Standard Model precision measurements Misure di precisione del modello standard

Standard Model precision measurements Misure di precisione del modello standard

Lesson 1: Measurements at Z pole

Stefano Lacaprara

INFN Padova

Dottorato di ricerca in fisica

Universit` a di Padova, Dipartimento di Fisica e Astronomia Padova, 5 March 2019

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 1/56

Outline

1 Introduction

2 Z-pole observables

3 Asymmetries

4 W mass and width

5 Top mass

6 Higgs mass and features

7 Global ElectroWeak fit

Introduction I

Stefano Lacaprara

I email: Stefano.Lacaprara@pd.infn.it

I tel: 049 9677100

I studio: st 137, Physics Dept. main building, 1 ^st floor SM precision measurements 5 lessons, ×2 hours each ; G.Simi will follow covering flavour physics (5x2h)

A.Palano (Bari) will follow covering new exotic states (tetra-penta quark) and Dalitz plot analysis methods in b-physics (6h)

All the slides available on moodle at

https://elearning.unipd.it/dfa/course/view.php?id=756

I All of you are subscribed to the course on moodle.

We will also record the class and put the registraton on moodle.

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 3/56

Introduction II

Final test: mandatory as per PhD school rules.

A short seminar ( ≈ 20 ⁰ ) on one of the topics covered during the course, including discussion with us about topics related to the presentation and the course in general.

I a list of possible topics will be provided, also topic suggest by students are fine (check with us in advance)

I the topic should not be the main theme of your PhD work.

Where to start?

“Begin at the beginning and go on till you come to the end; then stop.” L.Carrol

Starting from the end, instead: Global SM fit, aka the success of SM.

Fit vs indirect vs meas :

3

− −

2

−

1 0 1 2 3 tot O) /

σ

−

indirect (O

2) Z s(M α

2) Z (5)(M αhad

∆ mt

b R0 c R0 0,b AFB

0,c AFB

Ab Ac (Tevt.) lept Θeff sin2

FB) lept(Q Θeff sin2

(SLD) Al

(LEP) Al

0,l AFB

lep R0

0 had σ

ΓZ MZ ΓW MW MH

Global EW fit Indirect determination Measurement G

fitter

SM

Mar ’18

Pulls:

3

− −2 −1 0 1 2 3

σ

meas meas) / O

−

(Ofit 2) (MZ αs

2) (MZ (5) αhad

∆ mt

b R0

c R0 Ab Ac 0,b AFB

0,c AFB (Tevt.) lept eff 2Θ sin

FB) lept(Q Θeff sin2

(SLD) Al

(LEP) Al

0,l AFB

lep R0

0 had σ

ΓZ MZ ΓW MW MH

1.3 -0.2 0.5 -0.7 0.0 0.6 0.0 2.4 0.8 0.1 -0.7 -2.1 0.1 -0.9 -1.0 -1.5 -0.2 0.3 0.1 -1.5 G

fitter

SM 0.0

Mar ’18

Higgs mass prediction and measurement

60 70 80 90 100 110 120 130 140

[GeV]

MH 0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2χ∆

σ 1

σ 2 SM fit

measurement SM fit w/o MH

LHC combination [PRL 114, 191803 (2015)]

G fitter

SM

Mar ’18

Will cover (some) of the experimental aspect of SM precision measurements

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 5/56

Input to global EWK fit

(in parenthesis the order followed in these lessons)

3

− − 2 − 1 0 1 2 3

tot

O) / σ

−

indirect

(O

2) (MZ

α

s

2) (MZ (5)

α

had

∆

mt

b R0 c R0 0,b AFB

0,c AFB

Ab Ac (Tevt.) lept

Θ

eff sin2

) FB lept(Q

Θ

eff sin2

(SLD) Al

(LEP) Al

0,l AFB

lep R0

0

σ

had

Γ

Z MZ

Γ

W MW MH

Global EW fit Indirect determination Measurement

G fitter

SM

Mar ’18

Higgs mass (5)

I LHC

W mass and width (3)

I LEP2, Tevatron, LHC Z-pole observables (1,2)

I LEP1, SLD

I M Z , Γ Z I σ ^had ₀

I sin ² θ ^lept _eff (2)

I Asymmetries (2)

I BR R _lep,b,c ⁰ = Γ _had /Γ _{``,b ¯ b,c ¯ c} top mass (4)

I Tevatron, LHC other:

I α s (M _Z ² ), ∆α had (M _Z ² )

Input to global EWK fit

(in parenthesis the order followed in these lessons)

Higgs mass (5)

I LHC

W mass and width (3)

I LEP2, Tevatron, LHC Z-pole observables (1,2)

I LEP1, SLD

I M Z , Γ Z I σ ^had ₀

I sin ² θ ^lept _eff (2)

I Asymmetries (2)

I BR R _lep,b,c ⁰ = Γ _had /Γ _{``,b ¯ b,c ¯ c} top mass (4)

I Tevatron, LHC

other:

I α s (M _Z ² ), ∆α had (M _Z ² )

