[PPT] - Florian Divotgey Johann Wolfgang Goethe Universit at Frankfurt am PowerPoint Presentation

SLIDE 1

Basic Ideas of Technicolor

Florian Divotgey

Johann Wolfgang Goethe Universit¨ at Frankfurt am Main Fachbereich Physik Institut f¨ ur Theoretische Physik

09.05.2016

SLIDE 2

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Outline

1 Problems of the Fundamental Higgs 2 Is the Fundamental Higgs Necessary ? 3 Technicolor 4 Conclusions

SLIDE 3

Problems of the Fundamental Higgs

SLIDE 4

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 5

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 6

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 7

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 8

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 9

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 10

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Lagrangian

Standard Model (SM) unifies strong, electromagnetic, and weak interaction into SU(3)C × SU(2)L × U(1)Y gauge theory LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int + L (h) kin,int + L (ℓ) mass,int + L (q) mass,int ,

where L (g)

kin,int = − 1

2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (ℓ)

kin,int = 3

A=1
¯

LAiγµD(ℓ)

µ,LLA + ¯

RAiγµD(ℓ)

µ,RRA

, D(ℓ)

µ,L = ∂µ + igT iW i µ + ig′ Y

2 Bµ , D(ℓ)

µ,R = ∂µ + ig′ Y

2 Bµ , L (q)

kin,int = 3

A=1
¯

QA

LiγµD(q) µ,LQA L + ¯

QA

R,uiγµD(u) µ,RQA R,u + ¯

QA

R,diγµD(d) µ,RQA R,d

,

D(q)

µ,L = ∂µ + igCT aAa µ + igT iW i µ + ig′ Y

2 Bµ , D(u/d)

µ,L

= ∂µ + igCT aAa

µ + ig′ Y

2 Bµ , L (h)

kin,int =

D(h)

µ

Φ † D(h),µΦ − µ2Φ†Φ − λ

Φ†Φ

2 , D(h)

µ

= ∂µ + igT iW i

µ + ig′ Y

2 Bµ , L (ℓ)

mass,int = − 3

A=1
¯

LA Φ φ0 M A

(ℓ)RA + h.c.

,

L (q)

mass,int = − 3

A=1
¯

QA

L

Φ φ0 M AB

(d) QB R,d + ¯

QA

L

Φc φ0 M AB

(u) QB R,u + h.c.

.

SLIDE 11

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Matter Content

Matter content of SM can be summarized as follows: A 1 2 3 TW T 3

W

YW Q C ℓA L1 =

νe

eL

L2 =
νµ

µL

L3 =
ντ

τL

[2]

1/2 −1 [1] −1/2 −1 −1 [1] R1 = eR R2 = µR R3 = τR [1] −2 −1 [1] qA Q1

L =

uL

dL

Q2

L =

cL

sL

Q3

L =

tL

bL

[2]

1/2 1/3 2/3 [3] −1/2 1/3 −1/3 [3] Q1

R,u = uR

Q2

R,u = cR

Q3

R,u = tR

[1] 4/3 2/3 [3] Q1

R,d = dR

Q2

R,d = sR

Q3

R,d = bR

[1] −2/3 −1/3 [3] Φ Φ =

Φ+

Φ0

=

1 √ 2

π2 + iπ1

σ − iπ3

[2]

1/2 1 1 [1] −1/2 1 [1] Φc Φc =

Φ0∗

−Φ−

=

1 √ 2

σ + iπ3

−(π2 − iπ1)

[2]

1/2 −1 [1] −1/2 −1 −1 [1] Table: TW ˆ

= weak isospin, T 3

W ˆ

= third component of weak isospin, YW ˆ = weak hypercharge, Q ˆ = electric charge, C ˆ = color.

SLIDE 12

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: EWSB and Mass Terms

µ2 < 0, λ > 0: Higgs potential is realized in Nambu-Goldstone mode. ⇒ Electroweak symmetry breaking (EWSB): SU(2)L × U(1)Y − → U(1)e. Unitary gauge: Φ =

1 √ 2

π2 + iπ1

σ − iπ3

−

→

φ0 +

H √ 2

, where φ0 =
−µ2

2λ

=

v √ 2 .

