weak interactions slidescern.ch/hedberg/lectures/weak_interactions_slides.pdf · V. Hedberg Weak Interactions 2 Gauge invariant theories. The equation y=x2 is symmetric or invariant

V. Hedberg Weak Interactions 1

Weakinteractions


Gauge invariant theories.

The equation y=x2 is symmetric or invariant under the transformation A, i.e. it looks

The electroweak theoryy

x

y´

x´

y=x2 y´=x´2A

y´=yx´=-x

the same before and after the transformation.

Gauge invariant theories the main equations do not change a gauge transformation is performed.

Requiring gauge invarianiance deduce the various interactions.

when


What is a gauge transformation ?

The electroweak theory

Different gauge transformations different interactions.

Non-relativistic electromagnetism

The equation of motion: for a free non-relativistic particle:

The free particle Schroedinger equation

i x t t

------------------- 12m------- x t

2–=

Goal: modify this equation to describes particles that

Example:

interact electromagnetically.


The electroweak theoryAssumption: the new equation is invariant under a

U(1) phase transformation:

x t ' x t eiq x t x t =were is an arbirary continous function. x t

Failure: the transformed wavefunction is not a solution to the Schroedinger equation.

' x t

The Gauge principle Gauge principle: to keep the invariance condition satisfied it is necessary to add a minimal field to the Schroedinger equation

an interaction will have to be introduced.


The electroweak theoryThe electroweak theoryIntroduce interaction: require that the Schroedinger equationis also invariant under a gauge transformation of type

A A' A +=

V V' V t

------–=

i x t t

------------------- 12m------- p qA– qV+ x t =

Invariance: U(1) phase transformation + gauge transformation

where A and V are the vector and scalar potenials of the electro-magnetic field in which a particle with a charge q is moving.

The equation for a non-relativistic particle with charge q moving in an electromagnetic field.

new equation



Weak isospin charge I3 Weak hypercharge YW

w

massless gauge particles W+,W-,W0, B0

The gauge particles interact with massless fermions.

The electro weak theory by Glashow, Weinberg and Salam.

The EW or GWS model is a quantum field theory for both weakinteractions and electromagnetic interactions.

Electric charge QQ = I3 + YW/2 w

Gauge invariance


The Higgs field generates mass to gauge bosons and fermions.

W+ and W- weak radioactive decay

not observed experimentally

the electromagnetic interaction gauge boson for the weak neutral current interaction

B0 Wcos W0 Wsin+=

Z0 B0 Wsin– W0 Wcos+=

the weak mixing angle


W0 and B0

Photon gauge boson for Z0

W a parameter (not predicted).


Only W-exchange

The electroweak theory divergent processes

e+

e-

W-

W+

e+

e- W-

W+

e

Divergent integrals

The Z0-boson new diagrams cancel out the divergencies

e+

e-Z0

W-

W+

e+

e- Z0

Z0

e-

e+

e- Z0

e-

Divergent integrals

Non-divergent integrals

Non-divergent integrals

infinities


Coupling constants in EW e, gW and gZ


The coupling constants are not independent(in order for all the infinities to cancel out)

8 gW Wsin gZ Wcos= =

The weak mixing angle (Weinberg angle) WcosMWMZ----------=

The unification condition.

e/ g Wsin g Wcos=e = ´ 8 8g= gW g´= gZ

Alternatives

“Strength parameters”

= e2

4QED: s=

gs24QCD:137

1 91 EW: 850

1Z= gZ

2

42501W=

gW2

4


e- e

W-

e-

e

e e-

W- W+ W-

The electroweak theoryThe strength parameters contribution of different processes (diagrams) to the cross-section.

Example: muon-scattering on electrons

Diagrams with increasing complexity can contribute:

Second order diagram Sixth order diagram

gW

gW

gW gW gW

gW gW gW

Second order diagram cross section is proportional to

+ e- + e

aW2

aW6Sixth order diagram cross section is proportional to


e- e

W+

gW

gW

GFMW

e-

e

The electroweak theory Point-like interactions and low-energy measurements

Fermi’s theory of weak interactions four-fermion point-like interactions (without W and Z exchange).

W bosons are heavy charged current interactions can be approximated by a zero-range interaction at low energy

Fermi coupling constant (GF)

GF2

--------gW

2

MW2

----------4WMW

2----------------= =Relationship between gW and GF:

The strength of the zero-range interactionsnext slide


GF2

--------gW

2

MW2

----------= em

2------------------- gW Wsin= MW

2gW

2 2

GF----------------

em

2GF 2

Wsin-----------------------------------= =

MZ2

em

2GF 2

W 2

Wsincos-------------------------------------------------------=

and gives

WcosMWMZ----------= and MW

2em

2GF 2

Wsin-----------------------------------= gives

A bit of algebra:

GZ2

-------gZ

2

MZ2

--------= GZGF--------

2gZ2

2gW2

---------------MW

2

MZ2

----------

2 2

Wcos----------------------

2 2

Wsin------------------------------------------------

2W

2Wsin=cos= =which gives

The electroweak theoryThe unification condition

Definition Weinberg angle

GZ neutral current coupling constant in the low energy approximationzero-range



2

Wsin 0 277 0,014=

Measurement of the weak mixing angle predict the masses of the W and Z:

MW 78,3 2,4 GeV/c2=

MZ; 89,0 2,0 GeV/c2=

GZ/GF=sin2(W) Measurements of weak interaction rates at low energyGZ and GF

Discovery at CERN of W and Z at predicted massesconfirmation that the electroweak theory is correct.