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 6/56

Outline

1 Introduction

2 Z-pole observables Standard Model Z lineshape

3 Asymmetries

4 W mass and width

5 Top mass

6 Higgs mass and features

7 Stefano Lacaprara (INFN Padova) Global ElectroWeak fit Fit SM Padova 5/03/2019 7/56

Standard model lagrangian

− 1 2

∂

_ν

g

^a_µ

∂

_ν

g

_µ^a

− g

s

f

^abc

∂

_µ

g

^a_ν

g

_µ^b

g

_ν^c

− 1 4

g

_s²

f

^abc

f

^ade

g

_µ^b

g

_ν^c

g

_µ^d

g

_ν^e

+ 1 2

ig

_s²

( ¯ q

^σ_i

γ

^µ

q

^σ_j

)g

_µ^a

+ ¯ G

^a

∂

²

G

^a

+ g

_s

f

^abc

∂

_µ

G ¯

^a

G

^b

g

_µ^c

− ∂

ν

W

_µ⁺

∂

_ν

W

_µ⁻

− M

²

W

_µ⁺

W

_µ⁻

− 1 2

∂

_ν

Z

_µ⁰

∂

_ν

Z

_µ⁰

− 1 2c

_w²

M

²

Z

_µ⁰

Z

_µ⁰

−

1

2 ∂

µ

A

ν

∂

µ

A

ν

− 1

2 ∂

µ

H∂

µ

H − 1

2 m

²_h

H

²

− ∂

µ

φ

⁺

∂

µ

φ

⁻

− M

²

φ

⁺

φ

⁻

− 1

2 ∂

µ

φ

⁰

∂

µ

φ

⁰

− 1

2c

_w²

Mφ

⁰

φ

⁰

− β

h

[ 2M

²

g

²

+ 2M

g H + 1

2 (H

²

+ φ

⁰

φ

⁰

+ 2φ

⁺

φ

⁻

)] + 2M

⁴

g

²

α

_h

− igc

w

[∂

ν

Z

_µ⁰

(W

_µ⁺

W

_ν⁻

− W

_ν⁺

W

_µ⁻

) − Z

_ν⁰

(W

_µ⁺

∂

ν

W

_µ⁻

− W

_µ⁻

∂

ν

W

_µ⁺

) + Z

_µ⁰

(W

_ν⁺

∂

ν

W

_µ⁻

− W

_ν⁻

∂

ν

W

_µ⁺

)] − igs

w

[∂

ν

A

µ

(W

_µ⁺

W

_ν⁻

− W

_ν⁺

W

_µ⁻

) − A

ν

(W

_µ⁺

∂

ν

W

_µ⁻

− W

_µ⁻

∂

ν

W

_µ⁺

) + A

µ

(W

_ν⁺

∂

ν

W

_µ⁻

− W

_ν⁻

∂

ν

W

_µ⁺

)] − 1

2 g

²

W

_µ⁺

W

_µ⁻

W

_ν⁺

W

_ν⁻

+ 1

2 g

²

W

_µ⁺

W

_ν⁻

W

_µ⁺

W

_ν⁻

+ g

²

c

_w²

(Z

_µ⁰

W

_µ⁺

Z

_ν⁰

W

_ν⁻

− Z

_µ⁰

Z

_µ⁰

W

_ν⁺

W

_ν⁻

) + g

²

s

²_w

(A

µ

W

_µ⁺

A

ν

W

_ν⁻

− A

µ

A

µ

W

_ν⁺

W

_ν⁻

) + g

²

s

w

c

w

[A

µ

Z

_ν⁰

(W

_µ⁺

W

_ν⁻

− W

_ν⁺

W

_µ⁻

) − 2A

µ

Z

_µ⁰

W

_ν⁺

W

_ν⁻

] − g α[H

³

+ Hφ

⁰

φ

⁰

+ 2Hφ

⁺

φ

⁻

] − 1

8 g

²

α

h

[H

⁴

+ (φ

⁰

)

⁴

+ 4(φ

⁺

φ

⁻

)

²

+ 4(φ

⁰

)

²

φ

⁺

φ

⁻

+ 4H

²

φ

⁺

φ

⁻

+ 2(φ

⁰

)

²

H

²

] − gMW

_µ⁺

W

_µ⁻

H − 1 2 g M

c

²_w

Z

_µ⁰

Z

_µ⁰

H − 1

2 ig [W

_µ⁺

(φ

⁰

∂

µ

φ

⁻

− φ

⁻

∂

µ

φ

⁰

) −

W

_µ⁻

(φ

⁰

∂

µ

φ

⁺

− φ

⁺

∂

µ

φ

⁰

)] + 1 2

g [W

_µ⁺

(H∂

µ

φ

⁻

− φ

⁻

∂

µ

H) − W

_µ⁻

(H∂

µ

φ

⁺

− φ

⁺

∂

µ

H)] + 1 2

g 1 c

w

(Z

⁰_µ

(H∂

µ

φ

⁰

− φ

⁰

∂

µ

H) − ig s

²_w

c

w

MZ

_µ⁰

(W

_µ⁺

φ

⁻

− W

_µ⁻

φ

⁺

) + igs

w

MA

µ

(W

_µ⁺

φ

⁻

− W

_µ⁻

φ

⁺

) −

ig 1 − 2c

²_w

2c

w

Z

⁰_µ

(φ

⁺

∂

µ

φ

⁻

− φ

⁻

∂

µ

φ

⁺

) + igs

w

A

µ

(φ

⁺

∂

µ

φ

⁻

− φ

⁻

∂

µ

φ

⁺

) − 1

4 g

²

W

_µ⁺

W

_µ⁻

[H

²

+ (φ

⁰

)

²

+ 2φ

⁺

φ

⁻

] − 1 4 g

²

1

c

²_w

Z

_µ⁰

Z

⁰_µ

[H

²

+ (φ

⁰

)

²

+ 2(2s

_w²

− 1)

