Electroweak Physicspgl/talks/TASI08_2(PGL).pdfElectroweak Physics Tests of the Standard Model and Beyond Problems With the Standard Model (Structure Of The Standard Model, hep-ph/0304186.

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)


• 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))


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))


-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


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


• 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)


• 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)


-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 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


• 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?


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)


• 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


• 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)


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)


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 )


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))


Radiative Corrections

!

!

!


• 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). Also, mt from Zbbvertex.

t(b)

t(b)

Z(!) Z

t

b

W W

H

H

H

G

mixed


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-energies

and vertices, fermion masses)

– Awkward in on-shell

t(b)

t(b)

Z(!) Z

t

b

W W

H

H

H

G

mixed



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


• 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


• 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


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


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


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−→ 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.)


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)


• 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)


• 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)

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(νν)

(counts anything invisible in detector)


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


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


• 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)


• 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


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


• LEP 2

– e+e−→ ff

– MW , ΓW , B (also Tevatron)

– MH limits (hint?)

– WW production (triple gaugevertex)

– Quartic vertex

– SUSY/exotics searches


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−



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)


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


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



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

!



• 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


– 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)


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)



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

"



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


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


• 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


– 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


• 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



• 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



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


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%)


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


Beyond the standard model

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

" "

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∆m2

i (Ci = color factor)

∆m2 ≡ m21 +m2

2 −4m2

1m22

m21 −m2

2lnm1

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 →{ 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)


• 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


-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


• Supersymmetry

– decoupling limit (Mnew>∼

200 − 300 GeV): onlyprecision effect is light SM-like Higgs

– little improvement on SM fit

– 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 − 900 GeV (Tevatron, LEP 2, WNC),|θZ−Z′| < few × 10−3 (Z-pole)


−0.01 −0.005 0 0.005 0.010

500

1000

1500

2000

2500

sin θ

X

MZ [GeV]

05

CDF excluded

Zχ

1oo


• Other

– Exotic fermion mixings

– Large extra dimensions

– New four-fermi operator

– Leptoquark bosons

– Little Higgs


• 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


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.


• 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


• 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)?


• 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


Conclusions

• The standard model is spectacularly successful, but is incomplete

• Promising theoretical ideas at Planck and TeV scale

• Eagerly anticipate guidance from LHC


Electroweak Physicspgl/talks/TASI08_2(PGL).pdfElectroweak Physics Tests of the Standard Model and Beyond Problems With the Standard Model (Structure Of The Standard Model, hep-ph/0304186.

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