Modern estimation of the Weinberg angle (from many experiments)


2Wsin 0,2255 0,0021=

This value and the previous formulas give:

MZ; 89,0 GeV/c2=

MW 78,5 GeV/c2=while direct measurements give

MZ; 91,2 GeV/c2=

MW 80,4 GeV/c2=

The difference is caused by higher-order diagrams(not taken into account in the low-energy formulas)

e-e

W-

W-

W-

Z0

e-e

W-

W-

b t



e-e

W-

W-

W-

Z0

e-e

W-

W-

b t

Higher-order corrections with top-quarksmeasurement of electroweak processespredict the top-quark mass

mt 170 30 GeV/c2=

The directly measured mass of the top quark at Fermilab bythe CDF experiment gave a value

mt 176 5 GeV/c2=

Perfect agreement with the low-energy prediction !


The W and Z bosons The force carriers in weak interactions are spin-1 bosons (as in QED and QCD) that couple to quarks and leptons.

All observed low-energy weak processes charged current reactions mediated by W+ or W- bosons.

The Electroweak Theory predicted that neutral current reactions caused by the Z0 boson should exist.

the intermediate vector bosonsW+ , W- and Z0

that are the force carriers of weak interactions

have a very short range ( order of 2 x 10-3 fm ).( mW=80.4 GeV and MZ=91.2 GeV ) weak interactions W+, W- and Z0 bosons are very massive particles

(e.g. -decay)


Accelerator: The Proton Synchrotron (PS) at CERN

Discovery of the neutral current

The PS accelerator: Length = 628 m, Number of magnets = 277, Proton beam energy = 28 GeV Neutrino beams:

Step 2. Charged pions and kaons decay +++e++e++Step 1. Intense proton beam hits a target


Discovery of the neutral current Neutral current events was first observed by the Gargamelle experiment at CERN in 1973.

Magnet coils

N2 liquidpropane

Compressor-decompressor

system

Flash lights

Plastic membranes

Filmcameras

Step 1. The liquid propane is at a temperature below its boiling point.

Step 2. When the enters the propane, its pressure is lowered to make it superheated.Step 3. Charged tracks ionize the propane and these ions create bubbles in the liquid.Step 4. The bubble tracks are photographed by film cameras.


Discovery of the neutral current Elastic and inelastic neutral current reactions possible.

nucleon

hadrons

Main background neutron - nucleon interactions.


Discovery of the neutral current

e-

e+

e-e-

e+

Bremsstrahlung

Conversion

One of the first neutral current reactions seen by the Gargamelle experiment.


The discovery of the W and Z bosons

Dipole magnet

Quadrupol magnet

Cavity

The accelerator: The Super Proton Synchrotron

The SPS accelerator: Length = 6.9 km, Number of magnets = 960, Fixed target = 400 450 GeV

pp-collider = 540 630 900 GeV

The W and Z were discovered by the UA1 and UA2 experiments.


SPS(CERN)

Length: 7 km (960 magnets)Experiments: UA1, UA2

e

q

q

qg

g

g

hadrons

p

450 GeV

q

q

qg

g

gp

hadrons

g

450 GeV

The discovery of the W and Z bosonsLEP(CERN)

Length: 27 km (4184 magnets)Experiments: DELPHI, OPAL, ALEPH, L3

ee- ee+

46 GeV104 GeV

46 GeV104 GeV

hadrons

hadrons

Z0q

q-

The energy of the quarks and gluons carry only a fraction of the proton

To produce W- ans Z-bosons with a mass of 80-90 GeV a collider with a beam energy of 270 GeV was needed.

The beam energy was later increased to 450 GeV.

energy.


The discovery of the W and Z bosons

Gargamelle

ATLASUA1

DELPHI


The discovery of the W and Z bosonsThe experiment: UA1

Tracking detector: Central wire chamber with 0.7 T dipole magnet.Electromagnetic calorimeter: Lead/scintillator sandwichHadronic calorimeter: Iron/Scintillator sandwichMuon detector: 8 planes of drift chambers.


The discovery of the W and Z bosonsProduction of W and Z bosons

u + d W+ d + u W-

u + u Z0 d + d Z0

p

p

q

qW Z0

The W and Z bosons are in proton colliders produced byquark-antiquark annihilations:

The lifetime of both the W and the Z is about 3 x 10-25 sthey cannot be seen directly in the experiments.


The discovery of the W and Z bosonsThe decay of W and Z bosons

p + p W-+ X l- + l

p + p W++ X q´ + q

p + p W-+ X q´ + q

p + p Z0+ X q + q

p + p Z0+ X l+ + l-

p + p W++ X l+ + l

hadronic decays leptonic decays

Cannot be found amongall other hadrons produced.

The decays to leptonsare easy to identify


The discovery of the W and Z bosonsAnalysis of W-events in UA1

The analysis searched for events with a charged lepton + neutrino

A high momentum electron is indicated by the arrow.


The discovery of the W and Z bosonsTransverse momentum

The transverse momentum and energyof a particle: PT = P sin()

ET = E sin()

ET = PT if the mass of the particle issmall since E2=P2+m2

where is the angle to the beam.

The total momentum is zero of all the particles in a collision.

Neutrinos are not detectableif the total momentum = 0the event has missing momentum

pPT

PL

(or missing energy).


The discovery of the W and Z bosonsAnalysis of W-events in UA1

The analysis was looking for events with a charged lepton and The main selection criteria in the UA1 W-analysis was:i) A charged electron or muon with a large momentum (>10 GeV/c)ii) This lepton should be emitted at a wide angle to the beam (>5o)iii) There should be large missing transverse momentum in the event

The expected distribution of thetransverse energy of the selectedelectrons was compared with themeasured distribution.

