the structure of the standard model the mssm testing the...

Phenomenological Issues in Beyond the Standard Model

• The Structure of the Standard Model

• The MSSM

• Testing the Standard Model

• Neutrino Physics

• Beyond the MSSM

TASI (June 2, 2003) Paul Langacker (Penn)

The Structure of the Standard Model

Remarkably successful gauge theory of the microscopic interactions.

1. The Standard Model Lagrangian

2. Spontaneous Symmetry Breaking

3. The Gauge Interactions

(a) The Charged Current(b) QED(c) The Neutral Current(d) Gauge Self-interactions

4. Problems With the Standard Model

(See “Structure Of The Standard Model,” hep-ph/0304186)


Gauge Transformations

Φ → Φ′ ≡ UΦ

~Aµ · ~L → ~A′µ · ~L ≡ U ~Aµ · ~LU−1 +

i

g(∂µU)U−1

U = ei~β·~L

where Φ is an n component representation vector for fermions orspin-0, Li is the n×n dimensional representation matrix for theith generator (i = 1, · · · , N), βi (i = 1, · · · , N) is an arbitrarydifferentiable real function of space and time, andAµ areN Hermitiangauge fields.


The Standard Model Lagrangian

Group: SU(3)×SU(2)×U(1)

Gauge couplings: gs (QCD); g, g′ (electroweak)

Generators:

SU(3) (QCD): Li, i = 1, · · · , 8SU(2): T i, i = 1, 2, 3U(1): Y (weak hypercharge)

Gauge bosons:

SU(3) (QCD): Giµ, i = 1, · · · , 8SU(2): W i

µ, i = 1, 2, 3U(1): Bµ


Quarks/leptons:

Chiral Projections: ψL(R) ≡ 12(1 ∓ γ5)ψ

(Chirality = helicity up to O(m/E))L-doublets:

q0mL =

(u0m

d0m

)L

l0mL =(ν0m

e−0m

)L

R-singlets: u0mR, d

0mR, e

−0mR, (ν0

mR)(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). )

Higgs: Complex scalar doublet ϕ =(ϕ+

ϕ0

)TASI (June 2, 2003) Paul Langacker (Penn)

U(1)Q: Electric charge generator Q = T 3 + Y

YqL =1

6, YlL = −

1

2, YψR = qψ, Yϕ = +

1

2

Lagrangian: L = LSU(3) + LSU(2)×U(1)


Quantum Chromodynamics (QCD)

LSU(3) = −1

4F iµνF

iµν +∑r

qrαi 6Dαβ q

βr

F 2 term leads to three and four-point gluon self-interactions.

F iµν = ∂µGiν − ∂νG

iµ − gsfijk G

jµ G

kν

is field strength tensor for the gluon fields Giµ, i = 1, · · · , 8., gs = QCD gauge

coupling constant. No gluon masses.

Structure constants fijk (i, j, k = 1, · · · , 8), defined by

[λi, λj] = 2ifijkλk

where λi are the Gell-Mann matrices.


λi =(τ i 00 0

), i = 1, 2, 3

λ4 =

0 0 10 0 01 0 0

λ5 =

0 0 −i0 0 0i 0 0

λ6 =

0 0 00 0 10 1 0

λ7 =

0 0 00 0 −i0 i 0

λ8 = 1√

3

1 0 00 1 00 0 −2

The SU3 (Gell-Mann) matrices.


Quark interactions given by qrαi 6Dαβ q

βr

qr = rth quark flavor; α, β = 1, 2, 3 are color indices; Gauge covariant derivative

Dαµβ = (Dµ)αβ = ∂µδαβ + igs G

iµ L

iαβ,

for triplet representation matrices Li = λi/2.


Quark color interactions:

Diagonal in flavor

Off diagonal in color

Purely vector (parity conserving)

��

��

@@

@@@

�

IGiµ

uα

uβ

−igs2 λiαβγµ

Bare quark mass allowed by QCD, but forbidden by thechiral symmetry of LSU(2)×U(1) (generated by spontaneous

symmetry breaking)

Additional ghost and gauge-fixing terms

Can add (unwanted) CP-violating term Lθ = θg2s

32π2FiµνF

iµν, F iµν ≡12εµναβF iαβ


QCD now very well established

• Short distance behavior (asymptotic freedom)

• Confinement, light hadron spectrum (lattice)

• Approximate global SU(3)L×SU(3)R symmetry and breaking(π,K, η are pseudogoldstone bosons)

• Unique field theory of strong interactions


The Electroweak Sector

LSU2×U1= Lgauge + Lϕ + Lf + LYukawa

Gauge part

Lgauge = −1

4F iµνF

µνi −1

4BµνB

µν

Field strength tensors

Bµν = ∂µBν − ∂νBµ

Fµν = ∂µWiν − ∂νW

iµ − gεijkW

jµW

kν

g(g′) is the SU2 (U1) gauge coupling; εijk is the totally antisymmetric symbol

Three and four-point self-interactions for the Wi

B and W3 will mix to form γ, Z


Scalar part

Lϕ = (Dµϕ)†Dµϕ− V (ϕ)

where ϕ =(ϕ+

ϕ0

). Gauge covariant derivative:

Dµϕ =

(∂µ + ig

τ i

2W iµ +

ig′

2Bµ

)ϕ

where τ i are the Pauli matrices

Three and four-point interactions between the gauge and scalarfields


Higgs potential

V (ϕ) = +µ2ϕ†ϕ+ λ(ϕ†ϕ)2

Allowed by renormalizability and gauge invariance

Spontaneous symmetry breaking for µ2 < 0

Vacuum stability: λ > 0.