Nambu-Goldstone bosons (NGBs) π1, π2, π3 become longitudinal modes of W ± and Z0. Resulting mass matrix: Lmass = 1 2 φ2 2

W 1

µ, W 2 µ, W 3 µ, Bµ



   g2 g2 g2 −gg′ −gg′ g2         W µ,1 W µ,2 W µ,3 Bµ     . Chiral nature of quarks/leptons under EWS forbids hard mass terms: EWSB is communicated to quarks/leptons via Yukawa terms. Masses of physical gauge bosons: M 2

W = g2φ2

2 , M 2

Z = g2 + g′2

2 φ2

0 ,

M 2

A = 0 ,

fulfilling the tree-level relation ρ = M 2

W

M 2

Z cos2(θW ) = 1 .

ρ = 1: Consequence of accidental and approximate global symmetry of Higgs potential.

SLIDE 13

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Custodial Symmetry

Higgs potential can also be written as L (h)

kin,int = 1

2 Tr

(DµM)† DµM
− µ2

2 Tr

M†M
− λ

4

Tr
M†M

2 , where M = 1 √ 2 (σ + i τ · π) = 1 √ 2

σ + iπ3

π2 + iπ1 −(π2 − iπ1) σ − iπ3

=
Φc, Φ
and DµM = ∂µM + igT iW i

µM − ig′M τ3 2 Bµ.

EWS acts on M as M

SU(2)L

− → ULM , M

U(1)Y

− → Me−ig′ τ3

2

. g′ → 0: L (h)

kin,int has large global symmetry SO(4) ∼ SU(2)L × SU(2)R

M

SU(2)L×SU(2)R

− → ULMU †

R .

Higgs condensate M0 ∼

φ0

φ0

breaks global symmetry down to SO(3) ∼ SU(2)V .

⇒ NGBs provide masses to weak gauge bosons ! Consequences: W ±, Z0 are degenerate ! Custodial symmetry protects ρ against radiative corrections !

SLIDE 14

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

The SM: Problems

SM seems to work fine ! Why replace or extend it ? SM has phenomenological problems: Neutrino masses, dark matter, matter-antimatter asymmetry, ... ...and theoretical problems: EWSB is modelled, but not explained ! Which dynamics leads to µ2 < 0 ? Fundamental scalar fields require unnatural fine-tuning of parameters. EW scale is not shielded against higher scales. Example for fine-tuning: g0: Dimensionless coupling, µ0 = m0/ΛUV : Dimensionless bare mass, and ΛUV : Large cut-off scale (Planck scale, grand unification scale, ...). Fundamental scalar has a quadratic mass correction: m2 = m2

0 + ∆m2 = m2 0 + Λ2 UV g2 0 = Λ2 UV

µ2

0 + g2

⇒

µ2

0 =

m2 Λ2

UV

− g2 At a scale of m ≈ 1 GeV and with ΛUV ≈ 1019 GeV: µ2

0 ≈ −g2

1 − 10−38

. ⇒ Physical mass m requires ridiculous fine-tuning of µ2

0 to the 38th decimal

place !!! ⇒ No natural separation between EW and Planck scale.

SLIDE 15

Is the Fundamental Higgs Necessary ?

SLIDE 16

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Basic Setup

”Thought Experiment”: Consider SM without Higgs and only one family

f quarks/leptons !

˜ LSM = L (g)

kin,int + L (ℓ) kin,int + L (q) kin,int

Treat small EW gauge couplings as perturbation: g, g′ = 0. Leptonic part: Free theory. Quark part: Covariant derivatives become D(q/u/d)

µ,L/R

≡ D(q)

µ

= ∂µ + igCT aAa

µ, so

that L (q)

kin,int = ¯

QLiγµD(q)

µ,LQL + ¯

QR,uiγµD(u)

µ,RQR,u + ¯

QR,diγµD(d)

µ,RQR,d

= ¯ QLiγµD(q)

µ QL + ¯

QRiγµD(q)

µ QR

⇒ global chiral SU(2)L × SU(2)R symmetry ! Strong dynamics: gC becomes strong, such that ¯ QQ = 0. ⇒ SχSB: SU(2)L × SU(2)R − → SU(2)V . ⇒ Three NGBs: The pions. Each NGB ∼ one broken axial generator. ⇒ Pions are associated with axial-vector currents. Question: Where are the axial-vector currents in ˜ LSM and what happens to the NGBs ?