MW 83 5 2 8 GeV= W 6 5 GeV

From the first 148 electron and 47muon events it was estimated that:

Wjet-jet

Transverse Energy (GeV)Eve

nts

10

20

20 30 40 50

MeasuredDistribution

BackgroundSubtractedDistribution

SimulatedDistributionMW=83.5 GeV


The discovery of the W and Z bosonsAnalysis of Z-events in UA1

The analysis was looking for a pair of charged leptons.

e-

e+


The discovery of the W and Z bosonsInvariant mass

= 2 E1E2 ( 1 - cos )if m=0

E1

E2

Zmz

me

mz2

mz2 = ( P1 + P2 )2 ( 4-vectors )

E1me

E2 me

me

The invariant mass of a particle thatdecays to two other particles:


The discovery of the W and Z bosonsAnalysis of Z-events in UA1

Main search criteria require pair of electrons or muons with a large transverse energy.

The mass distributionof pairs of electronswhere each electron has ET>8 GeV.

MZ 93 0 1 4 GeV=

Z 8 1 GeV

20 40 60 80 100Mass (GeV)

4

8

Even

ts

jet-jetbackground

Z0

candidates

The first 18 electron pairsand 10 muon pairs in UA1


Precision studies of the W and Z bosonsThe accelerator: The Large Electron Positron Collider

Electrons-positrons collisions in four experiments.

Z mass maximum288 superconducting cavities.

Collision energy: 91 GeV 209 GeV


Precision studies of the W and Z bosons

Cavity

Dipole magnet

Quadrupol magnet


TEVATRON(FERMILAB)

Length: 6 km (990 magnets)Experiments: CDF, D0

e

q

q

qg

g

g

hadrons

p

1000 GeV

q

q

qg

g

gp

hadrons

g

1000 GeV

LHC (CERN)

Length: 27 km (1232 + 386 magnets)Experiments: ATLAS, CMS, LHCb, ALICE

e

q

q

qg

g

g

hadrons

p

7000 GeV

q

q

qg

g

gp

hadrons

g

7000 GeV

LEP(CERN)

Length: 27 km (4184 magnets)Experiments: DELPHI, OPAL, ALEPH, L3

ee- ee+

46 GeV104 GeV

46 GeV104 GeV

hadrons

hadrons

Z0q

q-

HERA (DESY)

Length: 6 km (1650 magnets)Experiments: H1, ZEUS

e

ee+

30 GeV

ee+q

q

qg

g

g

hadrons

p

920 GeV



Precision studies of the W and Z bosonsDifferences between proton and electron colliders.

Synchrotron radiation:Total energy loss is proportional to 1/mass4

1/radiusTotal energy loss is proportional to 4Ebeam Total energy loss is proportional to

Energy loss in an electron accelerator is 1013 times larger.

LEP: 344 cavities, accelerating voltage=3630 MV, energy=104 GeV LHC: 16 cavities, accelerating voltage = 16 MV, energy=7000 GeV

Beam momentumLength of bending field

Magnetic bending field LEP: 0.12 Tesla bending fieldLHC: 8.38 Tesla bending field } factor 70


Precision studies of the W and Z bosonsThe accelerator: The Large Electron Positron ColliderIn an electron-positron collider it is important to know the collision energy with a high accuracy. It took many years tounderstand the factors that influenced the collision energy in LEP.

Days

ΔE (

MeV

)

Energy calibrations

Horizontal Orbit (XARC)

Lake level fit

-20

-10

0

120 140 160 180 200 220 240

Geological shiftsDuring 1993 the LEP energy was observed to change with time.

Part of the change was due to

which caused small geologicalshifts of the accelerator.

Rainfalls and the water table

affected the LEP energy.

the water level in lake Geneva

in the Jura mountains also


Precision studies of the W and Z bosonsΔ

E [

MeV

]

November 11th, 1992

Δ E

[M

eV]

August 29th, 1993

Daytime

October 11th, 1993

-5

0

5

23:00 3:00 7:00 11:00 15:00 19:00 23:00 3:00

-5

0

5

11:0

0

13:0

0

15:0

0

17:0

0

19:0

0

21:0

0

23:0

0

18:0

0

20:0

0

22:0

0

24:0

0

2:00

4:00

6:00

8:00

Tides

Earth tides caused by the moon will produce small distortions of the earth’s crust.

This can affect the accelerator so that the electrons orbit change.

An orbit change of 1 mm would change the energy with about 10 MeV.


Vacuum Chamber Current Correlation

LEP

SPS

CERN

airpor

t

Belleg

arde

Lau

sann

e

La Versoix

Lac de

Geneve

Meyrin

Zimeysa

Cornavin

IP1

IP2

IP3

IP4IP5

IP6

IP7

IP8

1 km

1

Vol

tage

on

rails

[V]

RAIL

TGV

Gen

eve

Mey

rin

Zim

eysa

17.11.1995

Vol

tage

on

beam

pipe

[V]

LEP beam pipe

Time

Ben

ding

B f

ield

[Gau

ss]

LEP NMR

-7

0

-0.024

-0.02

-0.016

-0.012

746.28

746.30

746.32

746.34

746.36

16:50 16:55

Beampipe current

LEP Lake

Trains

River

Geneva

The trains from Geneva to Francecaused parasitic currents on the LEP beampipe.These currents (1 A) affected the magnetic field in the LEP magnetsand this changed the energy.



