E lectro- W eak measurements

Frank Linde, september 2005, BND summerschool, TexelFrank Linde, september 2005, BND summerschool, Texel

Electro-

Weakmeasurement

sBelgiëNederland BND summer school 2005DeutschlandThe good news: an excellent LEP I paper

“Precision Electroweak Measurements on the Z Resonance”

The bad news: I did not study it (and yesterday did not help)

22

The night after

25 ! free parameters

Standard Model

Strong interaction:s(mZ) 0.117

u’d’s’

=uds

V

ij

q

quark menging (4)

e

=1

2

3

V

ij

l

neutrino menging (4)

Electro-weak interaction:e(0) 1/137.036mW 80.42 GeVmZ 91.188 GeVmH > 114.3 GeV

me 0.51099890m 105.658357m 1777.0

mu 3mc 1200mt 178000

md 7ms 120mb 4300

Elementary particle masses (MeV):m < 0.000003m < 0.19m < 18.2

e

(“all” except gravity?)

44

Quantity Value Standard Model Pull

55

66

A. LEP e+e collider

B. Higgs

1. cross-section2. asymmetry3. Z-boson & W-boson decay widths & masses4. lepton universality5. infering t-quark & H-boson information

1. branching ratio’s 2. LEP’s screw-up? 3. discovery at LHC?4. self coupling at ILC?

My selection

77

LEP collider: EW goldmine

LEP: Nobel research

Higgs massa (GeV/c2)

s(Q

)

Q (GeV/c)

2

To elucidate the theory of the electro-weak interaction

For a colorful theory

99

LEP experimental programLEP I: Z-boson

1989 - 1995smZ91 GeVLpeak21031 cm2s1

Lintegrated200 pb1

LEP II: W- & H-bosons

1996 - 2000s2mW; smax=209

GeVLpeak1032 cm2s1

Lintegrated800 pb11 pb1 = 1036 cm2

Feynman diagrams

?

1010

1. crosssection

30 years of work!

1111

The beam energy: specialist job

E=0.2 MeV

1212

The moon (tidal) effect

1 MeV

1313

The beam energy: many effectsReference:

resonant depolarization

Complications:

flux loop measurement moon effect lake effect TGV effect beam energy spread synchrotron losses

Result (LEP I):

Ebeam 1.7 MeV

1414

The beam intensity: luminosityBhabha scattering

e+e e+e

alternatives:e+e

e+e e+ee+e

requirements: high statistics known theory small systematics

what are the requirements for a normalization process?

1515

The beam intensity: luminosity

1.trigger efficiency (99.xx 0.xx %)2.systematic uncertainties in the event selection (0.xx%)3.absolute acceptance i.e. xx.xx 0.xx nb

E, , error 0.1%

1616

Reducing the systematicsMeasured energy

distribution

Minimize:

N

ichannelsii

i

i

YXiYXi

E

E1 00

00

2

2

,;

,;

This gives you:• shower center coordinates (X0,Y0)

• observed energy fraction tot (i;X0,Y0) 1

Efit Ei /tot Eseen /tot

• quality of fit (figure of merit)• possibility to correct for dead channels

Fitted energy

distributions

N=11Eseen = 38 GeV(X0,Y0)=(0.4,0.2)tot = 0.852/DF=0.92Efit = Eseen/tot=45 GeV

Find the expected energy density

distribution (X,Y; X0,Y0)

(X0,Y0) is shower center

X0 X0

N=10Eseen = 31 GeV(X0,Y0)=(0.4,0.2)tot = 0.682/DF=0.94Efit = Eseen/tot=46 GeV

1717

Event selection: e+e, +, +, qq

multiplicitycharged trackstopology jets planarity acoplanarityenergy total energy missing energy energy balance minimal energykinematic fitsverticingneural networks

identify the

peaks

1818

The ‘real’ stuff: cuts, counting, …

e+ee+e

triggeracceptanceevent selectionbackgroundstatistics

important uncertaintie

s?


1919


e+e+



s?


2020


e+e+



s?