²

φ

⁺

φ

⁻

] − 1 2 g

²

s

_w²

c

w

Z

_µ⁰

φ

⁰

(W

_µ⁺

φ

⁻

+

W

_µ⁻

φ

⁺

) − 1 2 ig

²

s

_w²

c

w

Z

_µ⁰

H(W

_µ⁺

φ

⁻

− W

µ⁻

φ

⁺

) + 1

2 g

²

s

w

A

µ

φ

⁰

(W

_µ⁺

φ

⁻

+ W

_µ⁻

φ

⁺

) + 1

2 ig

²

s

w

A

µ

H(W

_µ⁺

φ

⁻

− W

µ⁻

φ

⁺

) − g

²

s

w

c

w

(2c

²_w

− 1)Z

µ⁰

A

µ

φ

⁺

φ

⁻

− g

¹

s

_w²

A

µ

A

µ

φ

⁺

φ

⁻

− ¯ e

^λ

(γ∂ + m

^λ_e

)e

^λ

−

¯

ν

^λ

γ∂ν

^λ

− ¯ u

_j^λ

(γ∂ + m

^λ_u

)u

_j^λ

− ¯ d

_j^λ

(γ∂ + m

^λ_d

)d

^λ_j

+ igs

w

A

µ

[−(¯ e

^λ

γ

^µ

e

^λ

) + 2

3 ( ¯ u

^λ_j

γ

^µ

u

^λ_j

) − 1

3 ( ¯ d

_j^λ

γ

^µ

d

_j^λ

)] + ig 4c

w

Z

_µ⁰

[( ¯ ν

^λ

γ

^µ

(1 + γ

⁵

)ν

^λ

) + (¯ e

^λ

γ

^µ

(4s

²_w

− 1 − γ

⁵

)e

^λ

) + ( ¯ u

^λ_j

γ

^µ

( 4 3 s

²_w

− 1 − γ

⁵

)u

_j^λ

) + ( ¯ d

_j^λ

γ

^µ

(1 − 8

3 s

²_w

− γ

⁵

)d

_j^λ

)] + ig 2 √

2 W

_µ⁺

[( ¯ ν

^λ

γ

^µ

(1 + γ

⁵

)e

^λ

) + ( ¯ u

^λ_j

γ

^µ

(1 + γ

⁵

)C

_λκ

d

_j^κ

)] + ig 2 √

2 W

_µ⁻

[(¯ e

^λ

γ

^µ

(1 + γ

⁵

)ν

^λ

) + ( ¯ d

^κ_j

C

_λκ^†

γ

^µ

(1 + γ

⁵

)u

^λ_j

)] + ig 2 √ 2

m

^λ_e

M [−φ

⁺

( ¯ ν

^λ

(1 − γ

⁵

)e

^λ

) + φ

⁻

(¯ e

^λ

(1 + γ

⁵

)ν

^λ

)] − g

2 m

^λ_e

M

[H(¯ e

^λ

e

^λ

) + i φ

⁰

(¯ e

^λ

γ

⁵

e

^λ

)] + ig 2M √

2

φ

⁺

[−m

^κ_d

( ¯ u

^λ_j

C

_λκ

(1 − γ

⁵

)d

_j^κ

) + m

^λ_u

( ¯ u

_j^λ

C

_λκ

(1 + γ

⁵

)d

_j^κ

] + ig 2M √

2

φ

⁻

[m

^λ_d

( ¯ d

_j^λ

C

_λκ^†

(1 + γ

⁵

)u

^κ_j

) − m

^κ_u

( ¯ d

^λ_j

C

_λκ^†

(1 −

γ

⁵

)u

^κ_j

] − g 2

m

^λ_u

M H( ¯ u

^λ_j

u

^λ_j

) − g

2 m

^λ_d

M H( ¯ d

^λ_j

d

_j^λ

) + ig 2

m

^λ_u

M φ

⁰

( ¯ u

^λ_j

γ

⁵

u

^λ_j

) − ig 2

m

_d^λ

M φ

⁰

( ¯ d

^λ_j

γ

⁵

d

^λ_j

) + ¯ X

⁺

(∂

²

− M

²

)X

⁺

+ ¯ X

⁻

(∂

²

− M

²

)X

⁻

+ ¯ X

⁰

(∂

²

− M

²

c

²_w

)X

⁰

+ ¯ Y ∂

²

Y + igc

w

W

_µ⁺

(∂

µ

X ¯

⁰

X

⁻

−

∂

µ

X ¯

⁺

X

⁰

) + igs

w

W

_µ⁺

(∂

µ

Y X ¯

⁻

− ∂

µ

X ¯

⁺

Y ) + igc

w

W

_µ⁻

(∂

µ

X ¯

⁻

X

⁰

− ∂

µ

X ¯

⁰

X

⁺

) + igs

w

W

_µ⁻

(∂

µ

X ¯

⁻

Y − ∂

µ

Y X ¯

⁺

) + igc

w

Z

⁰_µ

(∂

µ

X ¯

⁺

X

⁺

− ∂

µ

X ¯

⁻

X

⁻

) + igs

w

A

µ

(∂

µ

X ¯

⁺

X

⁺

− ∂

µ

X ¯

⁻

X

⁻

) − 1

2

gM[ ¯ X

⁺

X

⁺

H + ¯ X

⁻

X

⁻

H + 1 c

_w²

X ¯

⁰

X

⁰

H] + 1 − 2c

_w²

2c

w

igM[ ¯ X

⁺

X

⁰

φ

⁺

− ¯ X

⁻

X

⁰

φ

⁻

] + 1 2c

w

igM[ ¯ X

⁰

X

⁻

φ

⁺

− ¯ X

⁰

X

⁺

φ

⁻

] + igMs

w

[ ¯ X

⁰

X

⁻

φ

⁺

− ¯ X

⁰

X

⁺

φ

⁻

] + 1 2

igM[ ¯ X

⁺

X

⁺

φ

⁰

− ¯ X

⁻

X

⁻

φ

⁰

]

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 8/56

Standard model lagrangian

− 1

2 ∂

ν

g

_µ^a

∂

ν

g

_µ^a

− g

s

f

^abc

∂

µ

g

_ν^a

g

_µ^b

g

_ν^c

− 1

4 g

_s²

f

^abc

f

^ade

g

_µ^b

g

_ν^c

g

^d_µ

g

^e_ν

+ 1

2 ig

_s²

( ¯ q

^σ_i

γ

^µ

q

_j^σ

)g

^a_µ

+ ¯ G

^a

∂

²

G

^a

+ g

s

f

^abc

∂

µ

G ¯

^a

G

^b

g

_µ^c

− ∂

ν

W

_µ⁺

∂

ν

W

_µ⁻

− M

²

W

_µ⁺

W

_µ⁻

− 1

2 ∂

ν

Z

_µ⁰

∂

ν

Z

⁰_µ

− 1 2c

²_w

M

²

Z

_µ⁰

Z

_µ⁰

− 1

2 ∂

µ

A

ν

∂

µ

A

ν

− 1 2 ∂

µ

H∂

µ

H − 1

2 m

²_h

H

²

− ∂

_µ

φ

⁺

∂

µ

φ

⁻

− M

²

φ

⁺

φ

⁻

− 1

2 ∂

µ

φ

⁰

∂

µ

φ

⁰

− 1

2c

_w²

Mφ

⁰

φ

⁰

− β

_h

[ 2M

²

g

²

+ 2M

g H + 1

2 (H

²

+ φ

⁰

φ

⁰

+ 2φ

⁺

φ

⁻

)] + 2M

⁴

g

²

α

h

− igc

_w

[∂

ν

Z

⁰_µ

(W

_µ⁺

W

_ν⁻

− W

_ν⁺

W

_µ⁻

) − Z

_ν⁰

(W

_µ⁺

∂

ν

W

_µ⁻

− W

_µ⁻

∂

ν

W

_µ⁺

) + Z

⁰_µ

(W

_ν⁺

∂

ν

W

_µ⁻

− W

_ν⁻

∂

ν

W

_µ⁺

)] − igs

w

[∂

ν

A

µ

(W

_µ⁺

W

_ν⁻

− W

_ν⁺

W

_µ⁻

) − A

ν

(W

_µ⁺

∂

ν

W

_µ⁻

− W

_µ⁻

∂

ν

W

_µ⁺

) + A

µ

(W

_ν⁺

∂

ν

W

_µ⁻

− W

_ν⁻

∂

ν

W

_µ⁺

)] − 1

2 g

²

W

_µ⁺

W

_µ⁻

W

_ν⁺

W

_ν⁻

+ 1

2 g

²

W

_µ⁺

W

_ν⁻

W

_µ⁺

W

_ν⁻

+ g

²

c

_w²

(Z

_µ⁰

W

_µ⁺

Z

_ν⁰

W

_ν⁻

− Z

_µ⁰

Z

_µ⁰

W

_ν⁺

W

_ν⁻

) + g

²

s

_w²

(A

µ

W

_µ⁺

A

ν

W

_ν⁻

− A

_µ

A

µ

W

_ν⁺

W

_ν⁻

) + g

²

s

w

c

w

[A

µ

Z

_ν⁰

(W

_µ⁺

W

_ν⁻

− W

_ν⁺

W

_µ⁻

) − 2A

µ

Z

_µ⁰

W

_ν⁺

W

_ν⁻

] − g α[H

³

+ Hφ

⁰

φ

⁰

+ 2Hφ

⁺

φ

⁻

] − 1

8 g

²

α

h

[H

⁴

+ (φ

⁰

)