Precision studies of the W and Z bosonsThe DELPHI Experiment

DELPHIVertex Detector

Inner Detector

Time Projection Chamber

Small Angle Tile Calorimeter

Very Small Angle Tagger

Beam Pipe

Quadrupole

Barrel RICH

Outer Detector

High Density Projection Chamber

Superconducting Coil

Scintillators

Barrel Hadron Calorimeter

Barrel Muon ChambersForward Chamber A

Forward RICH

Forward Chamber B

Forward EM Calorimeter

Forward Hadron Calorimeter

Forward Hodoscope

Forward Muon Chambers

Surround Muon Chambers

The DELPHI ExperimentTracking detector:Time projectionchamber

Electromagneticcalorimeter:Lead absorber

Magnet

Hadronic calorimeterIron absorber

Muon detectors


The DELPHI Experiment


The DELPHI cavern The Time Projection chamber



TPC

Cerenkov

Electromag.calorimeter

Magnet

Hadroniccalorimeter

Muonspectrometer

Studies of the Z-boson

e

e-

+

e+

e Zo-

From the number of produced electronpair events one can calculate the crosssection for the following process:

Crosssection

Collision energy


TPCCherenkov


Magne t

Hadroniccalorimeter

Muonspectrometer

Precision studies of the W and Z bosonsStudies of the Z-boson

From the number of produced muonpair events one can calculate the crosssection for the following process:

Crosssection

Collision energy

-

+

e+

e Zo-


TPCCherenkov


Magne t

Hadroniccalorimeter

Precision studies of the W and Z bosonsStudies of the Z-boson

From the number of produced taupair events one can calculate the crosssection for the following process:

Crosssection

Collision energy

+

e+

e Zo-

-

Muonspectrometer


The number of neutrino families

(pb)

Center of mass energy (GeV)

e

e-

+

e+

e Zo-

-

+

-

+

q

qBranching ratio ( B ):

}0.10 0.20 0.70

Decay width ( ): 0.25 GeV 0.50 GeV 1.74 GeV

B---= Bxx

xxZ---------=

where the lifetime is given by

BZZ-------

Bhad Bll B+ +

had ll + +--------------------------------------------= =

Bhadhad-------------

Bllll-------

B---------- 3 25–10 s= = = =

1GeV 1– 6 582 25–10 s=Note:

The total decay width Z isthe sum of the partial decaywidths.



MZ

Z

: The total Z0 decay rateZ Z(Z0 X)

: The decay rate to final state XMZ : The mass of the Z0

where

B Z0 e+e- B Z0 X Z0 e+e-

Z-----------------------------------

Z0 X Z

---------------------------The height of the peak isproportional to the branching ratios:

It was possible to determine the partial decay widths of the Z0

by fitting Breit-Wigners to the measured distributions at LEP.

Collision energy - ECM

If Ecm=MZ:

e+e- 12MZ

2

ECM2

------------------ Z ee Z

ECM2

MZ2–

2

MZ2Z

2+

---------------------------------------------------------------=

e+e- 12

MCM2

--------------- Z ee Z

Z2

----------------------------------------------------------------=

Z0


The number of neutrino familiesThe fitted parameters of the Z0 peak gave the following result:MZ 91,187 0,007 GeV/c2=

Z 2,490 0,007 GeV=

Z0 hadrons 1,741 0,006 GeV= Z0 l+l- 0,0838 0,0003 GeV=

However, the leptonic and hadronic decays account for only 80%of all the Z0 decays.

The remaining decays are those to neutrinos that cannot bemeasured directly by the experiment

Z Z0 hadrons 3 Z0 l+l- ++= N Z0 ll

From the measured values of the decay widths one gets

N Z0 ll 0,498 0,009 GeV=



5

10

15

20

25

30

35

88 89 90 91 92 93 94 95

N=2

N=3

N=4

DELPHI

Energy, GeV

N 2,994 0,011=

The decay rate of the Z0 to neutrinos can be calculated:which together with

gives Z0 ll 0,166 GeV= N Z0 ll

0,498 GeV=

Z0 to There are no explicit restrictionson the number of generations in the standard model.

The study of the Z0 peak at LEPshows that there are onlythree types of light neutrinos(with a mass less than MZ.)

hadrons


Precision studies of the W and Z bosonsStudies of the W-boson

e+ e-

A WW-event with 4 jets

The W bosons were produced in pairs at LEP.

e+

e-

e+

e Zo-

e

W+

W-

/

W+

W-

The signature for WW-events was:

qq qq llqq l


Precision studies of the W and Z bosonsStudies of the W-boson

0

50

100

150

200

250

50 60 70 80 90 100

DATA

WW

(Mw = 80.35)

ZZ

QCD

W mass [ GeV/c2 ]

even

ts /

2 G

eV/c

2

Step 1. Select WW-pair events Step 2. Calculate the W-mass

qq qq

W

2= ( )PP +q q

_

W

2= 2 E E ( 1 - cos )q

_

if m = 0q

( 4-vectors )2

q

The mass distribution of jet-pairs


W and Z reactions

�l l+

W�

gW

- q q’

W�

Vqq’gW

�l

Z0

l+�l l-

Z0

gZ gZ

�l

Z0

l+�l l-

Z0

qq

Z0

gZ

qq

Z0

Leptonic reactions Hadronic reactions

Charge

Neutral

currentreactions

currentreactions


Charged current reactions

Purely leptonic processes:

Charged current reactions are reactions mediated by thecharged W-bosons.