Quartic self-interactions


Fermion part (F families)

LF =F∑m=1

(q0mLi 6Dq0

mL + l0mLi 6Dl0mL

+ u0mRi 6Du0

mR + d0mRi 6Dd0

mR + e0mRi 6De0

mR

)L-doublets

q0mL =

(u0m

d0m

)L

l0mL =(ν0m

e−0m

)L

R-singlets

u0mR, d

0mR, e

−0mR

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

Fermion mass terms forbidden by chiral symmetry

Can add gauge singlet ν0mR for Dirac neutrino mass term


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 B couplings to fermions

��

��

@@

@@@

�

IW iµ

−ig2τiγµ

(1−γ5

2

) ��

��

@@

@@@

�

IBµ

−ig′yγµ(

1∓γ52

)


Yukawa couplings (couple L to R

−LYukawa =F∑

m,n=1

[Γumnq

0mLϕu

0mR + Γdmnq

0mLϕd

0nR

+ Γemnl0mnϕe

0nR (+Γνmnl

0mLϕν

0mR)

]+ H.C.

Γmn are completely arbitrary Yukawa matrices, which determinefermion masses and mixings

d, e terms require doublet ϕ =(ϕ+

ϕ0

)with Yϕ = 1/2

u (and ν) terms require doublet

Φ =(

Φ0

Φ−

)with YΦ = −1/2

��

��

@@

@@@

�

IϕnR

mL

Γmn


In SU(2) the 2 and 2∗ are similar ⇒ ϕ ≡ iτ 2ϕ† =(

ϕ0†

−ϕ−

)transforms as a 2 with Yϕ = −1

2 ⇒ only one doublet needed.

Does not generalize to SU(3), most extra U(1)′, supersymmetry,etc ⇒ need two doublets.(Does generalize to SU(2)L×SU(2)R×U(1) )


Spontaneous Symmetry Breaking

Gauge invariance implies massless gauge bosons and fermions

Weak interactions short ranged ⇒ spontaneous symmetry breakingfor mass; also for fermions

Color confinement for QCD ⇒ gluons remain massless

Allow classical (ground state) expectation value for Higgs field

v = 〈0|ϕ|0〉 = constant

∂µv 6= 0 increases energy, but important for monopoles, strings,domain walls


Minimize V (v) to find v and quantize ϕ′ = ϕ− v

SU(2)×U(1) : introduce Hermitian basis

ϕ =(ϕ+

ϕ0

)=

(1√2(ϕ1 − iϕ2)

1√2(ϕ3 − iϕ4

),

where ϕi = ϕ†i .

V (ϕ) =1

2µ2

(4∑i=1

ϕ2i

)+

1

4λ

(4∑i=1

ϕ2i

)2

is O4 invariant.

w.l.o.g. choose 〈0|ϕi|0〉 = 0, i = 1, 2, 4 and 〈0|ϕ3|0〉 = ν

V (ϕ)→V (v) =1

2µ2ν2 +

1

4λν4


For µ2 < 0, minimum at

V ′(ν) = ν(µ2 + λν2) = 0

⇒ ν =(−µ2/λ

)1/2SSB for µ2 = 0 also; mustconsider loop corrections

ϕ→ 1√2

(0ν

)≡ v ⇒ the generators L1, L2, and L3 − Y

spontaneously broken, L1v 6= 0, etc (Li = τ i

2 , Y = 12I)

Qv = (L3 + Y )v =(

1 00 0

)v = 0 ⇒ U(1)Q unbroken ⇒

SU(2)×U(1)Y→U(1)Q


Quantize around classical vacuum

• Kibble transformation: introduce new variables ξi for rollingmodes

ϕ =1

√2ei

∑ξiLi

(0

ν +H

)• H = H† is the Higgs scalar• No potential for ξi ⇒ massless Goldstone bosons for global

symmetry• Disappear from spectrum for gauge theory (“eaten”)• Display particle content in unitary gauge

ϕ→ϕ′ = e−i∑ξiLiϕ =

1√

2

(0

ν +H

)+ corresponding transformation on gauge fields


Rewrite Lagrangian in New Vacuum

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

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


Masses

MW =gν

2, MZ =

√g2 + g′2ν

2=

MW

cos θW, MA = 0

(Goldstone scalar transformed into longitudinal components of W±, Z)

Weak angle: tan θW ≡ g′/g

Will show: Fermi constant GF/√

2 ∼ g2/8M2W , where GF =

1.16639(2)×10−5 GeV −2 from muon lifetime

Electroweak scale

ν = 2MW/g ' (√

2GF )−1/2 ' 246 GeV


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

MW = MZ cos θW ∼(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

Current:

MZ = 91.1876 ± 0.0021

MW = 80.449 ± 0.034


The Higgs Scalar H

Gauge interactions: ZZH,ZZH2,W+W−H,W+W−H2

ϕ→1

√2

(0

ν +H

)

Lϕ = (Dµϕ)†Dµϕ− V (ϕ)

= 12 (∂µH)2 +M2

WWµ+W−

µ

(1 +

H

ν

)2

+ 12M

2ZZ

µZµ

(1 +

H

ν

)2

− V (ϕ)


Higgs potential:

V (ϕ) = +µ2ϕ†ϕ+ λ(ϕ†ϕ)2

→ −µ4

4λ− µ2H2 + λνH3 +

λ

4H4

Fourth term: Quartic self-interaction

Third: Induced cubic self-interaction

Second: (Tree level) H mass-squared,

MH =√

−2µ2 =√

2λν


No a priori constraint on λ except vacuum stability (λ >0 ⇒ 0 < MH < ∞), butt quark loops destabilize vacuum unless MH

>∼ 115 GeV

Strong coupling for λ >∼ 1⇒MH>∼ 1 TeV

Triviality: running λ should not diverge below scale Λ at whichtheory breaks down ⇒

MH <

{O(200) GeV, Λ ∼ MP = G

−1/2N ∼ 1019 GeV

O(750) GeV, Λ ∼ 2MH

Experimental bound (LEP 2), e+e−→Z∗→ZH ⇒ MH>∼

114.5 GeV at 95% cl

Hint of signal at 115 GeV

Indirect (precision tests): MH < 215 GeV, 95% cl

MSSM: much of parameter space has standard-like Higgs withMH < 130 GeV


Theoretical MH limits, Hambye and Riesselmann, hep-ph/9708416


Decays: H→bb dominates for MH<∼ 2MW (H→W+W−, ZZ

dominate when allowed because of larger gauge coupling)

Production:LEP: Higgstrahlung (e+e−→Z∗→ZH)

Tevatron, LHC: GG-fusion (GG→H via top loop), WW fusion(WW→H), or associated production (qq→WH, ZH)


First term in V : vacuum energy

〈0|V |0〉 = −µ4/4λ

No effect on microscopic interactions, but gives negativecontribution to cosmological constant

|ΛSSB| = 8πGN |〈0|V |0〉| ∼ 1050|Λobs|

Require fine-tuned cancellation

Λcosm = Λbare + ΛSSB

Also, QCD contribution from SSBof global chiral symmetry


Yukawa Interactions

−LYukawa →F∑

m,n=1

u0mLΓ

umn

(ν +H

√2

)u0mR + (d, e) terms + H.C.

= u0L (Mu + huH)u0

R + (d, e) terms + H.C.

u0L =

(u0

1Lu02L · · ·u0

FL

)Tis F -component column vector

Mu is F×F fermion mass matrix Mumn = Γumnν/

√2 (need not be

Hermitian, diagonal, symmetric, or even square)

hu = Mu/ν = gMu/2MW is the Yukawa coupling matrix


Diagonalize M by separate unitary transformations AL and AR((AL = AR) for Hermitian M)

Au†L M

uAuR = MuD =

mu 0 00 mc 00 0 mt

is diagonal matrix of physical masses of the charge 2

3 quarks.Similarly

Ad†LM

dAdR = MdD

Ae†LMeAeR = Me

D

(Aeν†L MνAνR = Mν

D)

(may also be Majorana masses for νR)

Find AL and AR by diagonalizing Hermitian matrices MM† andM†M, e.g., A†

LMM†AL = M2D


Mass eigenstate fields

uL = Au†L u

0L = (uL cL tL)T

uR = Au†R u

0R = (uR cR tR)T

dL,R = Ad†L,Rd

0L,R = (dL,R sL,R bL,R)T

eL,R = Ae†L,Re0L,R = (eL,R µL,R τL,R)T

νL,R = Aν†L,Rν

0L,R = (ν1L,R ν2L,R ν3L,R)T

(For mν = 0 or negligible, define νL = Ae†L ν

0L, so that νi ≡ νe, νµ, ντ are

the weak interaction partners of the e, µ, and τ .)


Typical estimates: mu = 5.6 ± 1.1 MeV, md = 9.9 ±1.1 MeV, ms = 199±33 MeV, mc = 1.35±0.05 GeV, mb ∼4.7 GeV, mt = 174.3 ± 5.1 GeV

Implications for global SU(3)L×SU(3)R of QCD

These are current quark masses. Mi = mi + Mdyn, Mdyn ∼ΛMS ∼ 300 MeV from chiral condensate 〈0|qq|0〉 6= 0

mb,t are pole masses; others, running masses at 1 GeV2


Yukawa couplings of Higgs to fermions

LYukawa =∑i

ψi

(−mi −

gmi

2MW

H

)ψi

Coupling gmi/2MW is flavor diagonal and small except t quark

H→bb dominates forMH<∼ 2MW (H→W+W−, ZZ dominate

when allowed because of larger gauge coupling)

Flavor diagonal because only one doublet couples to fermions ⇒fermion mass and Yukawa matrices proportional

Often flavor changing Higgs couplings in extended models withtwo doublets coupling to same kind of fermion (not MSSM)

Stringent limits, e.g., tree-level Higgs contribution to KL−KS

mixing (loop in standard model) ⇒hds/MH < 10−6GeV −1






• Beyond the MSSM

(First lecture available at dept.physics.upenn.edu/∼pgl/tasi1.pdf)


The Weak Charged Current

Fermi Theory incorporated in SM and made renormalizable

W -fermion interaction

L = −g

2√

2

(Jµ

W W −µ + Jµ†

W W +µ

)

Charge-raising current

Jµ†W =

F∑m=1

[ν0

mγµ(1 − γ5)e0m + u0

mγµ(1 − γ5)d0m

]= (νeνµντ)γµ(1 − γ5)

e−

µ−

τ−

+ (u c t)γµ(1 − γ5)V

dsb

.