⁴

+ 4(φ

⁺

φ

⁻

)

²

+ 4(φ

⁰

)

²

φ

⁺

φ

⁻

+ 4H

²

φ

⁺

φ

⁻

+ 2(φ

⁰

)

²

H

²

] − gMW

_µ⁺

W

_µ⁻

H − 1 2 g M

c

²_w

Z

_µ⁰

Z

⁰_µ

H − 1

2 ig [W

_µ⁺

(φ

⁰

∂

µ

φ

⁻

− φ

⁻

∂

µ

φ

⁰

) −

W

_µ⁻

(φ

⁰

∂

µ

φ

⁺

− φ

⁺

∂

µ

φ

⁰

)] + 1

2 g [W

_µ⁺

(H∂

µ

φ

⁻

− φ

⁻

∂

µ

H) − W

_µ⁻

(H∂

µ

φ

⁺

− φ

⁺

∂

µ

H)] + 1 2 g 1

c

w

(Z

_µ⁰

(H∂

µ

φ

⁰

− φ

⁰

∂

µ

H) − ig s

_w²

c

w

MZ

_µ⁰

(W

_µ⁺

φ

⁻

− W

_µ⁻

φ

⁺

) + igs

w

MA

µ

(W

_µ⁺

φ

⁻

− W

_µ⁻

φ

⁺

) −

ig 1 − 2c

_w²

2c

w

Z

_µ⁰

(φ

⁺

∂

µ

φ

⁻

− φ

⁻

∂

µ

φ

⁺

) + igs

w

A

µ

(φ

⁺

∂

µ

φ

⁻

− φ

⁻

∂

µ

φ

⁺

) − 1

4 g

²

W

_µ⁺

W

_µ⁻

[H

²

+ (φ

⁰

)

²

+ 2φ

⁺

φ

⁻

] − 1 4 g

²

1

c

_w²

Z

⁰_µ

Z

_µ⁰

[H

²

+ (φ

⁰

)

²

+ 2(2s

²_w

− 1)