Purely hadronic processes:

Semileptonic reactions:

W-

e-

e

- e- + e +

+ p

n p + e- + e

du

sud u

ud

W-

p

du

dsu d

uu

W-

p

ddu

udu

e-

e

W-

n

p


Leptonic charged current reactions

+ + ...

e-

e-

e-

e-

e-

e+

l l-

W

l l+

W

All the electromagnetic interactions eight basic interactions:

Leptonic weak interaction described by basic vertices:

The basic vertex forelectron-photon interactions.

The two basic vertices for W-leptoninteractions..


l

W+

l+

l

W-

l-

l+

W+

l

W-

l+

l

l

l+

W+

W-

l-

l

l-

W+

l

l

W-

l+

l l- + W+

W+ l l-

l+ W+ + l

W-+ l+ l

l+ + l W+

W- l- + l

vacuum l- + l + W+ l+ + l + W- vacuum

Eight basic charged current reactions from two basic W vertices:



Weak interactions conserve lepton numbers: Le , L , L .

Feynman diagrams:1) at each vertex, there is one arrow pointing in and one out2) the lepton indices “l” are the same on both lines.

+ + ...

W

e-

e-

W+W-

e-

+ + ...

e

W

e-

e

e-

W+W-

e-

e

Allowed:

Forbidden:



Leptonic charged current reactionsThe weak strength parameter: W

W is the same at all leptonic vertices (do not depend on leptontype).

Example: The decay rate of W to e+

W e WMW W 80 GeVEstimation from theory

W e 0,2 GeVMeasurement

W=0.003

The electromagnetic strength parameter: em=0.007


Leptonic charged current reactionsWhy is the weak interaction so weak if W and em is ofa similar size ?

Compare the decay of charged and neutral pions:

u

u

{Electromagnetic decay

Lifetime = 8 x 10 s-17

-W-

du

Weak decay

{Lifetime = 3000000000 x 10 s

-17

(Lifetime of a real W = 0.00000003 x 10 s)-17

CONCLUSION: The apparent weakness of the weak interactionsis due to the very large W and Z masses.


W and Z reactions

�l l+

W�

gW

- q q’

W�

Vqq’gW

�l

Z0

l+�l l-

Z0

gZ gZ

�l

Z0

l+�l l-

Z0

qq

Z0

gZ

qq

Z0


Charge

Neutral

currentreactions

currentreactions


Hadronic charged current reactionsIn weak hadronic interactions, constituent quarks emit or absorb W or Z bosons.

ddu

udu

e-

e

gWW-

gudn

p

du

sud u

ud

W-

p

du

dsu d

uu

W-

p

Examples:

Neutron -decay.

The dominant quark diagrams for decay


Hadronic charged current reactionsASSUMPTION: Lepton-quark symmetry i.e. correspondinggenerations of quarks and leptons have identical weakinteractions.

- c

s

e

e- u

d

- t

b

u d

W

u d

W

c s

W W

gud gcsc s

gud gcsl l-

W

l l+

W

gW gW

The W-quark vertices for the first two generations, assuming lepton-quark symmetry.

The W-lepton vertices.

Interactions will then only take place within a family !


Hadronic charged current reactionsExperimental tests of the assumption of lepton-quark symmetry.

Some weak reactions should be allowed and some should beforbidden if lepton-quark symmetry is true:

du

K- su

-W-

du Allowed

-W-

su

Not AllowedK-

{

{Different families

Measurements of these decays give: Branching ratio = 0.9999 = 2.6 x 10-8 sK- Branching ratio = 0.6343 = 1.2x 10-8 s

CONCLUSION: Quarks from different generations canparticipate in charged current interactions !


Hadronic charged current reactionsCabibbo introduced the concept of quark mixing in order to explain the kaon decays.

Quark mixing scheme d- and s-quarks participate in weak interactions via the linear combinations:

d' d C s Csin+cos=

s' d C s Ccos+sin–=where C is called the Cabibbo angle.

The quark-lepton symmetry applies to doublets like

ud'

and cs'

+

u

W

d’gW

u

W

d u

W

sgud gus

gud=gWcosC gus=gWsinC

The ud’W vertex can beinterpreted as a sum ofthe udW and usW vertices:


Hadronic charged current reactionsWith the quark mixing hypothesis, more W-quark vertices:

u d

W

u d

W

c s

W W

gcsc s

gud gcs

u s

W

u s

W

c d

W W

gus gcdc dgus gcd

gW CcosgW Ccosgud

gW CcosgW Ccos

g– W Csing– W CsingW CsingW Csin

gud gcs gW Ccos= =

gus g– cd gW Csin= =

Within a generation:

Between generations:


Measurements of the Cabibbo angle.

Hadronic charged current reactions

The Cabibbo angle has to be measured.

Comparing the decay rates of with K-

K- -

- - ------------------------------------

gus2

gud2

--------- 2

Ctan= gives the result C 12,7 0,1=

gW Ccos 0 98gW=gW Csin 0 22gW=

The coupling constants within and between generations:


Charmed particle decays.

Hadronic charged current reactions

c

s

W+

gW Ccos

gW

c

d

W+

gW Csin

ll

ll

gW

Particles with charm quarks almost always give a strange particlein the final state because other decays are Cabibbo supressed:

gcd2

gcs2

--------- 2

Ctan 120------= =

The supression factor is given by:

C 12 6=if

The charmed quark couplings gcd and gcs have been measuredin neutrino scattering experiments with the result: C 12 1=


Two generation quark mixing can be written in matrix form:

Weak interactions and the third generation

d's'

Ccos Csin

Csin– Ccos

ds

=

This means that the following weak transitions are favoured:

C

s

u

d

And that the following weak transitions are surpressed:

C

s

u

d

While charge conservation forbids the following charged current

C

s

u

d

Charge = 2/3

Charge = -1/3

ud'

and cs'

with transitions within

transitions:


Weak interactions and the third generationWeak interactions and the third generationThe existence of the c-quark was predicted from lepton-quarksymmetry before it was discovered in experiments in 1974.

