Experimental tests of the Standard Model

0. Standard Model in a Nutshell

1. Discovery of W and Z boson

2. Precision tests of the Z sector

3. Precision test of the W sector

4. Radiative corrections and prediction of the

Higgs mass

5. Higgs searches

Literature for (2):

Precision electroweak measurement on the Z resonance,

Phys. Rept. 427 (2006), hep-ex/0509008.

http://lepewwg.web.cern.ch/LEPEWWG/1/physrep.pdf

1

0. Standard Model in a Nutshell

2

RRR

LLL

e

e

e

LH weak iso-

spin doublets

RH singlets

W )( 21

2

1i

Symmetry:

Additional fieId W3 which corresponds to the 3rd isospin operator 3.

W3 only couples to the particles of the weak isospin doublet!

In addition we have two more fields:

• Photon which couples to the LH and RH fermions with same strength.

• Z boson which couples to LH and RH fermions with different couplings gL

and gR

How can we associate the observed fields to W3?

weak isospin: T, T3

3

3,2,1iW i

,~ ii WigJiJ

Corresponding to J and J3 there are fields

321 and )(2

1WiWWW

g

BYJ

2

g

BJg

i Y

2~

convention

g, g are coupling

constants.

Additional gauge field B

Gauge field B couples to hyper-charge: Y = 2 [Q-T3]

couples to LH and RH fermions

T.Plehn

4

While the charged boson fields W correspond to the observed

W bosons, the neutral fields B and W3 only correspond to

linear combinations of the observed photon and Z boson:

WW

WW

WBZ

WBA

cossin

sincos

3

3

WW

WW

ZAW

ZAB

cossin

sincos

3

massless photon

massive Z boson

The weak mixing angle w (Weinberg angle) follows from coupling constants:

WW

eg

eg

cossin

W

W

W

Z ggg

gcos

sin

cos

Coupling to the

photon field ~e

e

e

W

Vertex factors

)1(2

1

2

5gi

e

e

Z

)(2

1

cos

5

AV

W

ggg

i

e

e

ie

Propagator

(unitary gauge)

22

2

Z

Z

Mq

Mqqg

22

2

W

W

Mq

Mqqg

2

1

q

Feynman rules

:02qW28 2

2

F

W

G

M

g

:02qZ2cos8 22

2

NC

ZW

G

M

g

22

NCF GGAssuming

universality follows 2

22cos

Z

WW

M

M

=0

= 1- =1

2

22cos

Z

WW

M

M

1. Discovery of the W and Z boson1983 at CERN SppS accelerator,

s 540 GeV, UA-1/2 experiments

1.1 Boson production in pp interactions

p

pu

d

Ws

q,

q, p

pu

u

Zs

q,

q,

XWpp XffZpp

Similar to Drell-Yan: (photon instead of W)

10 1001 ZWMs ,ˆ

)( ZW

nb1.0

nb1

nb10

12.0x mitˆqsxxs qq

22

q )GeV65(014.0xˆ sss

Cross section is small !7

1.2 Event signature:

p p

High-energy lepton pair:

222 )( ZMppm

XffZpp

GeV91ZM

8

1.3 Event signature: XWpp

p p

High-energy lepton:

Large transverse

momentum pt

Undetected :

Missing momentum

Missing pT vector

How can the W mass be reconstructed ?

9

W mass measurement

In the W rest frame:

•

•

2WM

pp

2WT M

p

Tp

Tdp

dN

2WM

In the lab system:

• W system boosted only

along z axis

• pT distribution is conserved:

maximum pT= MW / 2

Jacobian Peak:

• Trans. Movement of the W

• Finite W decay width

• W decay not isotropic

GeV80WM

21

22

4

2~ T

W

W

T

T

pM

M

p

p

dN

10

Jacobian Peak

21

22

4

2cos

cosT

W

W

T

TT

pM

M

p

dp

d

d

dN

dp

dN~

Assume isotropic decay of the W boson in its CM system:

.cos

constd

dN

(Not really correct: W boson has spin=1 decay is not isotropic!)

