University of Pennsylvania School of Arts and Sciencespgl/talks/baeza.pdfElectroweak Physics 140 150...

Electroweak Physics

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

• Origins of the Electroweak Theory

• The Standard Model Lagrangian

• Spontaneous Symmetry Breaking

• The Gauge Interactions

• Tests of the Standard Model and Beyond

(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.)

Baeza 2008 Paul Langacker (IAS)

The Weak Interactions

• Radioactivity (Becquerel, 1896)

• β decay appeared to violate energy(Meitner, Hahn; 1911)

• Neutrino hypothesis (Pauli, 1930)

– νe (Reines, Cowan; 1953)

– νµ (Lederman, Schwartz, Steinberger;1962)

– ντ (DONUT, 2000) (τ , 1975)


• Fermi theory (1933)

– Loosely like QED, but zero range (non-renormalizable) and non-diagonal (charged current)

pe!

!e

n

J†µ Jµ

e! !e

!e e!

Jµ J†µ e! !e

!e e!

!e e!

"W !

pe!

!e

n

g g "W +

e! !e

!e e!

g g

– Typeset by FoilTEX – 1

H ∼ GFJ†µJµ

J†µ ∼ pγµn+νeγµe− [n→ p, e−→ νe]

Jµ ∼ nγµp+eγµνe [p→ n, νe→ e− ( × → e−νe)]

GF ' 1.17×10−5 GeV−2 [Fermi constant]


• Fermi theory modified to include

– µ, τ decay

– strangeness (Cabibbo)

– quark model

– heavy quarks (CKM)

– ν mass and mixing

– parity violation (V −A) (Lee, Yang; Wu; Feynman-Gell-Mann)

• Fermi theory correctly describes (at tree level)

– Nuclear/neutron β decay (n→ pe−νe)

– µ, τ decays (µ− → e−νeνµ; τ− → µ−νµντ , ντπ−, · · · )

– π, K decays (π+ → µ+νµ, π0e+νe; K+ → µ+νµ, π

0e+νe, π+π0)

– hyperon decays (Λ→ pπ−; Σ− → nπ−; Σ+ → Λe+νe)

– heavy quark decays (c→ se+νe; b→ cµ−νµ, cπ−)

– ν scattering (νµe− → µ−νe; νµn→ µ

−p| {z }

“elastic”

; νµN → µ−X| {z }

deep−inelastic

)


• Fermi theory violates unitarity at high energy (non-renormalizable)

pe!

!e

n

J†µ Jµ

e! !e

!e e!

Jµ J†µ e! !e

!e e!

!e e!

"W !

pe!

!e

n

g g "W +

e! !e

!e e!

g g


– σ(νee−→ e−νe)→G2F s

π(s ≡ E2

CM)

– pure S-wave unitarity: σ < 16πs

– fails for ECM2 ≥√

πGF∼ 500 GeV

– Born not unitary; often restored by H.O.T.

– Fermi theory: divergent integrals∫d4k

( 6 k +me

k2 −m2e

) 6 kk2

pe!

!e

n

J†µ Jµ

e! !e

!e e!

Jµ J†µ e! !e

!e e!

!e e!

"W !

pe!

!e

n

g g "W +

e! !e

!e e!

g g



• Intermediate vector boson theory (Yukawa, 1935; Schwinger, 1957)

pe!

!e

n

J†µ Jµ

e! !e

!e e!

Jµ J†µ e! !e

!e e!

!e e!

"W !

pe!

!e

n

g g "W +

e! !e

!e e!

g g


pe!

!e

n

J†µ Jµ

e! !e

!e e!

Jµ J†µ e! !e

!e e!

!e e!

"W !

pe!