After the discovery of the lepton and the b-quark, the sixthquark was predicted to complete the symmetry the top quark was discovered in 1994

d's'b'

Vud Vus Vub

Vcd Vcs VcbVtd Vts Vtb

dsb

=

The third generation gives rise to the Cabibbo-Kobayashi-Maskawa (CKM) matrix V:

The relation between the matrix elements in the CKM-matrix and the coupling constants are given by g = gWV where=u,c,t and =d,s,b .



If the mixing between the b and t quarks with lighter quarkscan be neglected the CKM-matrix is reduced to:

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

Ccos Csin 0

Csin– Ccos 0

0 0 1

If Vub, Vcb, Vtd and Vts are not small The two-generation mixing model would not work

Weak transitions can now take place between:

u d’ = Vudd+Vuss+Vubb c s’ = Vcdd+Vcss+Vcbb t b’ = Vtdd+Vtss+Vtbb



Vub=Vcb=Vtd=Vts=0 t-quark decay only to b-quarks

b-quark is stable(since it cannot decay to u- or c-quarks)

Semileptonic decays of b-quarks to u- and c-quarks

The observed decay rate isproportional to the squared

are observed in experiments !

Not true

couplings: gub

2 Vub2gW

2=

W-l

b

l-

gub

u

gW

VubgW

b - quarks


Weak interactions and the third generationb - quarks

The most precise measurements at present give

Vub 0 004 and Vcb 0 04

This means that the CKM-matrix becomes

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

Ccos Csin 0 004

Csin– Ccos 0 04

1

0 0

0 98 0 22 0 0040 22– 0 98 0 04

1

0 0


Weak interactions and the third generationThe top quark

The top quark is much heavier than even the W-bosons and itcan decay by

t

d

W+

t

s

W+

t

b

W+

gtd 0 gts 0 gts= gW

Since gtd and gts are close to zero, the only significant decaymode of the t-quarks is

t W+ + b

with a rate proportional to W gW2 4= 0 0042

Estimation of the decay width of the top ( Wmt 1 GeV )suggests a very short lifetime

t 4 25–10 s


W, Z, top 3-4x10-13ps 0 Beampipe Not possible0 ( ) 0.0008 ps 0.025m Beampipe Not possibleCharm: D0/D /Ds 0.4-1 ps 150-350m Beampipe MicrovertexBottom: B0/B /Bs/ 1.5 ps 450m Beampipe MicrovertexKs ( ) 80 ps 2.7cm Tracker Tracker

KKL ( ) ( ee)

Particle Lifetime Decay Decay Decay Length Place Measurement

0.3 ps 90m Beampipe Microvertex

+-

+-+-

+- 10,000 ps 3.7m Tracker Not possible30,000 ps 7.8m No decay Not possible50,000 ps 16 m No decay Not possible2,000,000 ps 659 m No decay Not possible

Compare particles decay length



The discovery of the top quarkThe accelerator: The Tevatron

CDF

Tevatron Main injector

p 150 GeV900 GeV

Tevatron: pp-collider 4.5 T 6.3 km 1800 GeV

Type Bending field Length Collision energy

pp-collider 1.8 T 6.9 km 900 GeV SPS:pp-collider 8.4 T 27 km 14000 GeV LHC:

Superconducting magnets


The Tevatron

Old main ring

The discovery of the top quarkThe accelerator: The Tevatron

The Tevatron accelerator was put under the old main ring which was used as a pre-accelerator (it has since been removed).

One of thesuperconductingdipole bendingmagnets.

A cross sectionof a dipolemagnet showingthe coilstructure.


V. Hedberg Weak Interactions 108 Had. Calorimeter

Muon system

Drift chamber

Electromagn. Calorimeter

=0=1

The discovery of the top quarkThe experiment: The Collider Detector at Fermilab

Solenoidmagnet

Silicon Vertex Detector

Lead/Scintillator Iron/Scintillator


The discovery of the top quarkThe experiment: CDF


The discovery of the top quark

Production of top-quarks

In proton-antiproton colliders, pairs of top quarks are mostlyproduced by the quark-antiquark annihilation process:

q + q g t + t

t

t

g

q

q

p

p


The discovery of the top quarkThe decay of top-quarks

The most likely decay

p + p t + t + X

W+ + b

W- + b

l+ + lq + q{

l- + lq + q{

of a top quark is to ab quark and to a W.

W+l

t

l+

W- q

t

q

b

b

The W can decay to leptons or hadrons the final stateis a complex mixof jets and leptons.


The discovery of the top quark

Expected Signal

Expected Background

Mt 176 5 GeV=

After a selection of likely top event

mass distribution of the top-candidates.had been made, one could plot the

The resulting distribution hada large background componentbut one could neverthelessextract a top mass:


W and Z reactions

�l l+

W�

gW

- q q’

W�

Vqq’gW

�l

Z0

l+�l l-

Z0

gZ gZ

�l

Z0

l+�l l-

Z0

qq

Z0

gZ

qq

Z0


Charge

Neutral

currentreactions

currentreactions


Neutral current reactions

l l-

W

l l+

W

q q’

W

gW Ccos

gW CsingW gW

l

Z0

l+l l-

Z0

qq

Z0

gZ gZ gZ

The basic vertices with W bosons have:- Conserved lepton numbers- Not conserved quark flavour (quark mixing)

The basic vertices with Z bosons have:- Conserved lepton numbers- Conserved quark flavour (no quark mixing)

The basic W vertices The basic Z vertices


Neutral current reactionsIn processes in which a photon can be exchanged, a Z0 bosoncan be exchanged as well:

l

Z0

l+l l-

Z0

qq

Z0

gZ gZ gZ

Example: e+e- has two dominant contributions

e+

e-

e+

e-Z0


Neutral current reactionsEstimation of the cross-section for the photon- and

2

ECM2

---------------- Z GZ2ECM

2 where Ecm is the collision energy.

