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Lecture 14 – Neutral currents and electroweak unification

● Neutral currents ● Electroweak unification● Number of neutrinos and fermion generation● The Standard Model● The Higgs boson

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Basic diagrams for weak neutral currents

u c

Same quark flavour: u,d,s,c,b,t

Flavour changing: forbidden

u

c

Same quark flavour: u,d,s,c,b,t

Flavour changing: forbidden

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Using the mixed states', '

' cos sin ' sin cos

Discussed in lecture 13 that the weak force "saw" mixed states and this led to cross-generation interactions.

; (13.02)instead of physical states and .(S

C C C C

d s

d d s s d sd s

2 21 ' ' cos sin cos sin cos sin

imple two-doublet approximation.)Show that it doesn't matter whether we use the physical or Cabibbo-rotated states.

Contributions to amplitude:

C C C C C CM d d d s d s dd ss ds sd

2 22

1 2

2 2 2 2

sin cos

' ' sin cos sin cos sin cos sin cos

' ' ' '

cos sin sin cos sin cos

(14.01)

(14.02)

(14.03)

C C

C C C C C C C C

C C C C C C

M s s d s d s dd ss ds sd

M M M

d d s s

dd ss ds sd dd ss ds sd

sin cos

(14.04)Neutral currents don't change flavour.

C C

dd ss

+ +=

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Question0Draw Feynman diagrams for and

What are the decay rates for these processes ?Are these results in agreement with the assertion that flavour changing neutral currents are suppressed ?

e LK e K e e

0

053 10 .

has not been observed.

Best limits on decay rates are:

L

L

e

K e e

K e e

K e

K-us

e-

Z0

dK0

forb

idde

n

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ss

,Z0

Neutral currents

Evidence for charged current interactions via is readily available at low energies. In 1938 Klein proposed a heavy charged particle was responsible for weak processes. It was hard toavoid observi

W

0

.

.

,

ng their influence:

eg nuclear -decay and decays: +

Until 1973 all weak interactions could be understood with the

Evidence for the neutral partner of the the was mo

en p e

W

W Z

0 0

0

re difficult to obtain:

(1) There's no flavour changing allowed eg is forbidden as a -process.

(2) Any decays which would mediated by the heavy would also be mediated by thephoton and t

LK e e Z

Z

he weak contribution would be unobservable.

Eg ss

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Rare decays0The decay can take place but is predicted to be incredibly

rare since higher orders/internal loops are needed.

The search for rare decays is useful for (1) testing our theories to high precis

LK e e

ion(2) looking for evidence of "new physics".Eg supersymmetry predicts many new heavy particles which can also manifest themselves in loops at low energy and which can thus change decay rates.

s

d

Wu

u

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0

0

Bubble chamber experiment at CERN, 1973.

Look for interaction:

Obs! We used neutrino to find about that the exists.

Later in this lecture we'll use the to tell us how many neutrinos ex

e e

Z

Z

ist.

e-

First evidence for neutral current weak processes

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Electroweak theory0

0,

The existence of the was not a great surprise. Electroweak theory predicted it would exist

(and the masses). The is necessary to ensure that calculations for certain processes were not dive

Z

W Z Z

rgent.

Electroweak theory was developed by Glashow, Weinberg and Salam (Nobel prize 1979).

It unifies the the weak and electromagnetic forces in a single theoretical framework.The details are very complex but it the achievement is on the same footing as theunification of the electric and magnetic forces into a single electromagnetic forcewith the Maxwell equations and special relativity.

What concerns us are the predictions and how they were confirmed by experiment.

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2 26400 GeVWM

Electroweak unification

e

0, , .