²

φ

⁺

φ

⁻

] − 1 2 g

²

s

_w²

c

w

Z

⁰_µ

φ

⁰

(W

_µ⁺

φ

⁻

+

W

_µ⁻

φ

⁺

) − 1 2 ig

²

s

²_w

c

w

Z

_µ⁰

H(W

_µ⁺

φ

⁻

− W

_µ⁻

φ

⁺

) + 1

2 g

²

s

w

A

µ

φ

⁰

(W

_µ⁺

φ

⁻

+ W

_µ⁻

φ

⁺

) + 1

2 ig

²

s

w

A

µ

H(W

_µ⁺

φ

⁻

− W

_µ⁻

φ

⁺

) − g

²

s

w

c

w

(2c

_w²

− 1)Z

_µ⁰

A

µ

φ

⁺

φ

⁻

− g

¹

s

_w²

A

µ

A

µ

φ

⁺

φ

⁻

− ¯ e

^λ

(γ∂ + m

^λ_e

)e

^λ

−

¯

ν

^λ

γ∂ν

^λ

− ¯ u

^λ_j

(γ∂ + m

^λ_u

)u

_j^λ

− ¯ d

_j^λ

(γ∂ + m

^λ_d

)d

_j^λ

+ igs

w

A

µ

[−(¯ e

^λ

γ

^µ

e

^λ

) + 2

3 ( ¯ u

^λ_j

γ

^µ

u

^λ_j

) − 1

3 ( ¯ d

_j^λ

γ

^µ

d

_j^λ

)] + ig 4c

w

Z

_µ⁰

[( ¯ ν

^λ

γ

^µ

(1 + γ

⁵

)ν

^λ

) + (¯ e

^λ

γ

^µ

(4s

_w²

− 1 − γ

⁵

)e

^λ

) + ( ¯ u

^λ_j

γ

^µ

( 4 3 s

_w²

− 1 −

γ

⁵

)u

^λ_j

) + ( ¯ d

^λ_j

γ

^µ

(1 − 8

3 s

²_w

− γ

⁵

)d

_j^λ

)] + ig 2 √

2 W

_µ⁺

[( ¯ ν

^λ

γ

^µ

(1 + γ

⁵

)e

^λ

) + ( ¯ u

^λ_j

γ

^µ

(1 + γ

⁵

)C

λκ

d

_j^κ

)] + ig 2 √

2 W

_µ⁻

[(¯ e

^λ

γ

^µ

(1 + γ

⁵

)ν

^λ

) + ( ¯ d

_j^κ

C

_λκ^†

γ

^µ

(1 + γ

⁵

)u

^λ_j

)] + ig 2 √ 2

m

^λ_e

M [−φ

⁺

( ¯ ν

^λ

(1 −

γ

⁵

)e

^λ

) + φ

⁻

(¯ e

^λ

(1 + γ

⁵

)ν

^λ

)] − g 2

m

^λ_e

M [H(¯ e

^λ

e

^λ

) + i φ

⁰

(¯ e

^λ

γ

⁵

e

^λ

)] + ig 2M √

2 φ

⁺

[−m

^κ_d

( ¯ u

_j^λ

C

λκ

(1 − γ

⁵

)d

_j^κ

) + m

_u^λ

( ¯ u

_j^λ

C

λκ

(1 + γ

⁵

)d

_j^κ

] + ig 2M √

2 φ

⁻

[m

^λ_d

( ¯ d

_j^λ

C

_λκ^†

(1 + γ

⁵

)u

_j^κ

) − m

_u^κ

( ¯ d

_j^λ

C

_λκ^†

(1 −

γ

⁵

)u

^κ_j

] − g 2

m

^λ_u

M H( ¯ u

^λ_j

u

_j^λ

) − g

2 m

_d^λ

M H( ¯ d

_j^λ

d

_j^λ

) + ig 2

m

^λ_u

M φ

⁰

( ¯ u

_j^λ

γ

⁵

u

^λ_j

) − ig 2

m

^λ_d

M φ

⁰

( ¯ d

^λ_j

γ

⁵

d

_j^λ

) + ¯ X

⁺

(∂

²

− M

²

)X

⁺

+ ¯ X

⁻

(∂

²

− M

²

)X

⁻

+ ¯ X

⁰

(∂

²

− M

²

c

²_w

)X

⁰

+ ¯ Y ∂

²

Y + igc

w

W

_µ⁺

(∂

µ

X ¯

⁰

X

⁻

−

∂

µ

X ¯

⁺

X

⁰

) + igs

w

W

_µ⁺

(∂

µ

Y X ¯

⁻

− ∂

µ

X ¯

⁺

Y ) + igc

w

W

_µ⁻

(∂

µ

X ¯

⁻

X

⁰

− ∂

µ

X ¯

⁰

X

⁺

) + igs

w

W

_µ⁻

(∂

µ

X ¯

⁻

Y − ∂

µ

Y X ¯

⁺

) + igc

w

Z

_µ⁰

(∂

µ

X ¯

⁺

X

⁺

− ∂

µ

X ¯

⁻

X

⁻

) + igs

w

A

µ

(∂

µ

X ¯

⁺

X

⁺

− ∂

µ

X ¯

⁻

X

⁻

) − 1

2 gM[ ¯ X

⁺

X

⁺

H + ¯ X

⁻

X

⁻

H + 1 c

_w²

X ¯

⁰

X

⁰

H] + 1 − 2c

²_w

2c

w

igM[ ¯ X

⁺

X

⁰

φ

⁺

− ¯ X

⁻

X

⁰

φ

⁻

] + 1 2c

w

igM[ ¯ X

⁰

X

⁻

φ

⁺

− ¯ X

⁰

X

⁺

φ

⁻

] + igMs

w

[ ¯ X

⁰

X

⁻

φ

⁺

− ¯ X

⁰

X

⁺

φ

⁻

] + 1

2 igM[ ¯ X

⁺

X

⁺

φ

⁰

− ¯ X

⁻

X

⁻

φ

⁰

]

Just kidding

latex from T.Gutierrez, who also noted a sign error somewhere

Standard model lagrangian [1]

L = − 1

4 W µν · W ^µν − 1

4 B µν B ^µν

 W ^± , Z, γ kinetic energies and self-interactions

+¯ Lγ ^µ



i ∂ µ − g 1

2 τ · W ^µ − g ⁰ Y 2 B µ

 L + ¯ Rγ ^µ



i ∂ µ − g ⁰ Y 2 B µ

 R

 lepton and quark kinetic energies and interactions with W ^± , Z, γ

+    



i ∂ _µ − g 1

2 τ · W ^µ − g ⁰ Y 2 B _µ

 φ

   

2

− V (φ)

 W ^± , Z, γ, and Higgs masses and couplings

−G ⁱ (¯ LφR + ¯ Rφ ^∗† L).

 lepton and quark masses and coupling to Higgs

gauge fermions Higgs Yukawa

(flavour physics in L and R via CKM (q) and PMNS ν in fermions part)

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 9/56

SM free parameters

masses after spontaneous symmetry breaking:

Free parameters: g , g ⁰ , V (φ) = aφ ² + bφ ⁴ , G _i higgs boson

I ν = r −a

2b minimum of Higgs potential (vacuum expectation value)

I m H = 2 √ a vector bosons

I A µ = g ⁰ W _µ ³ + gB µ

p g ² + g ⁰² , m A = 0;

I W _µ ^± = W _µ ¹ ∓ W µ ²

√ 2 , m W = νg 2 ;

I Z µ = gW _µ ³ − g ⁰ B µ

p g ² + g ⁰² , m Z = ν p g ² + g ⁰²

2 ;

fermions (excluding ν ⁰ s)

I m fermions = G i ν

√ 2

Free parameters and boson masses

Excluding the fermion and Higgs masses

g , g ⁰ , ν OR

electron charge e = gg ⁰

p g ² + g ⁰² Millikan experiment Weinberg angle sin θ W = g ⁰

p g ² + g ⁰² pν, p ¯ ν scattering or σ(e _pol ⁻ d ) asymmetry Fermi constant G F = 1

ν ² √

2 µ lifetime

Notable SM relations M _W ² = e ²

4G F

√ 2 sin ² θ W

= πα

√ 2G F sin ² θ W

M Z = M W

cos θ W

ρ 0 = M _W ² M _Z ² cos ² θ W

= 1 Depends only on Higgs sector

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 11/56

W and Z discovery

Well before LEP

sin θ _W = 0.23 ± 10%, α = 1/137.035 . . ., G F = 1.16639(1) · 10 ⁻⁵ GeV ⁻² o Prediction: M _W = 82 ± 6 GeV and M Z = 92 ± 5 GeV

Need a new collider: build Sp ¯ pS and discover W and Z: UA1[2, 3]/UA2[4, 5]

Fermions-vector bosons couplings

γ

ff

f¯

−ieQ ^f γ _µ

^Z

f

f¯

−i g cos θ _W γ _µ 1

2



c _V ^f − c A ^f γ ⁵ 

W f

f¯′

−i g

√ 2 γ _µ 1

2 1 − γ ⁵
Where Q, c _V ^f =



T ⁽³⁾ − 2Q sin ² θ _W



, and c _A ^f = T ⁽³⁾ depends on fermion type:

fermion Q ^f T ⁽³⁾ c _A ^f c _V ^f

(ν e , ν µ , ν τ ) L 0 1/2 1/2 1/2 = 0.50 (e, µ, τ ) _L -1 -1/2 -1/2 −1/2 + 2 sin ² θ _W = 0.03 (e, µ, τ ) _R -1 0 0 +2 sin ² θ _W = 0.47 (u, c, t) L 2/3 1/2 1/2 1/2 + 4/3 sin ² θ W = 0.19 (u, c, t) _R 2/3 0 0 4/3 sin ² θ _W = 0.31 (d , s, b) _L -1/3 -1/2 -1/2 −1/2 + 2/3 sin ² θ _W = 0.34 (d , s, b) _R -1/3 0 0 2/3 sin ² θ _W = 0.16

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 13/56

Radiative corrections

Correction to propagator

Vertex corrections

Are absorbed using effective (complex) coupling g _{V /Af} and θ _W ^eff

sin ² θ _W ^eff = (1 + ∆κ f ) sin ² θ W

g Vf = p

(1 + ∆ρ f ) T ³ − 2Q sin ² θ _W ^eff
g Af = p

(1 + ∆ρ f ) T ³

∆ρ = 3G F M _W ² 8 √

2π ²

 M _t ²

M _W ² − tan ² θ _W

 ln M _H ²

M _W ² − 5 6



+ . . .