Ignore ν masses for now

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

V = Au†L Ad

L 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 Vub

Vcd Vcs Vcb

Vtd Vtd Vtd

Extensive studies, especially in B decays, to test unitarity of V asprobe 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 , neglectQ2 in W propagator

−Lcceff =

GF√2Jµ

W J†W µ

Fermi constantGF√

2'

g2

8M2W

=1

2ν2

Muon lifetime τ−1 =G2

F m5µ

192π3 ⇒ GF = 1.16639(2)×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 eX at high energy (HERA)

Electroweak radiative corrections (loop level)

MKS− MKL

, kaon CP violation, B ↔ B mixing (loop level)


Quantum Electrodynamics (QED)

Incorporated into standard model

Lagrangian:

L = −gg′√

g2 + g′2Jµ

Q(cos θW Bµ + sin θW W 3µ)

Photon field:

Aµ = cos θW Bµ + sin θW W 3µ

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


Electromagnetic current:

JµQ =

F∑m=1

[2

3u0

mγµu0m −

1

3d0

mγµd0m − e0

mγµe0m

]

=F∑

m=1

[2

3umγµum −

1

3dmγµdm − emγµem

]

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


Spectacularly successful:

Many low energy tests (e.g., cesium hfs, e anomalous magneticmoment, etc., to few ×10−8)

mA < 2×10−16 eV

Muon g − 2 sensitive to new physics. Anomaly?

Running α(Q2) observed

High energy well-measured


The Weak Neutral Current

Prediction of SU(2)×U(1)

L = −√

g2 + g′2

2Jµ

Z

(− sin θW Bµ + cos θW W 3

µ

)= −

g

2 cos θW

JµZZµ

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


Neutral current:

JµZ =

∑m

[u0

mLγµu0mL − d0

mLγµd0mL + ν0

mLγµν0mL − e0

mLγµe0mL

]− 2 sin2 θW Jµ

Q

=∑m

[umLγµumL − dmLγµdmL + νmLγµνmL − emLγµemL

]− 2 sin2 θW Jµ

Q

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 violated but not maximally: first term is pure V −A, secondis V


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

−LNCeff =

GF√2Jµ

ZJZµ

Coefficient same as WCC because

GF√2

=g2

8M2W

=g2 + g′2

8M2Z

WNC discovered 1973: Gargamelle at CERN, HPW at FNAL

Tested in many processes: νe→νe, νN→νN, νN→νX; e↑ ↓D→eX;atomic parity violation; e+e−, Z-pole reactions

WNC, W , and Z are primary test/prediction of electroweak model


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 −


The Z, the W , and the Weak Neutral Current

• Primary prediction and test of electroweak unification

• WNC discovered 1973 (Gargamelle, HPW)

• 70’s, 80’s: weak neutral current experiments (few %)

– Pure weak: νN , νe scattering

– Weak-elm interference in eD, e+e−, atomic parity violation

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


• 90’s: Z pole (LEP, SLD), 0.1%; lineshape, modes, asymmetries

• LEP 2: MW , Higgs, gauge self-interactions

• Tevatron: mt, MW

• 4th generation weak neutral current experiments

• Implications

– SM correct and unique to zeroth approx. (gauge principle,group, representations)

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

– TeV physics severely constrained (unification vs compositeness)

– Precise gauge couplings (gauge unification)


The LEP/SLC Era

• Z Pole: e+e− → Z → `+`−, qq, νν

– LEP (CERN), 2×107Z′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 = 2.986 ± 0.007 if mν < MZ/2– asymmetries: FB, polarization, Pτ , mixed

– lepton family universality


The Z Lineshape

Basic Observables: e+e−→ff (f = e, µ, τ, s, b, c, hadrons) (s =E2

CM)

σf(s) ∼ σf

sΓ2Z

(s − M2Z)2 + s2Γ2

Z

M2Z

(plus initial state rad. corrections)

Peak Cross Section:

σf =12π

M2Z

Γ(e+e−)Γ(ff)

Γ2Z


Partial Widths:

Γ(ff) ∼CfGF M3

Z

6√

2π

[|gV f |2 + |gAf |2

](plus mass, QED, QCD corrections; C` = 1, Cq = 3; gV,Af =effective coupling (includes ew)).

At tree level:

gAf = ±1

2, gV f = ±

1

2− 2sin2 θW qf

where sin2 θW ≡ 1 − M2W

M2Z

is the weak angle, ±12 is the weak

isospin (+ for (u, ν), − for (d, e−)), and qf is the electric charge


LEP averages of leptonic widths

Γe 83.92 ± 0.12 MeV

Γµ 83.99 ± 0.18 MeV

Γτ� 84.08 ± 0.22 MeV

Γl� 83.98 ± 0.09 MeV

mt� = 174.3 ± 5.1 GeV

mZ� = 91 188 ± 2 MeV

Γl� [MeV]

mH

[GeV

]

200

400

600

800

1000

83.5 84 84.5


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 = κfs2

W (on − shell)

= κf s2Z ∼ s2

Z + 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 : A0fF B '

3

4AeAf

(A0eF B = A0µ

F B = A0τF B ≡ A0`

F B→ 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) : A0F BLR =

3

4Af

Af ≡2gV F gAf

g2V F + g2

AF


The Z Pole Observables: LEP and SLC (01/03)

Quantity Group(s) Value Standard Model pull

MZ [GeV] LEP 91.1876 ± 0.0021 91.1874 ± 0.0021 0.1ΓZ [GeV] LEP 2.4952 ± 0.0023 2.4972 ± 0.0011 −0.9Γ(had) [GeV] LEP 1.7444 ± 0.0020 1.7436 ± 0.0011 —Γ(inv) [MeV] LEP 499.0 ± 1.5 501.74 ± 0.15 —