!e

n

g g "W +

e! !e

!e e!

g g


GF√2∼

g2

8M2W

for MW � Q

– no longer pure S-wave ⇒

– νee−→ νee

− better behaved


!e

W ! W +

e! e+

g g W 0

W ! W +

e! e+

g

g

Z

d s

d sK0

K0


– but, e+e− → W+W− violatesunitarity for

√s >∼ 500 GeV

– εµ ∼ kµ/MW for longitudinalpolarization (non-renormalizable)

– introduce W 0 to cancel

– fixes W 0W+W− and e+e−W 0

vertices

– requires[J, J†

]∼ J0

(like SU(2)× U(1))

– not realistic

!e

W ! W +

e! e+

g g W 0

W ! W +

e! e+

g

g

Z

d s

d sK0

K0



• Glashow model (1961) (W±, Z, γ, but no mechanism for MW,Z)

• Weinberg-Salam (1967): Higgs mechanism → MW,Z

• Renormalizable (1971) (’t Hooft, · · · )

• Flavor changing neutral currents (FCNC)

– very large K0 ↔ K0 mixing

– GIM mechanism (c quark) (1970)

– c discovered (1974)

!e

W ! W +

e! e+

g g W 0

W ! W +

e! e+

g

g

Z

d s

d sK0

K0



• Weak neutral current(1973)

• QCD (1970’s)

• W,Z (1983)

• Precision tests (1989-2000)

• CKM unitarity (∼ 1995-)

• t quark (1995)

• ν mass (1998-2002)

Measurement Fit |Omeas−Ofit|/σmeas

0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02758 ± 0.00035 0.02768mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1875ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4957σhad [nb]σ0 41.540 ± 0.037 41.477RlRl 20.767 ± 0.025 20.744AfbA0,l 0.01714 ± 0.00095 0.01645Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1481RbRb 0.21629 ± 0.00066 0.21586RcRc 0.1721 ± 0.0030 0.1722AfbA0,b 0.0992 ± 0.0016 0.1038AfbA0,c 0.0707 ± 0.0035 0.0742AbAb 0.923 ± 0.020 0.935AcAc 0.670 ± 0.027 0.668Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1481sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.398 ± 0.025 80.374ΓW [GeV]ΓW [GeV] 2.140 ± 0.060 2.091mt [GeV]mt [GeV] 170.9 ± 1.8 171.3


The Standard Model

• Gauge group SU(3)× SU(2)× U(1); gauge couplings gs, g, g′(ud

)L

(ud

)L

(ud

)L

(νee−

)L

uR uR uR νeR(?)dR dR dR e−R

( L = left-handed, R = right-handed)

• SU(3): u ↔ u ↔ u, d ↔ d ↔ d (8 gluons)

• SU(2): uL↔ dL, νeL↔ e−L (W±); phases (W 0)

• U(1): phases (B)

• Heavy families (c, s, νµ, µ−), (t, b, ντ , τ−)


The Electroweak Sector

LSU(2)×U(1) = Lgauge + Lϕ + Lf + LYukawa

Gauge part

Lgauge = −1

4F iµνF

µνi −1

4BµνB

µν

Field strength tensors

Bµν = ∂µBν − ∂νBµF iµν = ∂µW

iν − ∂νW

iµ − gεijkW

jµW

kν , i = 1 · · · 3

g(g′) is SU(2) (U(1)) gauge coupling; εijk is totally antisymmetric symbol

Three and four-point self-interactions for the Wi

B and W3 will mix to form γ, Z

g g2



U(1): Φj → exp(ig′yjβ)Φj, yj = qj − t3j = weak hypercharge

Scalar part

Lϕ = (Dµϕ)†Dµϕ− V (ϕ)

where ϕ =„ϕ+

ϕ0

«is the (complex) Higgs doublet with yϕ = 1/2.

Gauge covariant derivative:

Dµϕ =

(∂µ + ig

τ i

2W iµ +

ig′

2Bµ

)ϕ

where τ i are the Pauli matrices

Three and four-point interactionsbetween gauge and scalar fields g g2



Higgs potential

V (ϕ) = +µ2ϕ†ϕ+ λ(ϕ†ϕ)2

Allowed by renormalizability and gaugeinvariance

Spontaneous symmetry breaking for µ2 < 0

Vacuum stability: λ > 0.

Quartic self-interactions!+

!0

!!

