the standard model with four generations - kit · the standard model with four generations...

The Standard Model with four generations

Graduiertenkollegs-Workshop in Bad Liebenzell, 7. Oktober 2011

Otto Eberhardt, A. Lenz, U. Nierste & the CKMfitter group

Institut für Theoretische Teilchenphysik

Outline

◮ The fourth family – pros and cons

◮ The SM4 parameters

◮ Constraints to the SM4

◮ First results of a global fit

Otto Eberhardt The Standard Model with four generations 1 / 16

The fourth family

Another sequential generation of fermions

Leptons:

(

νe

e

)

,

(

νµµ

)

,

(

νττ

)

,

(

ν4

ℓ4

)

Quarks:

(

u

d

)

,

(

c

s

)

,

(

t

b

)

,

(

t ′

b′

)


The fourth family – pros ...

Some arguments in favour of the fourth family

◮ Baryogenesis (CP-violation and phase transition)[Hou ’08, Carena et al. ’04, Fok & Kribs ’08, Kikukawa et al. ’09]

◮ Solution to certain flavour physics problems[Hou ’06, Soni ’09]

◮ Unification of the gauge couplings[Hung ’97]

◮ Softening of the Higgs mass bounds[Novikov et al. ’02,’09, Frere et al. ’04, Kribs et al. ’07]


... and cons

Invisible Z decays

Nν = 2.9840 ± 0.0082

[LEP ’06]


... and cons

Invisible Z decays

Nlightν = 2.9840 ± 0.0082

[LEP ’06]

But neutrinos do have a mass.

[Super-Kamiokande ’98]


... and cons

Invisible Z decays

Nlightν = 2.9840 ± 0.0082

[LEP ’06]

But neutrinos do have a mass.

[Super-Kamiokande ’98]

Cosmology: Neffν = 4.34+0.86

−0.88

WMAP

WMAP+H0

+Galaxy

distributions

[7y WMAP ’10]


... and cons

Electroweak precision observables

History of the PDG reviews [Erler/Langacker]:

◮ 1994: “one heavy generation of ordinary fermions is allowed at 95%CL”


... and cons




◮ 1998: “an extra generation of ordinary fermions is now excluded atthe 99.2% CL”


... and cons




◮ 1998: “an extra generation of ordinary fermions is now excluded atthe 99.2% CL”

◮ 2010: “an extra generation of ordinary fermions is excluded at the 6σ level on the S parameter alone. This result assumes [. . . ] thatany new families are degenerate. [. . . ] a fourth family is disfavoredbut not excluded by current data.”


The SM4 parameters

The SM quark mixing matrix

cij ≡ cos θij

sij ≡ sin θij

VCKM3 ≡

VCKM3ud V

CKM3us V

CKM3ub

VCKM3cd V

CKM3cs V

CKM3cb

VCKM3td V

CKM3ts V

CKM3tb

=

1 0 0

0 c23 s23

0 −s23 c23

c13 0 s13e−iδ13

0 1 0

−s13eiδ13 0 c13

c12 s12 0

−s12 c12 0

0 0 1

=

c12c13 s12c13 s13e−iδ13

−s12c23 − c12s23s13eiδ13 c12c23 − s12s23s13e

iδ13 s23c13

s12s23 − c12c23s13eiδ13 −c12s23 − s12c23s13e

iδ13 c23c13


The SM4 parameters

The Wolfenstein parametrisation of the CKM matrix

VCKM3 ≈

1 − 12λ2 λ Aλ3(ρ− iη)

−λ 1 − 12λ2

Aλ2

Aλ3(1 − ρ− iη) −Aλ21

γ

α

α

dm∆

Kε

Kε

sm∆ & dm∆

SLubV

ν τubV

βsin 2(excl. at CL > 0.95)