2sin

w

TT

M

p

p

p

2

2

2cos1

w

T

M

p

cos2~cos

2T

w

T dp

M

pd

11Jacobian

W candidate from the LHC – they still exist!

eeWdu Anti-quarks from the sea! 12

Z bosons are alos produced at the LHC

13

14

Z and W production at LHC

P.Harris,

Moriond 2011

Instead of EeT

use ET (i.e. E T)

W-boson production at LHC

15

Valence quark +

sea quark

valence quark ratio u/d = 2 more W+ than W-

ATLAS 2010:

1.4 Production of Z and W bosons in e+e- annihilation

Precision tests

of the Z sector Tests of the W sector

qqW

16

2. Precision tests of the Z sector (LEP and SLC)

21sin

32

21

21sin

34

21

21sin2

21

21

21

2

2

2

W

W

W

AV

quarkd

quarku

gg

Z

f

f

5

2

1

cos

fA

fV

w

ggig

22

2

Mq

Mqqgi

)(2

1)(

2

1AVRAVL gggggg

32

3 and sin2 TgQTg AWV

w

eg

sin

Standard Model

2

22 1

Z

ww

M

Msin

17

WW

A

V QT

Q

g

g 22

3

sin41sin21

Cross section for ffZee /

2M

2

Z

eeA

eVe

ZZZ

Z

AV

W

Z

ee

uggviMMq

Mqqgvggu

giM

uvq

gvuieM

)(2

1

)()(

2

1

cos

)()(

5

22

25

2

2

2

2

ee for

Z propagator considering a

finite Z width (real particle)

With a “little bit” of algebra similar as for M ….18

One finds for the differential cross section:

2222

2

2222

22

)()(cos

)(

)()(cos)(cos

2cos ZZZ

Z

ZZZ

ZZ

MMs

sF

MMs

MssFF

sd

d

/Z interference Z

)cos1()cos1()(cos 2222QQF e

cos4)cos1(2cossin4

)(cos 2

22 A

e

AV

e

V

WW

e

Z ggggQQ

F

cos8)cos1)()((cossin16

1)(cos 22222

44 AV

e

A

e

VAV

e

A

e

V

WW

Z ggggggggF

Vanishes at s MZ

known

e e

19

At the Z-pole s MZ Z contribution is dominant

interference vanishes

222

22222

44

2

)()()()()()(

cossin163

4

ZZZ

AVeA

eV

ww

ZtotMMs

sgggg

s

2222 )()()()(3

AV

AVeA

eV

eA

eV

FBgg

gg

gg

ggA

cos3

8)cos1(~

cos

2

FBAd

d BF

BFFBA

Forward-backward asymmetry

with

coscos

)0(1

)1(0

)( dd

dBF

20

22

12

Z

e

Z

ZZM

Ms

22

22)()(

cossin12

fA

fV

ww

Zf gg

M

i

iZ

With partial and total widths:Cross sections and widths

can be calculated within the

Standard Model if all

parameters are known

222

22222

44

2

163

4

)()()()()()(

cossin ZZZ

AV

e

A

e

V

ww

ZMMs

sgggg

s

22222 )(12)(

ZZZZ

e

MMs

s

Ms

Breit-Wigner Resonance:

BW description is very general

Z

iiiZBR )(

21

Z Resonance curve:

220

12

Z

e

ZM

Initial state Bremsstrahlung corrections

22222 )(12)(

ZZZZ

e

MMs

s

Ms

s

EzdzzszG

sm

ffff

f

21)()(

1

/4

0

)(2

Peak:

2.2 Measurement of the Z lineshape

• Resonance position MZ

• Height e

• Width Z

E

Leads to a deformation of the resonance: large (30%) effect ! 22

Resonance shape is the same, independent of final state: Propagator the same!

hadronsee ee

23

e e

e e

k k

p p

e

e e

e

k

p p

k

channel schannel t

eeee t channel contribution forward peak

Effect of t

channel

s-channel contribution ~ ( e)2

24

MZ = 91.1876 0.0021 GeV

Z = 2.4952 0.0023 GeV

had = 1.7458 0.0027 GeV

e = 0.08392 0.00012 GeV

= 0.08399 0.00018 GeV

= 0.08408 0.00022 GeV

Z = 2.4952 0.0023 GeV

had = 1.7444 0.0022 GeV

e = 0.083985 0.000086 GeV

Z line shape parameters (LEP average)

Assuming lepton

universality: e = =

3 leptons are treated

independently

23 ppm (*)

0.09 %

*) error of the LEP energy determination: 1.7 MeV (19 ppm)

http://lepewwg.web.cern.ch/ (Summer 2005)

test of lepton

universality

(predicted by SM: gA and gV

are the same)

25

LEP energy calibration: Hunting for ppm effects

Changes of the circumference of the LEP

ring changes the energy of the electrons

and thus the CM energy (shifts MZ) :

• tide effects

• water level in lake Geneva

1992 1993

Changes of LEP circumference

C=1…2 mm/27km (4…8x10-8)

ppm100

Effect of moon Effect of lake

26

Effect of the French “Train a Grande Vitesse” (TGV)

In conclusion: Measurements at the ppm level are difficult to

perform. Many effects must be considered!

Vagabonding currents from trains

27