Γ(`+`−) [MeV] LEP 83.984 ± 0.086 84.015 ± 0.027 —σhad [nb] LEP 41.541 ± 0.037 41.470 ± 0.010 1.9Re LEP 20.804 ± 0.050 20.753 ± 0.012 1.0Rµ LEP 20.785 ± 0.033 20.753 ± 0.012 1.0Rτ LEP 20.764 ± 0.045 20.799 ± 0.012 −0.8AF B(e) LEP 0.0145 ± 0.0025 0.01639 ± 0.00026 −0.8AF B(µ) LEP 0.0169 ± 0.0013 0.4AF B(τ ) LEP 0.0188 ± 0.0017 1.4



Rb LEP/SLD 0.21664 ± 0.00065 0.21572 ± 0.00015 1.1Rc LEP/SLD 0.1718 ± 0.0031 0.17231 ± 0.00006 −0.2Rs,d/R(d+u+s) OPAL 0.371 ± 0.023 0.35918 ± 0.00004 0.5AF B(b) LEP 0.0995 ± 0.0017 0.1036 ± 0.0008 −2.4AF B(c) LEP 0.0713 ± 0.0036 0.0741 ± 0.0007 −0.8AF B(s) DELPHI/OPAL 0.0976 ± 0.0114 0.1037 ± 0.0008 −0.5Ab SLD 0.922 ± 0.020 0.93476 ± 0.00012 −0.6Ac SLD 0.670 ± 0.026 0.6681 ± 0.0005 0.1As SLD 0.895 ± 0.091 0.93571 ± 0.00010 −0.4ALR (hadrons) SLD 0.15138 ± 0.00216 0.1478 ± 0.0012 1.7ALR (leptons) SLD 0.1544 ± 0.0060 1.1Aµ SLD 0.142 ± 0.015 −0.4Aτ SLD 0.136 ± 0.015 −0.8Ae(QLR) SLD 0.162 ± 0.043 0.3Aτ(Pτ) LEP 0.1439 ± 0.0043 −0.9Ae(Pτ) LEP 0.1498 ± 0.0048 0.4QF B LEP 0.0403 ± 0.0026 0.0424 ± 0.0003 −0.8


• LEP 2

– MW , ΓW , B (also hadron colliders)

– MH limits (hint?)

– WW production (triple gauge vertex)

– Quartic vertex

– SUSY/exotics searches

• Other: atomic parity (Boulder); νe; νN (NuTeV); MW , mt

(Tevatron)


Non-Z Pole Precision Observables (1/03)


mt [GeV] Tevatron 174.3 ± 5.1 174.4 ± 4.4 0.0MW [GeV] LEP 80.447 ± 0.042 80.391 ± 0.018 1.3MW [GeV] Tevatron /UA2 80.454 ± 0.059 1.1g2

L NuTeV 0.30005 ± 0.00137 0.30396 ± 0.00023 −2.9g2

R NuTeV 0.03076 ± 0.00110 0.03005 ± 0.00004 0.6Rν CCFR 0.5820 ± 0.0027 ± 0.0031 0.5833 ± 0.0004 −0.3Rν CDHS 0.3096 ± 0.0033 ± 0.0028 0.3092 ± 0.0002 0.1Rν CHARM 0.3021 ± 0.0031 ± 0.0026 −1.7Rν CDHS 0.384 ± 0.016 ± 0.007 0.3862 ± 0.0002 −0.1Rν CHARM 0.403 ± 0.014 ± 0.007 1.0Rν CDHS 1979 0.365 ± 0.015 ± 0.007 0.3816 ± 0.0002 −1.0



gνeV CHARM II −0.035 ± 0.017 −0.0398 ± 0.0003 —

gνeV all −0.041 ± 0.015 −0.1

gνeA CHARM II −0.503 ± 0.017 −0.5065 ± 0.0001 —

gνeA all −0.507 ± 0.014 0.0

QW (Cs) Boulder −72.69 ± 0.44 −73.10 ± 0.04 0.8QW (Tl) Oxford/Seattle −116.6 ± 3.7 −116.7 ± 0.1 0.0103 Γ(b→sγ)

ΓSLBaBar/Belle/CLEO 3.48+0.65

−0.54 3.20 ± 0.09 0.5

ττ [fs] direct/Be/Bµ 290.96 ± 0.59 ± 5.66 291.90 ± 1.81 −0.4104 ∆α

(3)had e+e−/τ decays 56.53 ± 0.83 ± 0.64 57.52 ± 1.31 −0.9

109 (aµ − α2π) BNL/CERN 4510.64 ± 0.79 ± 0.51 4508.30 ± 0.33 2.5


Anomalies, Things to Watch

• AbF B = 0.0995(17) is 2.4σ below expectation of 0.1036(8)

– Rb = 0.21664 ± 0.00065 (SM: 0.21572 ± 0.00015, agrees at1.1σ)

– Ab = 0.922±0.020 (SM: 0.93476±0.00012 agrees at −0.6σ)

– Compensation of L and R couplings (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

– New physics or fluctuation/systematics lead to smaller MH


• aµ = (gµ − 2)/2

– More sensitive than ae to new physics

– BNL (2002) + other: aexpµ = 11659203(8)×10−10

– Hadronic light by light has settled down, but considerableuncertaintly from aHad

µ

– aexpµ −aSM

µ = (26±11)×10−10 (2.6σ) (using e+e− data for aHadµ )

→1.1σ (using τ decay data)

– New: radiative correction error should reduce discrepancy

– New physics? Supersymmetry: (m ∼ 55 GeV√

tan β)