!0

"



Fermion part

LF =F∑m=1

(q0mLi 6Dq

0mL + l0mLi 6Dl

0mL

+ u0mRi 6Du

0mR + d0

mRi 6Dd0mR + e0

mRi 6De0mR+ν0

mRi 6Dν0mR

)L-doublets

q0mL =

(u0m

d0m

)L

l0mL =(ν0m

e−0m

)L

R-singlets

u0mR, d

0mR, e

−0mR, ν

0mR(?)

(F ≥ 3 families; m = 1 · · ·F = family index;0 = weak eigenstates (definite SU(2) rep.), mixtures of mass eigenstates (flavors);

quark color indices α = r, g, b suppressed (e.g., u0mαL). )

Can add gauge singlet ν0mR for Dirac neutrino mass term


Different (chiral) L and R representations lead to parity and chargeconjugation violation (maximal for SU(2))

Fermion mass terms forbidden by chiral symmetry

Triangle anomalies absent for chosen hypercharges (quark-leptoncancellations)


Gauge covariant derivatives

Dµq0mL =

(∂µ +

ig

2τ iW i

µ + ig′

6Bµ

)q0mL

Dµl0mL =

(∂µ +

ig

2τ iW i

µ − ig′

2Bµ

)l0mL

Dµu0mR =

(∂µ + i

2

3g′Bµ

)u0mR

Dµd0mR =

(∂µ − i

g′

3Bµ

)d0mR

Dµe0mR = (∂µ − ig′Bµ) e0

mR

Read off W and Bcouplings to fermions W i

µ

!ig2! i"µ

“1!"5

2

”

Bµ!ig"y"µ

“1#"5

2

”



Spontaneous Symmetry Breaking (Higgs mechanism)

Higgs covariant kinetic energy terms:

(Dµϕ)†Dµϕ =1

2(0 ν)

[g

2τ iW i

µ +g′

2Bµ

]2(0ν

)+H terms

→ M2WW

+µW−µ +M2Z

2ZµZµ

+ H kinetic energy and gauge interaction terms

W

W

!

!

g2

eR

eL

!he


MW =gν

2

me =heν√

2W

W

!

!

g2

eR

eL

!he



Mass eigenstate bosons: W, Z, and A (photon)

W± =1√

2(W 1 ∓ iW 2)

Z = − sin θWB + cos θWW 3

A = cos θWB + sin θWW 3

Weak angle: tan θW ≡ g′/g

Masses:

MW =gν

2, MZ =

√g2 + g′2

ν

2=

MW

cos θW, MA = 0

(Goldstone scalars “eaten”→ longitudinal components of W±, Z )


Will show: Fermi constant GF/√

2 ∼ g2/8M2W

(GF = 1.166367(5)× 10−5 GeV −2 from muon lifetime)

Electroweak scale:

ν = 2MW/g ' (√

2GF )−1/2 ' 246 GeV

Will show: g = e/ sin θW (α = e2/4π ∼ 1/137.036) ⇒

MW = MZ cos θW =gν

2∼

(πα/√

2GF )1/2

sin θW

Weak neutral current: sin2 θW ∼ 0.23 ⇒ MW ∼ 78 GeV , andMZ ∼ 89 GeV (increased by ∼ 2 GeV by loop corrections)

Discovered at CERN: UA1 and UA2, 1983


The Weak Charged Current

Fermi Theory incorporated in SM and made renormalizable

W -fermion interaction

L = −g

2√

2

(JµWW

−µ + Jµ†WW

+µ

)

Charge-raising current (ignoring ν masses)

Jµ†W =F∑m=1

[ν0mγ

µ(1− γ5)e0m + u0

mγµ(1− γ5)d0

m

]= (νeνµντ)γµ(1− γ5)

e−

µ−

τ−

+ (u c t)γµ(1− γ5)V

dsb

.Baeza 2008 Paul Langacker (IAS)

Ignore ν masses for now

Pure V − A ⇒ maximal P and C violation; CP conserved exceptfor phases in V

V = Au†L AdL is F × F unitary Cabibbo-Kobayashi-Maskawa (CKM)

matrix from mismatch between weak and Yukawa interactions

Cabibbo matrix for F = 2

V =(

cos θc sin θc− sin θc cos θc

)

sin θc ' 0.22 ≡ Cabibbo angle

Good zeroth-order description since third family almost decouples


CKM matrix for F = 3 involves 3 angles and 1 CP -violating phase(after removing unobservable qL phases) (new interations involving qR

could make observable)