∆κ = 3G F M _W ² 8 √

2π ²



cotan ² θ W

M _t ² M _W ² − 10

9

 ln M _H ²

M _W ² − 5 6



+ . . . (extra M _f ²

M _W ² for f = b)

Strong dependence on M top , weak on M H , small dependence to flavour, with exception to b quarks

Radiative corrections (II)

Changes to SM relation due to radiative corrections (a different way to write the notable SM relations) cos ² θ _eff ^{(f )} sin ² θ ^{(f )} _eff = πα(0)

√ 2M _Z ² G F

1 1 − ∆r ^{(f )} where:

∆r ^{(f )} = ∆α + ∆r w ^{(f )} and ∆α(s) = ∆α _eµτ (s) + ∆α _top (s) + ∆α ⁽⁵⁾ _had (s) As before, absorb radiative correction using running α(s) = α(0)

1 − ∆α(s) α(q ² = 0) = 1/137.035 999 76(50) → α(M Z ² ) = 1/128.945

∆r w ^{(f )} is weak correction, flavour dependent ∆r w ^{(f )} = −∆ρ + . . . ρ = 1 + ∆ρ

And now the experimental part. . . mostly from [6]

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 15/56

Cross sections for Z and W boson production

CLEO@CESR [7]

I Cornell

DORIS@DESY [8](Υ) PETRA@DESY[9](gluon), BABAR@PEP-II [10], BELLE@KEKB [11], TOPAZ@TRISTAN [12]

I discovery of α em ( √ s)

I KEK

SLD@SLC

I Stanford

LEP and LEP II

Tristan today at KEK

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 17/56

cos θ is the angle between e ⁻ and µ ⁻ On resonance √

s = M _Z : γ/Z vanish ( ∼ 0.2% at √

s = M Z ± 3GeV ), γ ∼ 1%, Z dominates

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 18/56

cos θ is the angle between e ⁻ and µ ⁻ (1 + cos ² θ) terms contribute to σ _tot

(cos θ) terms introduce asymmetries forward-backward

if e ⁺ e ⁻ → q ¯ q: cos θ difficult to know (q vs ¯ q harder than ` vs ¯ `) Additional color term ×N c

and QCD final state radiative correction ×(1 + δ QCD ), see later

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 18/56

Cross section for e ⁺ e ⁻ → e ⁺ e ⁻

At tree level, two diagrams:

e

⁻

e

⁻

e

⁻

e

⁻

e

⁺

e

⁺

e

⁺

e

⁺

γ/Z γ/Z

t − channel s− channel

s-channel

I same as e ⁺ e ⁻ → f ¯ f ;

I dominates at large angle;

t-channel

I Bhabha scattering ^a

I largely dominates at small scattering angle

F σ ≈ 1/θ ³ : close to colliding e ⁻ beam

I very well known QED process;

I Used to measure LEP luminosity with large angle luminometer

a Bhabha Homi Jehangir, indian theoretical phys. (Bombay 1909 - m. Bianco 1966)

ISR/FSR

ISR

Emission of γ from initial state. Important effect (radiative return to Z peak).

σ(s) = Z 1

0

dz · H QED ^tot (z, s) · σ ew (zs) FSR

both QED and QCD (only for quarks) change partial and total width

Γ _h = Σ _f Γ ^f ₀ (1 + δ ^f _QED )(1 + δ ^f _QCD ) δ ^f _QED ≈ 3αQ _f ²

4π ∼ 0.17%, δ ^f _QCD ≈ α _s (M _Z ² )

π ∼ 3.8%

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 20/56

ISR impact on Z line-shape

Note the huge importance of ISR radiative (QED) corrections!

Decrease σ by 30% and shift peak position by ∼ 100 MeV

σ ^tot _had is measured

value reported and used for electroweak fit, is σ _had ⁰ , where QED correction are evaluated

pseudo-observable

Same also for R _f ⁰ , Γ ⁰ _Z , A ⁰ _FB , . . .

Measurement at the Z line-shape

Considering only hadronic final states:

σ(s) = 12π Γ e Γ had

M _Z ²

s

(s − M z ² ) ² + M _Z ² Γ ² _Z (neglecting the –small– γ contribution) At peak: σ 0 = 12π

M _Z ² Γ e Γ had

Γ Z

,

where: Γ had = Σ q6=t Γ q ¯ q and Γ Z = Γ ee + Γ µµ + Γ τ τ + Γ had + Γ inv

We can measure 6+1 parameters:

Z mass M Z from peak position;

Z total width Γ _Z from peak width;

hadronic pole cross-section σ ₀ from peak height;

Width ratios R ⁰ _` = R ⁰ _e,µ,τ = Γ _had /Γ _{ee,µµ,τ τ} from exclusive peak height;

Width ratios R ⁰ _b = Γ _bb /Γ _had as above;

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 22/56

Example of Z → ee event: OPAL

Very clean environment

Electron ID via tracks and ECAL clusters: E /p = 1 (B = 0.5T )

Example of Z → qqg ALEPH

Good example of FSR (QCD): slightly more complex events, larger hadron multiplicity, jet reco (E/HCAL) very good tracker B = 1.5T ,

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 24/56

Example of Z → µµ for L3

Even clearer environment: outer tracking detector for µ ID.

L3 had all detectors inside solenoid (0.5T ), excellent ECAL (BGO)

Z → ττ example for DELPHI

τ → 3hν ^τ three prong, and τ → hν ^τ one prong decays DELPHI had RICH (PID)

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 26/56

Event selection and classification

Event selection is quite easy thanks to the very clean environment:

E _ch (sum of tracks momenta) vs charged multiplicity.

L3 hadron selection

OPAL lepton selection

channel had ee µµ τ τ

efficiency % 99 − 95 98 − 97 98 − 95 70 − 90

background % 0.5 1 1 1 − 3

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 28/56

γγ cross section at LEP

LEP not so clean as one might imagine.

Gamma-Gamma interaction produce a lot of interaction in addition to Z production.

The scattered electrons escape in the beam pipe, undetected.

At Z peak, x-section is ~150nb (vs ~30nb for ee->Z), but it is reduced to ~6nb via pt and 

cuts

Statistics collected at LEP

In 1990, 91, 93, and 95 a total of 7 + 20 pb ⁻¹ lumi collected off-peak Actual L collected by each

experiment ∼ 10 − 15% less

Number of events ×1 · 10 ³

Total per experiment:

4M Z → q ¯ q 0.5M Z → ` <sup>+</sup> ` ⁻

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 30/56

Cross section measurement

σ tot = (N sel − N bg )

 _sel L Background and efficiency from MC.

Key issue is luminosity L measurement

e ⁺ e ⁻ → e ⁺ e ⁻ via t-channel dominates at low θ.

Collect Bhabha events with very forward calorimenters 25 to 60 mrad from beam.

x-section goes as 1/θ ³ : difficult to define the geometrical acceptance of forward calorimeters.

I common systematic uncert: . 0.05%,

I from theory ∼ 0.05%.

at LHC 2.6%, at BelleII 0.7%

Hadronic cross section vs √ s

Off-peak measurements M _Z ± 2 GeV are crucial for Γ Z

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 32/56

Hadronic and leptonic cross-section vs √ s

M Z from peak position

I ee → ee(γ) also t-channel and inteference

Γ _Z from peak width in hadronic final state (larger stats)

Width ratios R from exclusive cross-sections.