The Anomalous Magnetic Moment of the Muon

aµ ≡gµ − 2

2

aSMµ = aQED

µ + aHadµ + aEW

µ = 11659177(7)×10−10

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

= 11658470.57(0.29)×10−10


aHadµ = aHad

µ (vp)1+2 + aHadµ (ll)

= (692(6) − 10.0(0.6) + 8.6(3.2)) ×10−10

aEWµ (2 loop) = 15.1(0.4)×10−10

– More sensitive than ae to new physics

– BNL (2002) + other: aexpµ = 11659203(8)×10−10

– Hadronic light by light has settled down, but considerableuncertaintly from aHad

µ

– aexpµ − aSM

µ = (26 ± 11)×10−10 (2.6σ) (using e+e− data for aHadµ )

→1.1σ (using τ decay data)

– New physics? Supersymmetry: (m ∼ 55 GeV√

tan β)


• ∆α(5)had(MZ)

– Hadronic contribution to running of α up to Z-pole

– Largest theory uncertainty in MZ − s2Z

– Closely related to ahadµ

– Recent progress using improved QCD calculations (high energypart) and precise BES data


• NuTeV(−)ν µN→

(−)ν µX

(−)ν µN→µ∓X

– Little c threshold uncertaintly

– s2W = 0.2277(16), 3.0σ above SM value 0.2228(4)

∗ g2L = 0.3001(14) is 2.9σ below expected 0.3040(2)

∗ g2R = 0.0308(11) is 0.7σ above expected 0.0300(0)

– Possible QCD effects: Large isospin breaking is sea; large s − sasymmetry; nuclear shadowing; NLQCD

– Possible exotic effects: designer Z′; ν mixing with heavy neutrino(CKM universality?)


1000100�

101�0.10.01�

0.001�

Q [GeV]0.225

0.23

0.235

0.24

0.245

0.25

sin

2 θ W

weak mixing angle scale dependence in MS−bar scheme

NuTeV

E158QWEAK�

old Q�W(APV)

new QW(APV)

Z−pole�

MSSM

SM


Fit Results (06/02) (Erler, PL)

MH = 86+49−32 GeV,

mt = 174.2 ± 4.4 GeV,

αs = 0.1210 ± 0.0018,

α(MZ)−1 = 127.922 ± 0.020

s2Z = 0.23110 ± 0.00015,

χ2/d.o.f. = 49.0/40(15%)


• mt = 174.2 ± 4.4 GeV

– 174.0+9.9−7.4 GeV from indirect (loops) only (direct: 174.3 ± 5.1)

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&

$

%��

-

�Z Z

t, b

t, b

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-

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• αs= 0.1210 ± 0.0018

– Higher than world average αs =0.1172(20) (Hinchliffe (PDG)2001), because of τ lifetime

– insensitive to oblique new physics

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

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��

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AA

AA

AA

AA

AA

Z

q G q


• Higgs mass MH= 86+49−32 GeV

– direct limit (LEP 2): MH>∼

114.4 (95%) GeV

– SM: 115 (vac. stab.) <∼ MH<∼

750 (triviality)

– MSSM: MH<∼ 130 GeV (150 in

extensions)

– indirect: ln MH but significant

∗ fairly robust to new physics(except S < 0, T > 0)

∗ however, strong AF B(b) effect∗ MH < 215 GeV at 95%,

including direct

��' $

Z Z

H


100�

120� 140� 160� 180� 200�

mt [GeV]

10

20

50

100

200

500

1000

MH [

GeV

]

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asymmetriesν� scatteringMW

mt

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ed

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160� 170� 180� 190� 200�mt [GeV]

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80.3

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80.6

MW

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eV]

direct (1σ)

indirect (1σ)

all (90% CL)

MH [GeV]

100

200

400

800






• Beyond the MSSM

(Second lecture available at dept.physics.upenn.edu/∼pgl/tasi2.pdf)


Neutrino Preliminaries

• Weyl fermion

– Minimal (two-component) fermionic degree of freedom– ψL ↔ ψc

R by CPT

• Active Neutrino (a.k.a. ordinary, doublet)

– in SU(2) doublet with charged lepton → normal weakinteractions

– νL ↔ νcR by CPT

• Sterile Neutrino (a.k.a. singlet, right-handed)

– SU(2) singlet; no interactions except by mixing, Higgs, or BSM– NR ↔ Nc

L by CPT– Almost always present: Are they light? Do they mix?


• Dirac Mass

– Connects distinct Weyl spinors(usually active to sterile):(mDνLNR + h.c.)

– 4 components, ∆L = 0

– ∆I = 12 → Higgs doublet

– Why small? LED? HDO? 6

6

��νL

h

NR

v = 〈φ〉

mD = hv


• Majorana Mass

– Connects Weyl spinor with itself:12(mT νLν

cR + h.c.) (active);

12(mSN

cLNR + h.c.) (sterile)

– 2 components, ∆L = ±2

– Active: ∆I = 1 → triplet orseesaw

– Sterile: ∆I = 0 → singlet orbare mass 6

6

��@@

@@��

νL

νcR

?