V =

Vud Vus VubVcd Vcs VcbVtd Vtd Vtd

Extensive studies, especially in B decays, to test unitarity of V as

probe of new physics and test origin of CP violation

Need additional source of CP breaking for baryogenesis


Effective zero- range 4-fermi interaction (Fermi theory)

For |Q| � MW ,neglect Q2 in Wpropagator

−Lcceff =(

g

2√

2

)2

JµW

( −gµνQ2 −M2

W

)J†νW ∼

g2

8M2W

JµWJ†Wµ

Fermi constant: GF√2' g2

8M2W

= 12ν2

Muon lifetime: τ−1 =G2Fm

5µ

192π3 ⇒ GF = 1.17× 10−5 GeV−2

Weak scale: ν =√

2〈0|ϕ0|0〉 ' 246 GeV

Excellent description of β, K, hyperon, heavy quark, µ, and τdecays, νµe→ µ−νe, νµn→ µ−p, νµN → µ−X


Full theory probed:

e±p→(−)ν e X at high energy (HERA)

Electroweak radiative corrections (loop level)(Very important. Only calculable in full theory.)

MKS −MKL, kaon CP violation, B ↔ B mixing (loop level)

-1.5

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5 2

sin 2!

sol. w/ cos 2! < 0(excl. at CL > 0.95)

excluded at CL > 0.95

"

"

#

#

$md

$ms & $md

%K

%K

|Vub/Vcb|

sin 2!

sol. w/ cos 2! < 0(excl. at CL > 0.95)

excluded at CL > 0.95

#

!"

&

'

excluded area has CL > 0.95

C K Mf i t t e r

EPS 2005

(CKMFITTER group:

http://ckmfitter.in2p3.fr/)


Quantum Electrodynamics (QED)

Incorporated into standard model

Lagrangian:

L = −gg′√g2 + g′2

JµQ(cos θWBµ + sin θWW 3µ)

Photon field:

Aµ = cos θWBµ + sin θWW 3µ

Positron electric charge: e = g sin θW , where tan θW ≡ g′/g


Electromagnetic current:

JµQ =F∑m=1

[2

3u0mγ

µu0m −

1

3d0mγ

µd0m − e

0mγ

µe0m

]

=F∑m=1

[2

3umγ

µum −1

3dmγ

µdm − emγµem]

Electric charge: Q = T 3 + Y , where Y = weak hypercharge(coefficient of ig′Bµ in covariant derivatives)

Flavor diagonal: Same form in weak and mass bases because fieldswhich mix have same charge

Purely vector (parity conserving): L and R fields have same charge(qi = t3i + yi is the same for L and R fields, even though t3i and yi are not)


Experiment Value of α−1 Difference from α−1(ae)

Deviation from gyromagnetic 137.035 999 58 (52) [3.8× 10−9] –

ratio, ae = (g − 2)/2 for e−

ac Josephson effect 137.035 988 0 (51) [3.7× 10−8] (0.116± 0.051)× 10−4

h/mn (mn is the neutron mass) 137.036 011 9 (51) [3.7× 10−8] (−0.123± 0.051)× 10−4

from n beam

Hyperfine structure in 137.035 993 2 (83) [6.0× 10−8] (0.064± 0.083)× 10−4

muonium, µ+e−

Cesium D1 line 137.035 992 4 (41) [3.0× 10−8] (0.072± 0.041)× 10−4

Spectacularly successful:

Most precise: e anomalous magnetic moment → α

Many low energy tests to few ×10−8

mγ < 6× 10−17 eV

qγ < 5× 10−30|e|Running α(Q2) observed

High energy well-measured (PEP, PETRA, TRISTAN, LEP)

Muon g − 2 sensitive to new physics. Anomaly?