< 0βsol. w/ cos 2

α

βγ

ρ-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

η

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

excl

uded

are

a ha

s C

L >

0.9

5

ICHEP 10

CKMf i t t e r


The SM4 parameters

The 4 × 4 CKM matrix

cij ≡ cos θij

sij ≡ sin θij

VCKM4 =

1 0 0 0

0 1 0 0

0 0 c34 s34

0 0 −s34 c34

1 0 0 0

0 c24 0 s24e−iδ24

0 0 1 0

0 −s24eiδ24 0 c24

·

c14 0 0 s14e−iδ14

0 1 0 0

0 0 1 0

−s14eiδ14 0 0 c14

VCKM3

0

0

0

0 0 0 1


The SM4 parameters

The 4 × 4 CKM matrix

cij ≡ cos θij

sij ≡ sin θij

VCKM4 =

c12c13c14 c13c14s12 c14s13e−iδ13 s14e−iδ14

−c23c24s12 c12c23c24 c13c24s23 c14s24e−iδ24

−c12c24s13s23e iδ13 −c24s12s13s23e iδ13 −s13s14s24e−i(δ13+δ24−δ14)

−c12c13s14s24e i(δ14−δ24) −c13s12s14s24e i(δ14−δ24)

−c12c23c34s13e iδ13 −c12c34s23 c13c23c34 c14c24s34

+c34s12s23 −c23c34s12s13e iδ13 −c13s23s24s34e iδ24

−c12c13c24s14s34e iδ14 −c12c23s24s34e iδ24 −c24s13s14s34e i(δ14−δ13)

+c23s12s24s34e iδ24 −c13c24s12s14s34e iδ14

+c12s13s23s24s34e i(δ13+δ24) +s12s13s23s24s34e i(δ13+δ24)

−c12c13c24c34s14e iδ14 −c12c23c34s24e iδ24 −c13c23s34 c14c24c34

+c12c23s13s34e iδ13 +c12s23s34 −c13c34s23s24e iδ24

+c23c34s12s24e iδ24 −c13c24c34s12s14e iδ14 −c24c34s13s14e i(δ14−δ13)

−s12s23s34 +c23s12s13s34e iδ13

+c12c34s13s23s24e i(δ13+δ24) +c34s12s13s23s24e i(δ13+δ24)


The SM4 parameters

The “old” parameters

Quarks: mu,md ,ms ,mc ,mb,mt , θ12, θ13, θ23, ϕ13

Leptons: mνe ,mνµ ,mντ ,me ,mµ,mτ , θℓ12, θℓ13, θ

ℓ23, ϕℓ

13

Higgs: mH


The SM4 parameters




ℓ23, ϕℓ

13

Higgs: mH

The new parameters

Quarks: mb′ ,mt′ , θ14, θ24, θ34, ϕ14, ϕ24

Leptons: mν4 ,mℓ4 , θℓ14, θℓ24, θ

ℓ34, ϕℓ

14, ϕℓ24


The SM4 parameters




ℓ23, ϕℓ

13

Higgs: mH

The new parameters

Quarks: mb′ ,mt′ , θ14, θ24, θ34, ϕ14, ϕ24

Leptons: mν4 ,mℓ4 , θℓ14, θℓ24, θ

ℓ34, ϕℓ

14, ϕℓ24

14 free parameters


Constraints to the SM41. Masses

H

t ′

b′

ℓ4

ν4

t

b

τ

ντ

c

s

µ

νµ

u

d

e

νe

Higgs

Up-typeQuarks

Down-typeQuarks

ChargedLeptons

Neutrinos

m1 eV 1 keV 1 MeV 1 GeV 1 TeV


Constraints to the SM4

2. Tree-level observables

ff ′

W

VCKM4 =

Vud Vus Vub Vub′

Vcd Vcs Vcb Vcb′

Vtd Vts Vtb Vtb′

Vt′d Vt′s Vt′b Vt′b′




Vud Vus Vub Vub′

Vcd Vcs Vcb Vcb′

Vtd Vts Vtb Vtb′


β decays

W

d u




Vud Vus Vub Vub′

Vcd Vcs Vcb Vcb′

Vtd Vts Vtb Vtb′


β decays

W

c d

semileptonic

meson decays




Vud Vus Vub Vub′

Vcd Vcs Vcb Vcb′

Vtd Vts Vtb Vtb′


β decays

semileptonic

meson decays (single) top production

W

b

t




Vud Vus Vub Vub′

Vcd Vcs Vcb Vcb′

Vtd Vts Vtb Vtb′


β decays

semileptonic

meson decays (single) top production

γ ≡ argV

udV ∗

ub

Vcd

V ∗

cb

from CKMfitter fits

W → ℓν decays



3. Electroweak precision observables

SM4 loop contributions to Z and W processes (examples)

