. Examples include the decay of a scalar

May 5, 2010 19:41


Global Electroweak Fits

• much more information than individual experiments

• caveat: experimental/theoretical systematics, correlations

• PDG ’10 review ((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


Global Standard Model Fit Results

• PDG 2010 (11/09) (Erler,PL)

– χ2/df = 43.0/44

– Fully MS

– Good agreement withLEPEWWG up to knowneffects

MH = 90+27−22 GeV,

mt = 173.2± 1.3 GeVαs = 0.1183± 0.0015ŝ2Z = 0.23116± 0.00013s̄2` = 0.23146± 0.00012s2W = 0.22292± 0.00028

(1)


• mt = 173.2± 1.3 GeV

– 176.0+8.5−7.0 GeV from indirect (loops) only (direct: 173.1± 1.3)t(b)

t(b)

Z(γ) Z

t

b

W W

H

H

H

G

mixed


– Fit actually uses MS mass m̂t(m̂t) (∼ 10 GeV lower) and convertsto pole mass at end

– Significant change from previous analysis due to lower mt fromRun II


• αs= 0.1183± 0.0015

– Excellent agreement with otherdeterminations (e.g.,quarkonia/lattice, jets)

– World average: αs = 0.1184(7))(Bethke, 0908.1135)

– Z-pole alone: αs = 0.1198(28)

– insensitive to oblique new physics

– very sensitive to non-universalnew physics (e.g., Zbb̄ vertex)

G



• Higgs mass MH= 90+27−22 GeV– LEPEWWG: 89+35−26– direct limit (LEP 2): MH & 114.4 (95%) GeV

– SM: 85 (vac. stab.) . MH . 700 (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 < 149 GeV at 95%, including direct LEP 2

• Electroweak at multiloop level (include W , Z, γ)

self-energy vertex box


• (quadratic) mt and (logarithmic) MH dependence fromWW, ZZ, Zγ self-energies (SU(2)-breaking); mt from Zbb̄ vertex

t(b)

t(b)

Z(γ) Z

t

b

W W

H H


t

W

t

b b

Z

W

t

W

b b

Z


STIAS (January, 2011) Paul Langacker (IAS) 119STIAS (January, 2011) Paul Langacker (IAS) 146

145 150 155 160 165 170 175 180 185 190mt [GeV]

10

20

30

50

100

200

300

500

1000M

H [

GeV

]

LEP 2

Tevatron excluded (95% CL)

excluded

all data (90% CL)

(95% CL)

ΓZ, σ

had, R

l, R

q

Z pole asymmetriesMWlow energymt


160 165 170 175 180 185mt [GeV]

80.3

80.35

80.4

80.45M

W [

GeV

]

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%)


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 uncertaintyJuly 2010 mLimit = 158 GeV


1

10

100 110 120 130 140 150 160 170 180 190 200

1

10

mH(GeV/c2)

95%

CL

Lim

it/S

M

Tevatron Run II Preliminary, = 5.9 fb-1

ExpectedObserved±1σ Expected±2σ Expected

LEP Exclusion TevatronExclusion

SM=1

Tevatron Exclusion July 19, 2010


Beyond the standard model

• Oblique corrections: new particles which affect W ,Z, γ propagators but not the fermion vertices!

γ γ

t had


• 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∆m2i (Ci = color factor)

∆m2 ≡ m21 +m22 −4m21m

22

m21 −m22lnm1

m2≥ (m1 −m2)2

– Higgs triplets with non-zero VEVs


• 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 →{

23π

(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)


• ρ0; S, T, U : Higgs triplets, nondegenerate fermions or scalars;chiral families (ETC)

S = 0.03± 0.09 (−0.07)T = 0.07± 0.08 (+0.09)

for MH = 117 (300) GeV and U = 0

– ρ0 ' 1 + αT = 1.0008+0.0017−0.0007 and 114.4 GeV < MH < 427GeV (for S = U = 0) → ∑iCi∆m2i/3 < (106 GeV)2 (95% cl)

– Can evade Higgs mass limit for S < 0, T > 0 (Higgs doublet/tripletloops, Majorana fermions)

– Unmixed degenerate heavy family excluded at 6σ


-1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

S

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25T

all: MH = 117 GeV

all: MH = 340 GeV

all: MH = 1000 GeV

ΓZ, σ

had, R

l, R

q

asymmetries

MWν scatteringe scattering

APV


• Supersymmetry– decoupling limit

(Mnew & 200− 300 GeV):only precision effect is lightSM-like Higgs

– little improvement on SMfit

– Supersymmetry parametersconstrained


• 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− 1200 GeV (Tevatron, LEP 2, WNC),|θZ−Z′| < few × 10−3 (Z-pole)


-0.004 -0.002 0 0.002 0.0040

1

2

3

4

5

6

x

0.6 0.2

CDFD0LEP 2

MZ’

[TeV]

Zχ

sin θzz’

0.4 00.81

-0.004 -0.002 0 0.002 0.0040

1

2

3

4

5

6

x

CDF

MZ’

[TeV]

Z ψ

sin θzz’

00.50.751 0.25

D0LEP 2


Z′ MZ′ [GeV] sin θZZ′ χ2min

EW CDF DØ LEP 2 sin θZZ′ sin θminZZ′ sin θ

maxZZ′

Zχ 1,141 892 640 673 −0.0004 −0.0016 0.0006 47.3Zψ 147 878 650 481 −0.0005 −0.0018 0.0009 46.5Zη 427 982 680 434 −0.0015 −0.0047 0.0021 47.7ZI 1,204 789 575 0.0003 −0.0005 0.0012 47.4ZS 1,257 821 0.0003 −0.0005 0.0013 47.3ZN 754 861 −0.0005 −0.0020 0.0012 47.5ZR 442 0.0003 −0.0009 0.0015 46.1ZLR 998 630 804 −0.0004 −0.0013 0.0006 47.3ZSM 1,401 1,030 780 1,787 −0.0008 −0.0026 0.0007 47.2Zstring 1,362 0.0002 −0.0005 0.0009 47.7

SM ∞ 0 48.5

(Erler, PL, Munir, Peña, arXiv:0906.2435 [hep-ph])


• Other extensions of the standard model

– Exotic fermion mixings

– Large extra dimensions

– New four-fermi operator

– Leptoquark bosons

– Little Higgs

– Dynamical symmetry breaking


• Gauge unification: GUTs, stringtheories

– α+ ŝ2Z → αs = 0.130±0.010(MSSM) (non-SUSY: 0.073(1))

– Experiment: αs = 0.1183(15)

– MG ∼ 3× 1016 GeV– Perturbative string: ∼ 5×1017

GeV (10% in lnMG). Exotics:O(1) corrections.

• Gauge unification: GUTs, stringtheories

– α+ ŝ2Z → αs = 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) 40STIAS (January, 2011) Paul Langacker (IAS) 160

• The precision program:– SM correct and unique to zeroth

approx. (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|/σmeas0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02758 ± 0.00035 0.02768

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4959σhad [nb]σ

0 41.540 ± 0.037 41.479RlRl 20.767 ± 0.025 20.742AfbA

0,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 0.1723AfbA

0,b 0.0992 ± 0.0016 0.1038AfbA

0,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 0.1481sin2θeffsin

2θlept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.399 ± 0.023 80.379ΓW [GeV]ΓW [GeV] 2.085 ± 0.042 2.092mt [GeV]mt [GeV] 173.3 ± 1.1 173.4

July 2010


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