The photon exchange process will dominate at low energies.

At Ecm=Mz this low-energy approximation fails andthe Z0 peak is described by the Breit-Wigner formula:

ECM M2

ECM2

------------- CECM

2 M2–

2M2

2+

----------------------------------------------------------= where M is the mass of the resonanceand its decay width.

Z-exchange process in e+e- collisions at low energy:


Neutral current reactionse+

e-

e+

e-Z0

2

E2------- Z GZ

2E2

(pb)

Z

MZ

ee 12MZ

2

ECM2

------------------ Z0 ee Z0

ECM2 MZ

2–

2MZ

2Z

2+

-------------------------------------------------------------=

Center of mass energy (GeV)


Test of flavour conservationThat flavour is conserved at a Z0 vertex can be verified byexperiments.

Example: measurement of the decay rate of charged kaons

W+

su

uu

K+

Z0

lsu

du

K+

l

K+ K+ l + l

K+ + l l+ + l

K+ 0 + + + ----------------------------------------------------------- 10 7–

The measured upper limit on the ratio of the decay rate ofthese two processes was

until experiment E787 came along .....


Test of flavour conservationThe BNL experiment E787 was a fixed target experiment thatused a K+ beam created by 24 GeV protons from the AGS.

AGSE787

The 800 m long AGS

AGS

BoosterLinac

g-2 muonstorage ring

Tandem

Experimental Area

Van de Graaff

AGS to RHIC

has 240 magnets.


C

SC

ck

rel

Veto

ITarget

B4

o

EndcapT

ge

mTarget

Scintillating fibers DriftchamberMaterial

to slow down Kaons

0.8 GeV K+ beam

CsI Calorimeterto veto on photons

Tracking

Scintillators

Calorimeterto veto on photons

+

Test of flavour conservation

The Kaons were stopped in a target made of scintillating fibersand the decay of the K+ at rest was then studied.

The momentum, energy and range of the particle from thedecay was measured.

f

50 c(b)

TTarget

CalorimeterScintillators

Driftchambers

E787 K+ l + l


Test of flavour conservation

Target

Scintillating fibers

Drift chamber hits Scintillators

After many years of running two candidate events for K+ l + l were found.

The result from these two events were:

K+ + l l+ + l

K+ 0 + + + ----------------------------------------------------------- 1 6 10–

100 033

--------------------------- 5 9–10==


Test of flavour conservationThe events could, however, be explained by second-ordercharged current reactions rather than neutral current processes:

s

uu

dK+ +π

l

νν ν

l

νν

l

ν

s

uu

du c t+π+K

s

uu

dK +π+

w w w w w w

Due to the t-d vertex in the third diagram above, it was alsopossible to set limits on the Vtd element in the Cabibbo-Kobayashi-Maskawa matrix:

0 007 Vtd 0 030


The Higgs bosonGenerally, experimental data agrees extremly well with thepredictions of the gauge invariant electroweak theory.

Gauge invariance the gauge bosons have zero mass.True for photons in QED and gluons in QCD but not for W and Z.

A new scalar field called the Higgs field is introduced to generate mass to the W and Z bosons as well as fermion masses.

Associated with the field is a new particle called the Higgs boson.

particles but do not predict its mass.The theory predicts how the Higgs boson couples to other


The Higgs bosonThe Higgs field has the unusual characteristic of having anon-zero value 0 in vacuum (i.e. the field is not zero in itsgroundstate).

0

Since the vacuum expectation value is not zero, the vacuum issupposed to be populated with massive Higgs bosons and when a gauge field interacts with the Higgs field it acquires mass.


The Higgs bosonFrom the interaction with the Higgs field, the W and Z bosons require masses with the ratio given by

WcosMWMZ----------=

H0 gHff

f

f

gHff2 2GFmf

2=

In the same way, fermions acquire mass by interacting withthe Higgs bosons.

The coupling constant for this process depends on the fermionmass:

The existance of the Higgs boson has not been experimentallyverified despite many years of searches.


Search for the Higgs boson at LEPThe LEP project had two phases:

LEP 1: The collision energy was equal to the mass of the Z0.LEP 2: The collision energy was increased gradually during several

years by adding superconducting cavities until it reached its maximum energy (209 GeV).

In this case the Higgs particle would be lighter than the Z0

Higgs search at LEP 1

Z0 H0 + l+ + l-

Z0 H0 + l + l

e+

e

H0

Zo

bb

ee

-

Zo

*


Search for the Higgs boson at LEPThe predicted branching ratio for Higgs production is low

3 6–10

Z0 H0l+l- tot

----------------------------------------- 10 4–

but millions of Z0s were produced in the LEP experiments andso the experiments were still sensitive to a Higgs signal.

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60 70 800

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60 70 80

Mass of hadrons (GeV)

Even

ts Data

Background The DELPHI experiment lookedat one million Z0 events and selected those that containedboth leptons and hadrons.

No signal was observed and oneconcluded that mH > 56 GeV.