SLIDE 17

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Axial-Vector Currents and NGBs

Turn EW gauge couplings on and consider L (q)

kin,int

L (q)

kin,int = ¯

QLiγµ

∂µ + igCT aAa

µ + igT iW i µ + i g′

6 Bµ

QL

+ ¯ QR,uiγµ

∂µ + igCT aAa

µ + i 2g′

3 Bµ

QR,u

+ ¯ QR,diγµ

∂µ + igCT aAa

µ − i g′

3 Bµ

QR,d

= ¯ QiγµD(q)

µ Q + ¯

Qiγµ iT iW i

µ

PLQ + ¯

Qiγµ

ig′
1

2 PL − 1 3 + 1 + τ 3 2 PR

Bµ
Q

Gauge Bosons couple to axial-vector currents via ∼ g 2 ¯ Qγµγ5T iQ

=Jµ,i

A

W i

µ

, ∼ − g′ 2 ¯ Qγµγ5T 3Q

=Jµ,3

A

Bµ . NGBs couple to axial-vector currents via Ω|Ji

µ,A|πj ∼ −ifπpµδij

, Ω|J3

µ,A|πj ∼ −ifπpµδ3j ,

so that W i

µ

πj ∼ g 2 fπpµδij , Bµ πj ∼ − g′ 2 fπpµδ3j .

SLIDE 18

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Generation of Masses

NGBs contribute to gauge boson self-energy via W i

µ

W j

ν

∼ g 2 fπpµδik

iδkl

p2 − g 2

fπpνδlj = − g2

4 f 2

π

ipµpν p2 δij W i

µ

Bν ∼ g 2 fπpµδik

iδkl

p2

g′

2 fπpνδl3 = gg′ 4 f 2

π

ipµpν p2 δi3 Bµ Bν ∼ − g′ 2 fπpµδ3k

iδkl

p2

g′

2 fπpνδl3 = g′2 4 f 2

π

ipµpν p2 . Exact gauge boson propagator is given by ∆µν,ij(p) = − i p2

p2gµν − pµpν

δij 1 − Π(p2) , where Π(p2) is defined by the 1PI two-point function iΠµν(p) = iΠ(p2)

p2gµν − pµpν

. Therefore ΠW W (p2) = g2f 2

π

4 1 p2 , ΠW B(p2) = − gg′f 2

π

4 1 p2 , ΠBB(p2) = − g′2f 2

π

4 1 p2 .

SLIDE 19

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Mass Matrix

The self-energy contributions result in the following gauge boson mass matrix ˜ Lmass = 1 2 f 2

π

4

W 1

µ, W 2 µ, W 3 µ, Bµ



   g2 g2 g2 −gg′ −gg′ g2         W µ,1 W µ,2 W µ,3 Bµ     , such that M 2

W = g2f 2 π

4 , M 2

Z = g2 + g′2

4 f 2

π ,

M 2

A = 0 .

Same tree-level ρ-ratio of the gauge boson masses as in the SM ρ = M 2

W

M 2

Z cos2(θW ) = 1 ,

which is a consequence of the custodial SU(2)L × SU(2)R symmetry of the quark Lagrangian L (q)

kin,int.

SLIDE 20

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Achievements

Physical explanation for EWSB: Strong dynamics ! Fundamental scalar field is not required in order to generate gauge boson masses. ρ-ratio is the same as in the SM. Theory is natural, since strong interacting part is asymptotically free µ dgC dµ = −Kg3

C

⇒ 1 g2(µ) = 2K ln

µ

ΛUV

+ 1

g2 , where g0 ≡ g(ΛUV ) and K ≡ 9/(24π2) for Nf = 2. ⇒ g(m) becomes strong at a certain mass scale µ = m, such that 2K ln

m

ΛUV

= − 1

g2 ⇒ m ΛUV = exp

−

1 2Kg2

.

⇒ It follows that m ΛUV ∼ 10−19 = exp

−

1 2Kg2

⇒

g2

0 =

1 38 ln(10)K ≈ 0.3 . ⇒ No unnatural fine-tuning necessary ! ⇒ Scales are separated !