I σ _{had ,e,µ,τ} ⁰ ∝ Γ ^e Γ had ,e,µ,τ

For M _Z critical is the determination of √

s for LEP.

LEP √

s: resonant depolarization [13]

Electron with momentum p in uniform vertical magnetic field B

E ∼ p = eBR = e 2π BL B is not uniform, LEP ring not a circle

E _beam = e 2π

I

B · d`

Dipole B field is vertical.

Electron spin aligns with B

Sokolov-Ternov theo., patent in ’73!.

Due to spin-B interaction: E _ > E _↑↓ .

spin flip due to synchrotron radiation, but flip rate is not symmetric.

Pol trans ∝ 

1 − e ^−t/τ 

, with τ 10h

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 34/56

LEP √

s: resonant depolarization

spin precess in B field, with a ν proportinal to B (Larmor precession)

I number of precessions per turn:

ν s = g e − 2 2

e 2πm e

I

B · d` = g e − 2 2

E beam

m e I ν s is proportional to E Beam

apply an additional, radial B field, oscillating with freq ν

I if ν = ν s , the spin is rotated until it becomes horizontal

I about 10 ⁴ turns (1s) to rotate by 90 deg

I stochastic sync. rad.: horizonal pol is unstable → destroyed.

LEP √

s: resonant depolarization

External freq is: f dep = (k ± [ν]) · f rev

where f _rev = 11.25 kHz is that of LEP, k is an integer;

[ν] = ν scan is the non-integer part of the ν of the bending field;

a freq scan is performed, ν scan is moved slowly

then the polarization is measured (Compton scattering), then repeat for different bunches

Process is slow, and can be done only at the end of a fill

precision (limited to ν _scan step) is

≈ 100 keV Ultimate LEP √

s resolution ≈ 2.2 MeV.

Why?

At LEP start, exp. σ( √

s) ∼ 10 MeV

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 36/56

Tidal movement of earth at LEP [14]

Tidal movement of earth at LEP [14]

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 37/56

Tidal movement of earth at LEP [14]

Tidal movement of earth at LEP [14]

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 37/56

Tidal movement of earth at LEP [14]

Tidal movement of earth at LEP [14]

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 37/56

Tidal movement of earth at LEP [14]

Tidal movement of earth at LEP [14]

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 37/56

Tidal movement of earth move the dipole magnets.

Typical displacement 1mm (in 27km), giving a 10 MeV peak-to-peak change.

Other ground distortion from Geneva lake level, heavy rain . . .

Vagabond electric currents from trains.

Final M _Z syst from √

s about 1.7 MeV

Results

M Z = 91.1875 ± 0.0021 GeV (23ppm)

±1.7 MeV LEP √ s scale

±0.3 MeV QED corr (ISR)

±0.1 MeV fit parametrization

±0.05 MeV L

±0.05 MeV α had

Contribution γ − Z interference

Γ _Z = 2.4952 ± 0.0023 GeV

±1.2 MeV from QED corr (ISR)

±0.2 MeV from QED corr (FSR)

±0.1 MeV from fit parametrization

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 39/56

Lepton universality

Partial width: R ⁰ _{`</sub> = Γ <sub>had</sub> /Γ <sub>`}

R _e ⁰ =20.804 ± 0.050 R _µ ⁰ =20.785 ± 0.033 R _τ ⁰ =20.764 ± 0.045

R τ ⁰ expected to be smaller due to m τ > m µ  m e

Assuming lepton universality:

R ` ⁰ =20.767 ± 0.25

σ ⁰ had =41.541 ± 0.037 nb

Number of neutrino families

With lepton universality:

Γ Z =2495.2 ± 2.3 MeV Γ _had =1744.4.8 ± 2.0 MeV

Γ ` =83.895 ± 0.086 MeV Γ _inv =499.0 ± 1.5 MeV

Γ ^SM _inv = 501.7 ± 0.2 ^+0.1 −0.9 (m _H ) MeV

Γ ^x _inv = −2.7 ^+1.8 −1.5 MeV N ν = 2.9840 ± 0.0082 δN _ν ≈ 10.5 δn _had

n had ⊕ 3.0 δn _lep

n lep ⊕ 7.5 δ L L

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 41/56

R _b,c

It is not possible, in general, to distinguish quark flavour, with the exception of b and c-quarks, using different techniques:

Useing two features: long b (and c) lifetime and exclusive b and c decays.

lifetime tagging;

I cτ for b is ∼ 450µm (in lab ×γ)

I cτ for c is ∼ 150µm (in lab ×γ)

I detect displaced secondary vertex via impact parameter or decay length measurements exclusive decays:

I leptonic decay;

I decay with D mesons;

Correction to R _b,c from QCD (gluon radiation from final state quarks), in addition to QED correction

and LEP energy scale.

lifetime tagging

Heavy hadrons have long lifetime and large boost at LEP

Impact Parameter (d ₀ ):

I d ₀ is the distance of closest approach from the primary vertex of the extrapolated track;

I the resolution depends on the track reconstruction and primay vertex knowledge;

I silicon microvertex close to beam pipe for resolution, PV depends on accelerator (SLC better than LEP);

I a signed quantity wrt the jet dir.

F badly measured track can intercept the “wrong-side” of the beam-spot;

I d ₀ ^sign = d 0 /σ(d 0 );

Decay length (L)

I Signed as well

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 43/56

lifetime tagging

d ₀ significance L significance and NN

b ↔ c separation via M vtx

Resolution

δ _IP ∼ 16 − 100µm (Rφ/Z ) , δ b ∼ 300µm

b-tagging performance

Lepton tagging

A lepton inside a jet is a stong indication of a b or c flavour.