Higgs search at LEP 2

Search for the Higgs boson at LEP

At LEP 2 one expects the main Higgs production to happen byso-called Higgs strahlung:

e+

e

H0

Zo

bb WW gg cc

qq ee

74% 8% 8% 6% 4%

70% 20% 3% 3% 3%

-

Zo*

Most of the Higgs events would

Two of these should be coming

have 4 jets in the final state.

from b-quarks.

e+ + e- H0 + Z0

Example of a Higgs candidate in DELPHI


Search for the Higgs boson at LEPDuring the last year of operation of LEP 2, the ALEPH experiment recorded a couple of events which could be due to the decays of a Higgs boson with a mass of about 115 GeV.

The other experimentsat LEP did not see a signaland when all data was addedtogether there was nodiscovery.

The DELPHI experiment puta limit on the Higgs mass of:

MH 114 GeV/c2

DELPHI, L3ALEPH, OPAL


Search for the Higgs boson at LEPThe measurement of many electroweak parameters at LEP (andother places) makes it possible to make a global fit with theHiggs mass as a free parameter.

Fit without using the result of directsearches:

Fit using the limits from direct searches;

mH = 80+30 GeV < 154 GeV-23mH = 120+15 GeV < 144 GeV-5


Search for the Higgs boson at LHC

ATLAS

CMS

LHCb

ALICE

CERN

Experiments

ATLAS: Proton-proton collisions

CMS:Proton-protoncollisions

ALICE:Atom-atomcollisions

LHCb:Proton-protoncollisions giving b quarks

CERN

The Large Hadron Collider (LHC)The 27 km long proton-proton collider has a 14 TeV collision energy (1150 TeV for lead-lead collisions).


Search for the Higgs boson at LHCThe 1232 dipole magnets produce a8.3 Tesla magnetic field which areused to bend the proton trajectory.

The current in the super-conducting magnet coils is 11800 Ampere.

The protons are travelling in 2808bunches that each contain 1011

protons.

pp


Search for the Higgs boson at LHCIn addition to the dipole bending magnets there are some 386quadrupole magnets used to focus the protons beams.

Cavities with strong high-frequency electric fields are used toprovide the energy to the beams. The LHC has 2x8 cavities thatgive 16 MV at 400 MHz.


Search for the Higgs boson at LHC The ATLAS experiment

ATLAS is the worlds largest particle physics experiment.

Muon detector Hadron calorimeter

Electromagnetic calorimeter

Tracking detectors

Length: 44 m Diameter: 22 mWeight: 6000 tonnes

The collaboration:3000 physicists>160 universities34 countries


Search for the Higgs boson at LHC Higgs boson production

LEP limit

WW, ZZ fusion

W,Z bremsstrahlung

tt fusion

gg fusion gg fusion

WW, ZZ fusion


Search for the Higgs boson at LHC Higgs boson decay

10%

40%

1%

0.1%100 200 300 400 500 700 1000

Higgs mass (GeV)

Bra

nch

ing

rati

o

bbWW

ZZt t

γγ

4%

has to select decays that arebackground

The background is huge and one

are visible above the

The cleanest process is if the Higgs has a large enough mass so that itcan decay to two Z0 that then decay to leptons.

There is 109-1010 inelastic interactions for every Higgs bosonthat is produced. At low mass most decay to bb and at highmass most decay to WW and ZZ.

(bb is for example hopeless).



[GeV]4lm200 220 240 260 280 300 320 340 360 380 400

Even

ts/(5

GeV

)

0

10

20

30

40

50

[GeV]4lm200 220 240 260 280 300 320 340 360 380 400

Even

ts/(5

GeV

)

0

10

20

30

40

504l→ZZ*→H

ZZZbbtt

-1 L=30 fb∫ATLAS

e e

H

Z Z

e+ e- �+ �-

p p

Short lifetime

Short lifetime

Long lifetime

Computer simulations of collisions in which Higgs bosons are detected by finding four leptons show a very clear signal if the Higgs mass is 300 GeV.

Higgs signal

background

Mass of the 4 leptons


[GeV]4lm100 110 120 130 140 150 160 170 180 190 200

Even

ts/(2

.5 G

eV)

02468

101214161820

[GeV]4lm100 110 120 130 140 150 160 170 180 190 200

Even

ts/(2

.5 G

eV)

02468

101214161820 4l→ZZ*→H

ZZZbbtt

-1 L=30 fb∫ATLAS

Search for the Higgs boson at LHC It is possible to use the 4-lepton channel also if mH < 2mZ, but then the Higgs decays to one real andone virtual Z0.

Higgs signalif mH=130 GeV

2mz

At a Higgs mass close to the LEP limit, the branching ratio for H0 ZZ leptons is very small and one is also considering using H0 but this process also has a minute branching ratio:

Br = 1-2 x 10-3

H0

W+

W+

W-

H0

t

t

t Production diagrams:


1

10

10 2

102

103

mH (GeV)

Sig

nal s

igni

fican

ce H → γ γ ttH (H → bb) H → ZZ(*) → 4 l

H → ZZ → llνν H → WW → lνjj

H → WW(*) → lνlν

Total significance

5 σ

∫ L dt = 30 fb-1

(no K-factors)

ATLAS

Higgs mass

DiscoveryLimit

ZZ

WW WW

One can estimate the signal significance for different search channels:


Documents

weak interactions slidescern.ch/hedberg/lectures/weak_interactions_slides.pdf · V. Hedberg Weak Interactions 2 Gauge invariant theories. The equation y=x2 is symmetric or invariant