6

��@@

@@��

νL

νL

• Mixed Masses

– Majorana and Dirac mass terms

– Seesaw for mS � mD

– Ordinary-sterile mixing for mS and mD both small andcomparable (or mS � md (pseudo-Dirac))


• 3 ν Patterns

– Solar: LMA (SNO,Kamland)

– ∆m2� ∼ (10−5 − 10−4)

eV2 for LMA

– Atmospheric: ∆m2Atm ∼

3×10−3 eV2, near-maximal mixing

– Reactor: Ue3 small

100

10–3

∆m

2 [

eV

2]

10–12

10–9

10–6

10210010–210–4

tan2θ

LMA

LOW

SMA

VAC

SuperKCHOOZ

Bugey

LSNDCHORUS

NOMAD

CHORUS

KA

RM

EN

2

PaloVerde

νµ↔ν

τ

νe↔ν

X

νe↔ν

τ

NOMAD

νe↔ν

µ

CDHSW

KamLAND

BNL E776

LMA

– Mixings: let ν± ≡ 1√2(νµ ± ντ):

ν3 ∼ ν+

ν2 ∼ cos θ� ν− − sin θ� νe

ν1 ∼ sin θ� ν− + cos θ� νe

12

3

3

12

– Hierarchical pattern

∗ Analogous to quarks,charged leptons

∗ ββ0ν rate very small

– Inverted quasi-degenerate pattern

∗ ββ0ν if Majorana

∗ SN1987A energetics(if Ue3 6= 0)?

∗ May be radiative unstable


– Degenerate patterns

∗ Motivated by CHDM (no longer needed)

∗ Strong cancellations needed for ββ0ν if Majorana

∗ May be radiative unstable


• 4 ν Patterns

– LSND: ∆m2LSND ∼ 1 eV 2

– Z lineshape: 2.986(7) active ν’s lighter than MZ/2 → fourthsterile νS

– 2 + 2 patterns– 3 + 1 patterns

2 + 2 3 + 1

• Pure (νµ − νs) excluded for atmospheric by SuperK, MACRO

• Pure (νe − νs) excluded for solar by SNO, SuperK

• More general admixtures possible, but very poor global fits


Problems with the Standard Model

Lagrangian after symmetry breaking:

L = Lgauge + LHiggs +∑

i

ψi

(i 6∂ −mi −

miH

ν

)ψi

−g

2√

2

(Jµ

WW−µ + Jµ†

WW+µ

)− eJµ

QAµ −g

2 cos θW

JµZZµ

Standard model: SU(2)×U(1) (extended to include ν masses) +general relativity

Mathematically consistent, renormalizable theory

Correct to 10−16 cm


However, too much arbitrariness and fine-tuning (O(20) parameters,not including ν masses/mixings, which add at least 7 more, andelectric charges)

• Gauge Problem

– complicated gauge group with 3 couplings

– charge quantization (|qe| = |qp|) unexplained– Possible solutions: strings; grand unification; magnetic

monopoles (partial); anomaly constraints (partial)

• Fermion problem

– Fermion masses, mixings, families unexplained– Neutrino masses, nature?– 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

Possiblesolutions: supersymmetry; dynamical symmetry breaking; large extradimensions; Little Higgs

• 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?


The Two Paths: Unification or Compositeness

• The Bang

– unification of interactions

– grand desert to unification (GUT) or Planck scale

– elementary Higgs, supersymmetry (SUSY), GUTs, strings

– possibility of probing to MP and very early universe

– hint from coupling constant unification

– tests

∗ light (< 130 − 150 GeV) Higgs (LEP 2, TeV, LHC)

∗ absence of deviations in precision tests (usually)

∗ supersymmetry (LHC)

∗ possible: mb, proton decay, ν mass, rare decays

∗ SUSY-safe: Z′; seq/mirror/exotic fermions; singlets

– variant versions: large dimensions, low fundamental scale, braneworlds


• The Whimper

– onion-like layers

– composite fermions, scalars (dynamical sym. breaking)

– not like to atom → nucleus +e− → p+ n → quark

– at most one more layer accessible (LHC)

– rare decays (e.g., K → µe)

∗ severe problem

∗ no realistic models

– effects (typically, few %) expected at LEP & other precisionobservables (4-f ops; Zbb; ρ0; S, T, U)

– anomalous V V V , new particles, future WW → WW– recent variant: Little Higgs


Beyond the MSSM

(aka, what to look for in string constructions)

Even if supersymmetry holds, MSSM is unlikely to be the full story

Most of the problems of standard model remain (hierarchy ofelectroweak and Planck scales is stabilized but not explained)

µ problem introduced

Could be that all new physics is at GUT/Planck scale, but therecould be remnants surviving to TeV scale


Extreme example: Fundamental scale MF ∼ 1 − 100 TeV �MP l = 1/

√8πGN ∼ 2.4 × 1018 GeV

Assume δ extra dimensions with volume Vδ � M−δF

M2P l = M2+δ

F Vδ � M2F

(Introduces new hierarchy problem)

Black holes, graviton emission at colliders!


Second extreme example: time varying couplings and parameters

(Murphy et al, astro-ph/0209488)


Suggested by absorption by molecular clouds (Webb et al)

Expected at some level in string/brane models in which couplingsare related to moduli, which could be time varying

Lelm ∼1

4

[1 +

λφ

MPL

]FµνF

µν + · · ·

However, natural scale

α/α ∼ MPL ∼ 10+43s−1,

while Webb et al. results suggest

α/α ∼ 10−15yr−1 ∼ 10−66MPL

May be analogous to dark energy: Type IA supernova and CMBsuggest

ρvac ∼ 10−124M4PL 6= 0


α variation likely correlated with variations in other dimensionlesscouplings, mass ratios (PL, Segre, Strassler; Calmet, Fritzsch)

Will mainly consider less extreme examples of new interactions,particles at TeV scale