The Weak Neutral Current

Prediction of SU(2)× U(1)

L = −√g2 + g′2

2JµZ

(− sin θWBµ + cos θWW 3

µ

)= −

g

2 cos θWJµZZµ

Neutral current process and effective 4-fermi interaction for|Q| �MZ


Neutral current:

JµZ =∑m

[u0mLγ

µu0mL − d

0mLγ

µd0mL + ν0

mLγµν0mL − e

0mLγ

µe0mL

]−2 sin2 θWJ

µQ

=∑m

[umLγ

µumL − dmLγµdmL + νmLγµνmL − emLγµemL

]−2 sin2 θWJ

µQ

Flavor diagonal: Same form in weak and mass bases because fieldswhich mix have same charge

GIM mechanism: c quark predicted so that sL could be in doubletto avoid unwanted flavor changing neutral currents (FCNC) attree and loop level

Parity and charge conjugation violated but not maximally: first termis pure V −A, second is V


Effective 4-fermi interaction for |Q2| �M2Z:

−LNCeff =GF√

2JµZJZµ

Coefficient same as WCC because

GF√2

=g2

8M2W

=g2 + g′2

8M2Z


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))

• Future: NuSOnG proposal ((−)νµe,

(−)νµN

NC,CC)


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 →︸︷︷︸WCC

gνeV,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!)


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 =E2CM)

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


1. Electroweak model and constraints on new physics 25

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 14, 2008 13:05


• 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)

• Future: NuSOnG proposal ((−)νµe,

(−)νµN

NC,CC)


32 1. Electroweak model and constraints on new physics

Table 1.8: Values of the model-independent neutral-current parameters, comparedwith the SM predictions. There is a second g!e

V,A solution, given approximately by

g!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,7 C1u + 3 C1d = "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 "0.01

C1u " C1d "0.514 ±0.015 "0.5298(3) "0.27 "0.02

C2u + C2d "0.23 ±0.57 "0.0095 "0.30

C2u " C2d "0.077 ±0.044 "0.0623(5)

Most of the parameters relevant to $-hadron, $-e, e-hadron, and e+e! processes aredetermined uniquely and precisely from the data in “model-independent” fits (i.e., fitswhich allow for an arbitrary electroweak gauge theory). The values for the parametersdefined in Eqs. (1.12)–(1.14) are given in Table 1.8 along with the predictions of the SM.The agreement is reasonable, except for the value of g2

L, which reflect the discrepancy inthe NuTeV results. (The $-hadron results without the NuTeV data can be found in the1998 edition of this Review, and the fits using the original NuTeV data uncorrected for thestrange quark asymmetry in the 2006 edition.). The o! Z pole e+e! results are di"cult

January 14, 2008 13:05


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


• 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) 40Baeza 2008 Paul Langacker (IAS)

Conclusions

• WNC, Z, W are primary predictions and test of electroweakunification

• SM correct and unique to first approx. (gauge principle, group,representations)

• SM correct at loop level (renorm gauge theory; mt, αs, MH)

• Watershed: TeV physics severely constrained (unification vscompositeness)

– unification (decoupling): expect 0.1%

– TeV compositeness/dynamics: several % unless decoupling

– Z′,WR; 4-Fermi; exotic fermions/mixings; extended Higgs; · · ·

• Precise gauge couplings (gauge unification)


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

"



Running of α

• Largest theory uncertainty in MZ − sin2 θW (cf. ahadµ )

α(M2Z) =

α

1−∆α !

" "

t had


∆α = ∆α` + ∆αt + ∆α(5)had

∼ 0.03149769− 0.000070(5) + ∆α(5)had

α−1 ∼ 137.036

• α(M2Z)−1 ∼ 129


• Measurements: DORIS, PEP, PETRA, TRISTAN, LEP II

105

110

115

120

125

130

135

140

145

150

155

0 25 50 75 100 125 150 175 200Q / GeV

α-1

(Q)

α-1(0)

αSM(Q)α-1

TOPAZ µµ/eeµµ: qq:Fits to leptonic data from:

DORIS, PEP, PETRA, TRISTAN

OPAL


• e+e−→ `+`−, ` = µ or τ (t-channel for Bhabha, e+e− → e+e− )