Electroweak theory states that the weak and electromagnetic forces look different at low

energies due to the masses of and At high energies combined electroweak force.From lecture 13:

Z W

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Electroweak theory predictions

2

0

12

0

4

sin cos2 2 2

Unification condition links the electromagnetic and weak couplings:

= =electromagnetic coupling constant (1.24)

(14.05) neutral current coupling (14.06)

Weak mixi

W W Z W Z

e

e g g g

02

3 0

ng angle cos (14.07)

Anomaly condition:

; sum over all leptons and quarks (14.08)

lepton charge , quark charge Also, each family individually satis

WW W

Z

aa

a

MM

Q Q a

Q Q

2 13 - 3 03 3

fies the anomaly condition.Eg first generation of lepton and quarks

(14.09)

ee u dQ Q Q Q e e e

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2 22

2

2 22 2

5 2

2

22

2sin 2 sin

1.166 10

For low energy charged current interactions, recall:

(2.39)

From (14.05) (14.10)

Fermi constant= GeV (2.37)

Using (14.07)

W WFW

W F

W WW F W

F

Z

g gG MM G

g MG

G

M

2 2

2 20 2

2

222

2 2

2 sin cos

22

sin

sin

(14.11)

Low energy weak interaction: (14.12) (14.13)

(14.14)

measure from rates of low energy charged and neutral curr

F W W

Z Z ZZ

Z Z

WZ ZW

F W Z

W

G

G g gZ MM G

MG gG g M

2

0

sin 0.227 0.014

78.3 2.4 89.0 2.0

ent processes.

Measurement (1981): (14.15)

Predicted and masses from the couplings. GeV ; GeV (14.16)

Consistent with masses measured i

W

W Z

W ZM M

n 1983 (UA1, UA2 experiments). Nobel prize (1983, Carlo Rubbia and Simon Van der Meer).

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A small correction2sin 0.2315 0.0001 (14.17)

77.5 0.03 88.41 0.04

80.4 0.02 91.188 0.002

Current measurement: from (14.10) and (14.11) GeV ; GeV (14.18)

Current direct mass measurements: GeV ; Ge

W

W Z

W Z

M M

M M

2 2

2 22 2

V (14.19)

We were wrong to use (2.39) and (14.12)

This neglected loop contributions as below. More precise calculations take these into account and obtain good agreement with t

WF Z Z

W Z

gG G gM M

†

†

he directly measured

masses

Hidden in this is an interesting principle - that the measured masses of particles are sensitive to the existence and properties (eg mass) of other particles.

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Strategy for directly observing Z0

0(1) Demonstrate how to measure the mass of the .

(2) Demonstrate how the same experiments also allow us to answer an interesting question.

We know there are three lepton doublets. Each doublet has on

Z

200

e charged lepton with massand a (just about) massless neutrino . Has nature only given us 3 families ?Are there more families i.e. heavier charged leptons (> GeV) that we can'tdirectly disco

ver at current colliders which are associated with light neutrinos in a doublet ?

Eg when we turn on the LHC is it likely we'll extend our table of leptons with a new

lepton pair: and YY

Lepton Charge (e) Mass (GeV)

e- -1 0.0005

e 0 0

-1 0.105

0 0

-1 1.8

0 0

Y- -1 > 200

Y 0 0?

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Measuring the mass and decays of a Z0

0

0

0

.

-interactions reminder.

Any process in which a photon is exchanged can also take place with a

In addition, the interacts with neutrinos.

Z

Z

Z

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Energy dependence

mostly

mostly

0 91.2 GeVZ

M

0

0

Consider annihilation reaction in centre-of-mass frame.

Can be mediated by photon or .

When is the photon contribution big

and the contribution small andvice versa ?

Photon contribution

e e

Z

Z

0

2

2

0

2 2

0

)

2

: (14.20)

contribution:

(for (14.21)

beam energy

mass of photon/ (14.22)

Z ZZ

CM

EZ

G E E M

E

E E Z

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LEP

0

Large Electron-Positron Collider at CERN, Geneva.Started 1989: 45 GeV + 45 GeV electrons and positrons.

Designed as a factory. Similar facility at SLAC, California: SLC. LEP was later upgraded to

Zhigher energies, eventually reaching 209 GeV

and almost finding (or finding depending on who you talk to) the Higgs boson.

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hadrons from LEP and other colliderse e

The Z0 resonance is what concerns us. What can we learn from it ?