2121


e+eqqg



s?


Feynman rules with , W- & Z-bosons

W

l l

5

cossin2

4cc

eiAV

ww

Vertices

Z

51

sin22

4

w

ei

l l f f

mq

mqqgi22

2/

Propagators mq

mqi22

W, Z

External lines u u

v v

*

, W, ZcA=½cV=2qsin2 ½

e+e Z0, ff cross section (fe)

e

e+

f

fZ0

e

e+

f

f

use:

e+e Z0, ff cross section (fe)

And hence for total amplitude:

With:

And furthermore with:

You find for the differential cross section:

Cross section near sMZ

With the following notation and approximations:

and

You find for the differential cross section:

And hence for the total (peak) cross section:

And hence for sMZ:

2626

Results: cross section

2727

Results: Z-boson parameters

2828

Results: # of light neutrino’s

N=2.9840 ± 0.0082

more neutrino families:

• Z-boson width larger

• hadronic branching fraction smaller & therefore lower peak cross section

2929

Direct counting of # light neutrino’s

e

e+

e

e

W

e,,

e,,

eZ

e+

The issue: trigger!

LEP I: tricky LEP II: “easy”

3030

2. asymmetry

3131

Asymmetry formula

AfFB = ¾ AeAf

Af = 2cf

VcfA

(cfV)2+(cf

A)2

3232

AFB can be extracted using Born level prediction for the distribution:

cos-1 0 +1

d/d

cos combined

acceptanc& efficiency

fitted d/dcos

“data”

How to extract the asymmetry?

which real

world effects?

3333

counting or 2-fit or likelihood-fit

counting:

2-fit (correct for ):

Likelihood-fit:

3434

Results: cV & cA measurements

cA

cV

3636

3. Z-boson & W-bosondecay widths & masses

37

W-boson & Z-boson decay widths

px

p1

p2

e

e+

Z0

e

e+

W+

px

p1

p2

To be efficient, I perform calculation for X-boson with vertex factor: (gX/2)(cV-cA5)(in addition I work in X-boson rest frame and I mess around with u- and v-spinor states)

4-vectors:

Generic expression decay width:

X-boson polarization sum spin states:

Traces of -matrices:

38

The amplitude 5

2

1ccg AVX

px

p1p2

ee-

X

22

2

2

2

1

22 2+2

p·p1= p·p2=M2/2

p1·p2=M2/2

p·p=M2

39

px

p1

p2

e

e+

Z0

For the Z-boson:

The decay width

Plug into the decay width expression:

e

e+

W+

px

p1

p2

For the W-boson:

Use the 4-vectors: 2

2

40

W-boson

Z-boson

Z- & W-boson partial decay widths

41

Z- & W-boson partial decay widths

ee

eell

bbssdd

ttccuuqqZ-boson

tbcsudqq '

ee

W-boson

4242

Z-boson leptonic cross sections

“simple” (but correct!) counting and you get branching fractions

4343

W-boson cross section (LEP II)

e

e+

W

W+

e

e+

W

W+

Z0

e

e+

W

W+

e

4444

W+W event topologies

“simple” (but correct!) counting and you get branching fractions

“all hadronic”(4 jets)

“all leptonic”(no jets)

(2 jets)

4545

W-mass

bestaccuracy

:2 jets

no interplay between differentW-boson

decay products

4646

mW: screams for kinematic fit!

4-momentum conservation: (2Ebeam,0,0,0)(4)

2 W-bosons: equal mass? One condition.(1)

All hadronic: constraint improves E for jets2-jets: three constraints for neutrino

one constraint leftall leptonic: hopeless

(can also use the equal mass, but masses (width!) are not that equal

Constraints:

4747

4. leptonuniversality

48The decay of the muon

()

p

k

p’

k’

e

e

W

ee

Calculation: tedious

Rewards: precisionGF determinationnice experiment!