To distinguish from b to ¯ b use semileptonic decay of b quarks.

b → ` ⁻ ; ≈ 10%

c → ` ⁺ ; ≈ 13%

b → c → ` ⁺ cascade decay ;

Distinguish between direct and cascade decay using lepton p _T and p lower purity and efficiency wrt lifetime tagger

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 45/56

D-Meson Tags

Tagging via reconstruction of charmed meson and barions in jet:

direct evidence of a jet originated by an heavy quark.

low B ∼ O(%)

b → c fragmentation is small

distinguish c from b decay by charmed mesons momentum;

I D 0 → K ⁻ π ⁺

I D ⁺ → K ⁻ π ⁺ π ⁺

I D _s → K ⁺ K ⁻ π ⁺

I Λ ⁺ _c → pK ⁻ π ⁺

I D ^∗+ → π ⁺ D ⁰

F slow π ⁺ , no need for PID

R _q for b and c

Single-tag (one b/c) or double-tag methods (both sides: allows to extract tag ε from data)

charm R c beauty R _b

Dotted line is systematic uncertainties

Contribution from SLD (next lesson): smaller interaction region, better b-tagging, smaller uncertainties

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 47/56

Input to global EWK fit

(in parenthesis the order followed in these lessons)

3

− − 2 − 1 0 1 2 3

tot

O) / σ

−

indirect

(O

2) (MZ

α

s

2) (MZ (5)

α

had

∆

mt

b R0 c R0 0,b AFB

0,c AFB

Ab Ac (Tevt.) lept

Θ

eff sin2

) FB lept(Q

Θ

eff sin2

(SLD) Al

(LEP) Al

0,l AFB

lep R0

0

σ

had

Γ

Z MZ

Γ

W MW MH

Global EW fit Indirect determination Measurement

G fitter

SM

Mar ’18

Higgs mass (5)

I LHC

W mass and width (3)

I LEP2, Tevatron, LHC Z-pole observables (1,2)

I LEP1, SLD

I M Z , Γ Z I σ ^had ₀

I sin ² θ ^lept _eff

I Asymmetries (2)

I BR R _lep,b,c ⁰ = Γ _had /Γ _{``,b ¯ b,c ¯ c} top mass (4)

I Tevatron, LHC other:

I α s (M _Z ² ), ∆α had (M _Z ² )

Input to global EWK fit

(in parenthesis the order followed in these lessons)

Higgs mass (5)

I LHC

W mass and width (3)

I LEP2, Tevatron, LHC Z-pole observables (1,2)

I LEP1, SLD

I M Z , Γ Z I σ ^had ₀

I sin ² θ ^lept _eff

I Asymmetries (2)

I BR R _lep,b,c ⁰ = Γ _had /Γ _{``,b ¯ b,c ¯ c} top mass (4)

I Tevatron, LHC

other:

I α s (M _Z ² ), ∆α had (M _Z ² )

Stefano Lacaprara (INFN Padova) Fit SM Padova 5/03/2019 48/56

Further Reading I

I F. Halzen and A. D. Martin, Quarks and Leptons: an introductory course in modern particle physics.

Wiley, New York, USA, 1984.

I G. Arnison, A. Astbury, B. Aubert, C. Bacci, G. Bauer, A. B´ ezaguet, R. B¨ ock, T. Bowcock, M. Calvetti, T. Carroll, P. Catz, P. Cennini, S. Centro, F. Ceradini, S. Cittolin, D. Cline, C. Cochet, J. Colas, M. Corden, D. Dallman, M. DeBeer, M. D. Negra, M. Demoulin, D. Denegri, A. D. Ciaccio, D. DiBitonto, L. Dobrzynski, J. Dowell, M. Edwards, K. Eggert, E. Eisenhandler, N. Ellis, P. Erhard, H. Faissner, G. Fontaine, R. Frey, R. Fr¨ uhwirth, J. Garvey, S. Geer, C. Ghesqui‘ere, P. Ghez, K. Giboni, W. Gibson, Y. Giraud-H’eraud, A. Givernaud, A. Gonidec, G. Grayer, P. Gutierrez, T. Hansl-Kozanecka, W. Haynes, L. Hertzberger, C. Hodges, D. Hoffmann, H. Hoffmann, D. Holthuizen, R. Homer, A. Honma, W. Jank, G. Jorat, P. Kalmus, V. Karimaki, R. Keeler, I. Kenyon, A. Kernan, R. Kinnunen, H. Kowalski, W. Kozanecki, D. Kryn, F. Lacava, J.-P. Laugier, J.-P. Lees, H. Lehmann, K. Leuchs, A. L´ evˆ eque, E. Linglin, E. Locci, M. Loret, J.-J. Malosse, T. Markiewicz, G. Maurin, T. McMahon, J.-P. Mendiburu, M.-N. Minard, M. Moricca, H. Muirhead, F. Muller, A. Nandi, L. Naumann, A. Norton, A. Orkin-Lecourtois, L. Paoluzi, G. Petrucci, G. Mortari, M. Pimia, A. Placci, E. Radermacher, J. Ransdell, H. Reithler, J.-P. Revol, J. Rich, M. Rijssenbeek, C. Roberts, J. Rohlf, P. Rossi, C. Rubbia, B. Sadoulet, G. Sajot, G. Salvi, J. Salvini, J. Sass, A. Saudraix, A. Savoy-Navarro, D. Schinzel, W. Scott, T. Shah, M. Spiro, J. Strauss, K. Sumorok, F. Szoncso, D. Smith, C. Tao, G. Thompson, J. Timmer, E. Tscheslog, J. Tuominiemi, S. V. der Meer, J.-P. Vialle, J. Vrana, V. Vuillemin, H. Wahl, P. Watkins, J. Wilson, Y. Xie, M. Yvert, and E. Zurfluh, “Experimental observation of isolated large transverse energy electrons with associated missing energy at s=540 gev,” Physics Letters B 122 no. 1, (1983) 103 – 116. http://www.sciencedirect.com/science/article/pii/0370269383911772.

I UA1 Collaboration, G. Arnison et al., “Experimental Observation of Lepton Pairs of Invariant Mass Around 95-GeV/c**2 at the CERN SPS Collider,” Phys.

Lett. B126 (1983) 398–410. [,7.55(1983)].

I M. Banner, R. Battiston, P. Bloch, F. Bonaudi, K. Borer, M. Borghini, J.-C. Chollet, A. Clark, C. Conta, P. Darriulat, L. D. Lella, J. Dines-Hansen, P.-A.

Dorsaz, L. Fayard, M. Fraternali, D. Froidevaux, J.-M. Gaillard, O. Gildemeister, V. Goggi, H. Grote, B. Hahn, H. Hanni, J. Hansen, P. Hansen, T. Himel, V. Hungerb˜ A 1

4 hler, P. Jenni, O. Kofoed-Hansen, E. Lan¸ con, M. Livan, S. Loucatos, B. Madsen, P. Mani, B. Mansoulie, G. Mantovani, L. Mapelli, B. Merkel,

M. Mermikides, R. M˜ A¸llerud, B. Nilsson, C. Onions, G. Parrour, F. Pastore, H. Plothow-Besch, M. Polverel, J.-P. Repellin, A. Rothenberg, A. Roussarie,

G. Sauvage, J. Schacher, J. Siegrist, H. Steiner, G. Stimpfl, F. Stocker, J. Teiger, V. Vercesi, A. Weidberg, H. Zaccone, and W. Zeller, “Observation of single

isolated electrons of high transverse momentum in events with missing transverse energy at the cern pp collider,” Physics Letters B 122 no. 5, (1983) 476 –

485. http://www.sciencedirect.com/science/article/pii/0370269383916052.