Unification: from the Top Down

Bottom up: usually motivated by SM problems

Top down:

• Ambitious/promising string/M theory paradigm. However:

– many realms of perturbative and non-perturbative M theory

– compactification

– dilaton/moduli

– SUSY breaking, Λcosm


• Detailed study of specific constructions:

– develop techniques

– suggest new TeV-scale physics

– suggest promising new directions

(M. Cvetic, PL; G. Cleaver, L. Everett, J.R. Espinosa, J. Wang, G. Shiu)

• Unlikely to find fully realistic theory soon. Studies emphasizespecific features:

– fundamental scale Mfund � Mpl (LED)

– SUSY breaking, Λcosm

– dilaton/moduli stabilization

– semi-realistic 4D gauge theories containing MSSM (Mfund ∼Mpl)


To GUT or not to GUT

• String → GUT → MSSM (+ extended?) or String → MSSM (+extended?)

– gauge unification

– quantum numbers for family (15-plet)

– seesaw ν mass scale/leptogenesis

– mb/mτ

– large lepton mixings

– other fermion mass relations

– additional GUT scale; no adjoints in simple heterotic

– hierarchies, e.g. doublet-triplet

– proton decay


• Gauge unification: GUTs, string theories

– α+ s2Z → αs = 0.130 ± 0.010

– MG ∼ 3 × 1016 GeV

– Perturbative string: ∼ 5 × 1017 GeV (10% in lnMG). Exotics:O(1) corrections.


Discovery of Pluto

1781: Uranus observed by Sir William Herschel

1846: Uranus orbit anomalies → Neptune predicted (John Adams,Jean Leverrier)

1846: Neptune observed in predicted location (in Berlin)

1900’s: Further Uranus anomalies → Pluto predicted by “computers”(several possible locations)

1930: Pluto discovered in one of predicted locations (ClydeTombaugh)

1978: Charon discovered → mPluto too small to affect Uranus orbit


Direct compactification

• String → MSSM (+ extended?) in 4D

• Constructions with SU(3) × SU(2) × U(1) and 3 families

• Usually additional surviving gauge groups

– quasi-hidden non-abelian– U(1)′ (non-anomalous), often family non-universal

• Usually exotic chiral supermultiplets

– standard model singlets

– quarks/leptons w. non-standard SU(2)×U(1)– extra Higgs doublets

– possibly Higgs/lepton mixing (6RP )


Things to watch for

Examples of new physics which could emerge in specific constructions


Gauge unification?

• Gauge unification usually present in modified form (higher Kac-Moody, exotics, moduli boundary conditions)

– no new exotics?

– complete GUT multiplets?

– cancellations (accidental or otherwise)?


A TeV scale Z′?

• Motivations

– Strings, GUTs, DSB often involve extra U(1)′(GUTs require extra

fine tuning for MZ′ � MGUT)

– String models: radiative breaking of electroweak (SUGRA orgauge mediated) often yield EW/TeV scale Z′ (unless breaking

along flat direction → intermediate scale)

– Solution to µ problem

W ∼ hSHuHd,

S = standard model singlet, charged under U(1)′. 〈S〉 breaksU(1)′, µeff = h〈S〉 (like NMSSM, but no domain walls)


• Experimental limits (precision and collider) model dependent, buttypically MZ′ > (500 − 800) GeV and Z − Z′ mixing |δ| <few×10−3

• Models: MZ′ >∼ 10MZ by either modest tuning (Demir et al), or bysecluded sector (Erler, PL, Li)

• Implications

– Exotics

– FCNC (especially in string models)

– Non-standard Higgs masses, couplings (doublet-singlet mixing)

– Non-standard sparticle spectrum

– Enhanced possibility of EW baryogenesis (Kang, Liu, PL, Li)


Exotics

• L-singlets

• R-doublets

• Standard model singlets

• Extra Higgs doublets

• Fractional charges (e.g., 1/2)

• Ordinary/hidden sector mixing

• Higgs/lepton mixing


Flat directions

• Two SM singlets charged under U(1)′

V (S1, S2) = m21|S

21| +m2

2|S22| +

g′2Q′2

2(|S2

1| − |S22|)

2

Break at EW scale for m21 + m2

2 > 0, at intermediate scale form2

1 +m22 < 0 (stabilized by loops or HDO)

• Small Dirac (or other fermion) masses from

W ∼ H2LLνcL

(S

M

)PD

• Possible cosmological implications


Family Structure/Fermions

• Differences in embeddings for third family? (Family symmetries in 4d

effective field theory vs string dynamics)

– Hierarchy of masses– Mixings?– FCNC

• Sources/magnitudes of CP phases. Strong CP.

• Majorana neutrino masses? Diagonal terms?

• WYSINWYG

– Some particles may be composite (e.g., intersecting braneconstruction)

– Family disappearance under vacuum restabilization


Asymptotic freedom in quasi-hidden sector

• SUSY breaking/moduli stabilization

• Motivated parametrizations of SUSY breaking

• Compositeness

• Fractional charge confinement


Conclusions

• Standard Model extremely successful, but is clearly incomplete

• Most aspects tested. Precision electroweak points towardsdecoupling types of new physics (e.g., SUSY, unification)

• Superstring/M theory extremely promising theoretical direction

• Need vigorous bottom-up experimental and theoretical probes totest SM/MSSM and search for alternatives

• Need vigorous top-down program to connect to experiment andsuggest new TeV scale physics

• May be much beyond MSSM at TeV scale


the structure of the standard model the mssm testing the...

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