Z

b̄t̄ ′

t ′ b

W

W

b̄t̄

b′ t

W

Z Zb′

b̄′

W Wb′

t̄ ′

Z

H




Fermion mass differences

-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

(mH fixed, VCKM4 diagonal)

[GeV]4

d - m4um

-100 -50 0 50 100

[GeV

]4l

- m

4νm

-200

-150

-100

-50

0

50

100

150

2004th Generation

68%, 95%, 99% CL fit contours (allowed)

=120 GeVHMpreliminary

[GeV]4

d - m4um

-100 -50 0 50 100

[GeV

]4l

- m

4νm

-200

-150

-100

-50

0

50

100

150

200

G fitter SMB

Aug 10

-

-





-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

(mH fixed, VCKM4 diagonal) (mH fixed)

-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

0

0.2

0.4

0.6

0.8

1

p-va

lue

-

-

-

-





-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

(mH fixed, VCKM4 diagonal) (Cartman)

-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

0

0.2

0.4

0.6

0.8

1

p-va

lue

-

-

-

-





-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

(mH fixed, VCKM4 diagonal)

-150 -100 -50 0 50 100 150mt'-md' [GeV]

-200

-100

0

100

200

mν 4

-ml 4 [G

eV]

0

0.2

0.4

0.6

0.8

1

p-va

lue

(mH free)

-

-

-

-



4. Flavour observables

s u, c , t, t ′

b̄

W W

s̄

b

u, c , t, t ′

Bs B̄s

b s

γq̄q̄

W

u, c , t, t ′


First results of o global fit

Moduli of the CKM matrix without and with EW and flavour constraints:

0

1

0.9735 0.9745|Vud|

0

1

0.215 0.23|Vcd|

0

1

0 0.025 0.05|Vtd|

0

1

0 0.05 0.1|Vt'd|

0

1

0.224 0.228|Vus|

0

1

0.93 0.95 0.97|Vcs|

0

1

0 0.1 0.2|Vts|

0

1

0 0.1 0.2|Vt's|

0

1

0.003 0.004|Vub|

0

1

0.04 0.042|Vcb|

0

1

0.8 0.9 1|Vtb|

0

1

0 0.3 0.6|Vt'b|

0

1

0 0.025 0.05|Vub'|

0

1

0 0.15 0.3|Vcb'|

0

1

0 0.35 0.7|Vtb'|

0

1

0.7 0.85 1|Vt'b'|


Outlook

◮ Global fit combining all observables

◮ Allowing for non-trivial PMNS structure

◮ Waiting for new experimental results


Back-up slides


Inputs I

mt′ ∈ [150, 1000] GeV

mb′ ∈ [128, 1000] GeV

mν4∈ [46, 1000] GeV

mℓ4 ∈ [100, 1000] GeV

mH ∈ [116, 1000] GeV

|Vud | = 0.97421+0.00034−0.00029

|Vus | = 0.2254 ± 0.0013

|Vub | =(

3.92 ± 0.09 (stat) ± 0.45 (sys)

)

· 10−3

|Vcd | = 0.230 ± 0.011

|Vcs | = 0.98 ± 0.01 (stat) ± 0.1 (sys)

|Vcb| =(

40.89 ± 0.37 (stat) ± 0.59 (sys)

)

· 10−3

|Vtb | = 1.0 ± 0.099


Inputs II

S 0.03 ± 0.09 0.867

T 0.07 ± 0.08

U

B(W → eν) 0.1075 ± 0.0013 0.110 -0.195

B(W− > µν) 0.1057 ± 0.0015 -0.132

B(W− > τν) 0.1125 ± 0.0020


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