SLIDE 21

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Achievements

Physical explanation for EWSB: Strong dynamics ! Fundamental scalar field is not required in order to generate gauge boson masses. ρ-ratio is the same as in the SM. Theory is natural, since strong interacting part is asymptotically free µ dgC dµ = −Kg3

C

⇒ 1 g2(µ) = 2K ln

µ

ΛUV

+ 1

g2 , where g0 ≡ g(ΛUV ) and K ≡ 9/(24π2) for Nf = 2. ⇒ g(m) becomes strong at a certain mass scale µ = m, such that 2K ln

m

ΛUV

= − 1

g2 ⇒ m ΛUV = exp

−

1 2Kg2

.

⇒ It follows that m ΛUV ∼ 10−19 = exp

−

1 2Kg2

⇒

g2

0 =

1 38 ln(10)K ≈ 0.3 . ⇒ No unnatural fine-tuning necessary ! ⇒ Scales are separated !

SLIDE 22

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Achievements

Physical explanation for EWSB: Strong dynamics ! Fundamental scalar field is not required in order to generate gauge boson masses. ρ-ratio is the same as in the SM. Theory is natural, since strong interacting part is asymptotically free µ dgC dµ = −Kg3

C

⇒ 1 g2(µ) = 2K ln

µ

ΛUV

+ 1

g2 , where g0 ≡ g(ΛUV ) and K ≡ 9/(24π2) for Nf = 2. ⇒ g(m) becomes strong at a certain mass scale µ = m, such that 2K ln

m

ΛUV

= − 1

g2 ⇒ m ΛUV = exp

−

1 2Kg2

.

⇒ It follows that m ΛUV ∼ 10−19 = exp

−

1 2Kg2

⇒

g2

0 =

1 38 ln(10)K ≈ 0.3 . ⇒ No unnatural fine-tuning necessary ! ⇒ Scales are separated !

SLIDE 23

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Thought Experiment: Achievements

Physical explanation for EWSB: Strong dynamics ! Fundamental scalar field is not required in order to generate gauge boson masses. ρ-ratio is the same as in the SM. Theory is natural, since strong interacting part is asymptotically free µ dgC dµ = −Kg3

C

⇒ 1 g2(µ) = 2K ln

µ

ΛUV

+ 1

g2 , where g0 ≡ g(ΛUV ) and K ≡ 9/(24π2) for Nf = 2. ⇒ g(m) becomes strong at a certain mass scale µ = m, such that 2K ln

m

ΛUV

= − 1

g2 ⇒ m ΛUV = exp

−

1 2Kg2

.

⇒ It follows that m ΛUV ∼ 10−19 = exp

−

1 2Kg2

⇒

g2

0 =

1 38 ln(10)K ≈ 0.3 . ⇒ No unnatural fine-tuning necessary ! ⇒ Scales are separated !

SLIDE 24

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

SLIDE 30

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: A Simple Setup

Technicolor sector has SU(3)T C gauge symmetry. One doublet of techniquarks, T =

U

D

,

with TL transforming as SU(2)L doublet and UR, DR transforming as singlets. Ignoring leptons, the Lagrangian for NT f = 2 techniquark flavors and Nf = 2 quark flavors is given by ˜ LSM,T C = L (g)

kin,int + L (q) kin,int + L (t) kin,int ,

where L (g)

kin,int = − 1

2 TrT C

GµνGµν

− 1 2 TrC

FµνF µν

− 1 2 TrL

WµνW µν

− 1 4 BµνBµν , L (q)

kin,int = ¯

Qiγµ

∂µ + igCT aAa

µ + igT iW iPL + ig′

1

2 PL − 1 3 + ✶ + τ 3 2 PR

Bµ
Q ,

L (t)

kin,int = ¯

T iγµ

∂µ + igT CT AGA

µ + igT iW iPL + ig′

1

2 PL − 1 3 + ✶ + τ 3 2 PR

Bµ
T .

SLIDE 31

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: TC Dynamics

TC dynamics: gT C becomes strong, such that ¯ T T = 0. ⇒ STχSB: SU(2)T L × SU(2)T R − → SU(2)T V . ⇒ Three NGBs: The technipions. Coupling of technipions to techni-axial-vector currents determines technipion decay constant Ω|Ji

µ,T A|Πj ∼ −iFπpµδij .