49

Remainder: “standard (but tedious) tricks”:

summing and averaging over the spin states look for the appropriate trace theorem integrate over the e(p’) + e(k’) + (k) phase space

-decay calculation

e

e

Wp

k

p’

k’

Kinematics:

With the standard Feynman rules you get for the amplitude:

Plugging this in the decay width “master” formula:

50

Spin:

Note: happily include in the summation non-existent -spin states

(0 contribution)

-decay: trace reduction

Kinematics & me20:

And finally the amplitude:

0: odd #

0: PL PR

51

Left with:

-decay: phase space integral

3-particle phase space yields 9-dimensional integral:

Using the -function yields a 6-dimensional

integral

Relevant variables: EeE’, E’ and angle between the electron and the anti-electron neutrino.

3-dimensional integral. The cos integration can be performed using:

52

-decay: what to measure?

’

E’

M/2

M/2

integration

region

M/2

M/2-E’

Experimentally only the electron can be observed. Hence integrate over ’ (and E’):

Maximum energy e , e en : M/2Minimal energy any particle pair: M/2

d/dE’

53-decay: measurements!

M/253 MeV

ee

54

-decay: for high schools

55-decay: equipment

56-decay: result

et/

constant background

dagelijks paar 100 -vervallen

57

The decay of the tau () ee

Calculation: just copy!

Rewards: lepton universalitynice experiment!

p

k

p’

k’

e

e

W

58

The tau lifetime

59

Lepton universality test-lifetime

+leptonic

branching ratio+

-mass

60

Another cute idea: -mass

+

KK+

KK++

select multi-prong -decays with lots of

visible mass

little room left for -mass

(in particular if you are lucky)

95% CL upper limit: 18.2 MeV

6161

5. inferringt-quark &H-bosoninformation

6262

t-quark mass: mt2 dependence

LEP’sfrustratio

ni.e. LEP should have

discovered the t-quark

6363

H-boson mass: ln(mH) dependence

LEP’s realfrustratio

ni.e. LEP should have

discovered the Higgs

6464

Higgs: the next discovery?

LEP

LHC ILC

6565

1. branching ratio

6666

Higgs to fermions: ff

H

f

f

H ff)()(2

fvfum

mg

W

fM

pm

mg

W

f 22

22

2M2

mm

pmg

m

p

WH

f

HffH 22

3222

2 48

M

6868

Higgs branching ratio’s

light Higgs: mH<150 GeVH bb, , cc

intermediate Higgs: 150<mH<350 GeV

H WW, ZZ heavy Higgs:

mH>350 GeVH WW, ZZ, tt

factortwo?

6969

2. LEP’s screw-up?

7070

Production process: Ecm>mZ+mH

H

Ze

e+ e+e-Z*ZH

HZ,W

e

e+

,e+

,e+

e+e- e+e-He+e- H

100 150 200 250

0.5 pb

1.0 pb

Ecm

607090

MH

(e

+e

- Z

H)

7171

ZH Analysis strategy: b-tagging

Hbb 4 jetsZqqH

2 jets + ee/Z ee/ H

2 jets + Z H

2 jets + EmissZ

H

7272

Higgs candidates or ZZ events

7373


H bbZ bb

Best Higgs fit:mH=113.4 GeV

7474


H bbZ

Best Higgs fit:mH=114.4 GeV

7575

Statistical analyses: 1-2 sigma’s

7676

3. discovery at LHC?

7777

m

100 fb-1

ppXH, HZZ4-leptons

“golden” channelmH: 4-lepton mass

7878

m

100 fb-1

ppXH, H (crazy coincidence)

Low mass HiggsmH: mass

7979

mbb

100 fb-1

ppttH, Hbb, tb(qq), tb(l)

Low mass HiggsmH: bb mass

e

e

q

q

qq

q

q

8080

4. self coupling at ILC?

8181mH

e+e- HHZHHZ

(fb)

ZHl+l-bbZHqqbb

Higgs at ILC

8282

Summary1st: find the one missing member: Higgs

2nd: better understanding of the “arbitrary” Standard Model parameters.3rd: lots of other open issues: monopoles, three families, gravity, dark matter, …

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E lectro- W eak measurements