– Rate: R = rate relative to pure QED

– Forward-backward asymmetry: AFB ≡ σF−σBσF+σB

R = F1 AFB = 3F2/4F1

where

F1 = 1− 2χ0 geV g

`V cos δR + χ2

0

(ge2V + ge2

A

) (g`2V + g`2A

)F2 = −2χ0 g

eA g

À cos δR + 4χ2

0 geA g

À g

eV g

`V

with

χ0 =GF

2√

2πα

sM2Z

[(M2Z − s)2 +M2

ZΓ2Z]1/2 tan δR =

MZΓZM2Z − s

– SM: gÀ = −12 g`V = −1

2 + 2 sin2 θW


e+e- → µ+µ-

AFB

√s [GeV]

LEP

L3

TRISTAN

AMY

TOPAZ

VENUS

PETRA

CELLO

JADE

MARK J

PLUTO

TASSO

PEP

HRS

MAC

MARK II

SPEAR

MARK I

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

0 20 40 60 80 100 120 140 160 180

(J. Mnich, Phys.Rept. 271, 181 (1996))


AbFB, A`, and Ab

• AbFB = 0.0992(16) is 2.5σ below expectation of 0.1033(7)

– Favors large MH. New physics or fluctuation/systematics leadto smaller MH

– AbFB = 34AlAb; Ab agrees with SM, Al (SLC) is 2.0σ high

– New physics in AbFB would require compensation of L and Rcouplings ( to preserve Rb)

– 5% effect, but ∼ 25% in κ→ probably tree level affecting thirdfamily

– New physics possibilities include Z′ with non-universal couplings,or bR mixing with BR in doublet with charge −4/3

• Tension between leptonic (low MH) and hadronic (high MH)determinations of s2

`


AFB

0,bb_

LEPWinter 2005

<AFB

0,bb_

> = 0.0992 ± 0.0016

OPAL inclusive 1991-2000

0.0994 ± 0.0034 ± 0.0018

L3 jet-ch 1994-95

0.0948 ± 0.0101 ± 0.0056

DELPHI inclusive 1992-2000

0.0978 ± 0.0030 ± 0.0015

ALEPH inclusive 1991-95

0.1010 ± 0.0025 ± 0.0012

OPAL leptons 1990-2000

0.0977 ± 0.0038 ± 0.0018

L3 leptons 1990-95

0.1001 ± 0.0060 ± 0.0035

DELPHI leptons 1991-95

0.1025 ± 0.0051 ± 0.0024

ALEPH leptons 1991-95

0.1003 ± 0.0038 ± 0.0017

Include Total Sys 0.0007With Common Sys 0.0004

mt = 178.0 ± 4.3 GeV

∆αhad = 0.02761 ± 0.00036

10 2

0.09 0.1 0.11

AFB

0,bb_

mH

[GeV

]

150 200mt [GeV]

0.8

0.9

1

0.14 0.145 0.15 0.155Al

A

b68.3 95.5 99.5 % CL

SM


10 2

10 3

0.23 0.232 0.234

sin2!lepteff

mH

[GeV

]

"2/d.o.f.: 11.8 / 5

A0,lfb 0.23099 ± 0.00053

Al(P#) 0.23159 ± 0.00041

Al(SLD) 0.23098 ± 0.00026

A0,bfb 0.23221 ± 0.00029

A0,cfb 0.23220 ± 0.00081

Qhadfb 0.2324 ± 0.0012

Average 0.23153 ± 0.00016

$%had= 0.02758 ± 0.00035$%(5)

mt= 172.7 ± 2.9 GeV


Electroweak Theory Probed at Loop Level

• Higher order corrections essentialfor agreement

• Depend on mt, αs, and MH

• Good agreement with direct mt

and other αs measurements; MH

prediction

t(b)

t(b)

Z(!) Z

t

b

W W

H

H

H

G

mixed


G


t(b)

t(b)

Z(!) Z

t

b

W W

H

H

H

H

G

mixed



University of Pennsylvania School of Arts and Sciencespgl/talks/baeza.pdfElectroweak Physics 140 150...

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