Same mechanism as in ”thought experiment” yields the gauge boson mass matrix ˜ Lmass,T C = 1 2 F 2

π

4

W 1

µ, W 2 µ, W 3 µ, Bµ



   g2 g2 g2 −gg′ −gg′ g2         W µ,1 W µ,2 W µ,3 Bµ     , such that M 2

W = g2F 2 π

4 , M 2

Z = g2 + g′2

4 F 2

π ,

M 2

A = 0 .

Physical gauge boson masses lead to Fπ ∼ 250 GeV.

SLIDE 32

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: Achievements and Problems

EWS is dynamically broken. Weak gauge bosons receive their physical masses without a fundamental scalar field. Pions do not disappear from the physical hadron spectrum. ⇒ Largest contribution of the absorbed NGBs comes from the technipions. Theory is natural with well separated scales, since QCD and QTD are asymptotically free theories mQCD mQT D ≈ exp

− 1

2

1

KQCDg2

C

− 1 KQT Dg2

T C

,

which can easily be ∼ 10−3 for natural assignments of KQCD, gC and KQT D, gT C. Quarks (and also leptons) stay massless !

SLIDE 33

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: Achievements and Problems

EWS is dynamically broken. Weak gauge bosons receive their physical masses without a fundamental scalar field. Pions do not disappear from the physical hadron spectrum. ⇒ Largest contribution of the absorbed NGBs comes from the technipions. Theory is natural with well separated scales, since QCD and QTD are asymptotically free theories mQCD mQT D ≈ exp

− 1

2

1

KQCDg2

C

− 1 KQT Dg2

T C

,

which can easily be ∼ 10−3 for natural assignments of KQCD, gC and KQT D, gT C. Quarks (and also leptons) stay massless !

SLIDE 34

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: Achievements and Problems

EWS is dynamically broken. Weak gauge bosons receive their physical masses without a fundamental scalar field. Pions do not disappear from the physical hadron spectrum. ⇒ Largest contribution of the absorbed NGBs comes from the technipions. Theory is natural with well separated scales, since QCD and QTD are asymptotically free theories mQCD mQT D ≈ exp

− 1

2

1

KQCDg2

C

− 1 KQT Dg2

T C

,

which can easily be ∼ 10−3 for natural assignments of KQCD, gC and KQT D, gT C. Quarks (and also leptons) stay massless !

SLIDE 35

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: Achievements and Problems

EWS is dynamically broken. Weak gauge bosons receive their physical masses without a fundamental scalar field. Pions do not disappear from the physical hadron spectrum. ⇒ Largest contribution of the absorbed NGBs comes from the technipions. Theory is natural with well separated scales, since QCD and QTD are asymptotically free theories mQCD mQT D ≈ exp

− 1

2

1

KQCDg2

C

− 1 KQT Dg2

T C

,

which can easily be ∼ 10−3 for natural assignments of KQCD, gC and KQT D, gT C. Quarks (and also leptons) stay massless !

SLIDE 36

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Technicolor: Achievements and Problems

EWS is dynamically broken. Weak gauge bosons receive their physical masses without a fundamental scalar field. Pions do not disappear from the physical hadron spectrum. ⇒ Largest contribution of the absorbed NGBs comes from the technipions. Theory is natural with well separated scales, since QCD and QTD are asymptotically free theories mQCD mQT D ≈ exp

− 1

2

1

KQCDg2

C

− 1 KQT Dg2

T C

,

which can easily be ∼ 10−3 for natural assignments of KQCD, gC and KQT D, gT C. Quarks (and also leptons) stay massless !

SLIDE 37

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Conclusions

SLIDE 38

Problems of the Fundamental Higgs Is the Fundamental Higgs Necessary ? Technicolor Conclusions

Conclusions

Strong dynamics is able to generate gauge boson masses. Fundamental scalar fields and unnatural parameter assignments are not necessary. TC is a true ”extension” of the SM. Most simple TC setup is not able to explain quark/lepton masses ⇒ extended Technicolor (ETC), walking Technicolor (WTC), ...