LEP + SLD (at Z0)

Lower energy experiments

W W

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Resonances reminder

2

20

1

4

(4.11)m m

From lecture 4 Short-lived particles simply don’t have well-defined masses. Their masses follow a Breit-Wigner distribution

:decay from tedreconstruc Mass

770 MeV – ”nominal” mass

2

1 (4.12)

1 (nu) (MKS)

Consistent with uncertainty principle (1.27).

Γ Δm τ

Δmτ Δm c τ

E t

1 m E

:decay from mass Measured

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What an experiment observes

What is meant by ? What is ?Eg OPAL experiment at LEP.

Observe and count , eg number of hadronsevents.

Similarly could be observed andcounted - select events appropriate t

e e X X

e e

e e

, , .o the lepton species:

can't be observed in the detector.The neutrinos interact so weakly that they are never seen. We can still, however, work out that they were produced and count

e

e e

how many neutrino species exist!

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The Z0 resonance

01 25

0 02

22 2 2 2 2

1

2.495 0.0021 0.4 10

2.5

12

(4.12)

GeV (14.23)

GeV (14.24)

Consider any chosen observed final states,

(14.25)

Z

Z

Z

CM CM Z Z Z

m

m

s

e e XX

Z e e Z XMe e XE E M M

0 0

0 0

strength of production (time reversal symmetry) (14.26)

= decay rate of after production to specific final state . (14.27)

Z e e Z

Z X Z X

LEP

2.5 GeVm

hadronse e

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0 0

0

1

0 00 0

0 0 0 0

0

, ,

1.744 0.00

Recall: branching ratio for a given decay (2.11)

(14.28)

Measure measure

Fits to observed data:

hadrons

itot

Z Z

Z

i B

Z e e Z XB Z e e B Z X

B Z e e B Z X Z e e Z X

Z

0

0 0

0

0

0 0 0

0

2

0.0840 0.0009 , , .

, , .

3

GeV hadrons (14.29)

GeV for each lepton species: (14.30)

Make an assumption that decays only via:

hadrons

hadronsZ

Z Z qq

Z e

Z

Z Z Z

Z Z

0 0

0 0.499 0.004

(14.31)

number of neutrino species

GeV (14.32)

N Z

N

N Z

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There are three light neutrino species

Combined data from LEP experiments

0 0.166

3.00 0.05

GeV (calculated) (14.33)

(14.34)

A stunning result demonstrating the precision of particle physics measurements and theory.

there aren't any heavy chargedleptons with a

Z

N

ssociated light neutrinos.

from anomaly condition: neutrinos are massless there are only 3 generations of leptons and quarks. We've already found the fundamental fermions.

if

This is where we end the story.

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Goal: a theory which describes all of the fundamental constituents of nature and theirinteractions with the minimum of assumptions and free parameters. Ultimately describe all interactions over small distance scales and cosmological observations.The Standard Model is our best attempt at this - assess how successfult it is in lecture 15.

6 quarks, 6 leptons, 3 exchange bosons + antiparticles. Two independent forces (electroweak and QCD).

19 free parameters: particle masses, mixing angles,CP-violating term, couplings....

Consistent method of introducing interactions via so-called gauge invariance and Feynam diagram formalism (next lecture course).

The Standard Model assumes massless neutrinos but this is easily fixed.

Barring neutrino oscillations, the Standard Model has never failed a single experimental test.There is still one test left to pass - finding the Higgs boson.

The Standard Model

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The most rigorous test of the Standard Model to date: g-2

22

From the Dirac equation : Dipole moment and spin for a point-like fermion related by:

; (1.23)

This can be measured by experiments studying the response of an electron in a mag

e eeg S gm

12

12

2 1159652180.7 0.3 102

2 1159652153.5 28 102

netic field. Need to calculate higher orders:

Precision experimental result:

(14.35)

Dirac prediction + quantum corrections:

(14.36)

g

g

Basic interactionwith B field photon

Next to leading order correction

Higher order corrections

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Summary

● Neutral currents Flavour changing vertices

● Electroweak unification and measurement of the Z0 resonance 3 light neutrinos 3 fermion generations