The Standard Model and Beyond
[Secs 17.1 Dunlap]
Electro-Weak Unification
Sheldon Glashow
Abdus Salam
Steven Weinberg
The 1979 Nobel Prize went to Glashow, Salam and Weinberg for:
“for their contributions to the theory of the unified weak and
electromagnetic interaction between elementary particles”
It is arguably one of the most important theoretical achievements
of the 20th century. They predicted the W and Z particles
The Universal Fermi Interaction (UFI)
Not
but
n
p
Around 1935 Fermi had
postulated that particles carried
a “WEAK CHARGE” – just as
particles carried a “EM Charge”
– it should be the SAME IN ALL
WEAK processes – but no:
By 1963 Cabbibo mixing of
quarks had brought the UFI
back into line.
g
e
g
e
p→n 7% slower than
expected from muon decay.


W+
g


W+
e
g
e
Electro-Weak Unification
By the mid 1960s physicists started applying the principle of
“gauge invariance” to Weak interactions.
Application of “gauge invariance” to the EM field had led to
the knowledge of the  boson being force mediator.
e
e

Application of “gauge invariance” to the Weak field led to
another triplet set W-, W+, W0 of bosons being force mediators
(uw )
(uw ) (dw , uw , e ) (dw , uw , e )
(d w ) (d w )



e

e
e
e
e
e
W+
W-
W0
Electro-Weak Unification
 
uw
e
W±
e
W0
dw

W0
 
W0
e
W±
e

g+
uw
W±
dw
g-
SU2 (Special Unitary 2) symmetry
group – similar to pion (ud) and
nucleon (NN) symmetry
The neutrino was to the electron what the up
quark was to the down – members of a charge
doublet – but a weak charge doublet
Electro-Weak Unification
It was first proposed that the electro-weak force was governed
by the triplet of new bosons plus a singlet (another case of
2+2=3+1, 2 electric charge states – 2 weak charge states).
W-
W0
B0
W+
Triplet
Singlet
This theory required that (i) the masses of the Ws should be
zero and (ii) that the neutral W0 currents (force) be as strong
as that of the W± . But the Ws had to have mass to make the
weak force weaker than the electric force. Moreover the W0
force was found to be experimentally weaker than the W±.
Something was wrong!
Electro-Weak Unification
W-
W0
W+
B0
(Triplet)
(Singlet)
H0
(Higgs scalar field)
Z0
W-

W+
(Quartet)
It was discovered that the W0 is not the observed particle
eigenstate, but that a Higgs Field Particle H0 was mixing things up
to make a Z0 and a  ! The H0 also gave the W and Z mass.
Electro-Weak Unification
(Higgs scalar field)
H0
Z0
W-

W+
(Quartet)
The observed states  and Z0 are
mixtures of more the more
fundamental bosons W0 and a B0
B0
Where θW is the Weinberg angle ~28°
Electro-Weak Unification
Observed Strength GF of the Weak Interaction (as seen for
example in beta decay) relates to the electric force e2 /(40 )c

 e2
GF 

2
2
2.MW sin W
2  4 0  c.MW2 sin 2 W
The theory tells us that the observed force is much less than the
electric force by ~ (MW.sin θW)2. [θw=Weinberg angle ~ 28°]
Measurement of GF and sin2θW (as obtained from weak neutral
currents) was thus was able to predict the value of MW.
Neutral Weak Current (Z) GZ

 sin 2 W
Charged Weak Current (W) GF
Predicted masses of W and Z are 78
GeV/c2 and 89GeV/c2 which are close
to the observed values.
MZ
W
MW
Spontaneous Symmetry Breaking
Maxwell’s equations are spatially symmetric – defining no special
direction – yet a set of magnets (i.e. Fe atoms) tends to line up in some
arbitrary direction. There is a spontaneous breaking of the symmetry of
the EM laws.
In the same way the Higgs field breaks the massless symmetry of the
weak massless W fields. This causes the differentiation of the EM force
from the weak force at low energies < 100,000MeV (T= 1012K)
Most physicists believe that at the highest energy the universe has a
single symmetry – that has been broken down into the 4 forces.
The discovery of the W and Z
Carlo Rubbia
Simon Van-der-Meer
The 1984 Nobel Prize in physics was awarded to Rubbia and
Van-der-Meer who led the CERN team in finding the W and Z
particles.
Searching for the Higgs particle
Theoretician Peter Higgs postulated the
existence of the particle that bears his
name in 1964. No one has yet discovered
it – but the hunt is on.
It is expected to be produced in
the high energy interaction of
quarks, but no one really knows
how heavy it is. It is known to
be heavier than 60 GeV/c2.
LEP gave some evidence at
115GeV/c2 (1999). The Large
Hadron Collider (LHC) at CERN
– aimed at achieving 14TeV
(14,000GeV/c2) should be able
to find it – if it is there!
The Standard Model c2000
LEPTONS (E-W)
Leptons
e
e

HADRONS (S+E-W)

u
d
c
s
t
b
Quarks
Baryons
p
n
 ++  +  0  -
 0  + 
FERMIONS
 0

Mesons
0
-
K K0
0
Gauge
Bosons

W
W
Z0
 0
gi
BOSONS


The Standard Model c2000
LEPTONS (E-W)

Leptons
Gauge
Bosons
e
e



-
HADRONS (S+E-W)


W
W
-
u
d
c
s
t
b
g (1-8)
Z0
FERMIONS
Quarks
BOSONS
H0
The Higgs “H0” is expected to be responsible for the masses
of all the Fermions and Quarks as well as the W and Z.
Grand Unified Theories
EM
STRONG
WEAK
(i) The EM interaction gets stronger the closer one gets to the
particle, because surrounding the particle is a cloud of e+epairs from virtual photons that screen the central charge.
(ii) The Strong interaction – the color charge gets extended in
space. Shown is a red quark that has emitted RB gluons.
Penetrating particles see less Red charge.
(iii)The Weak interaction – same as the strong – an electron emits
W- particles that spread out the weak charge. A penetrating
particle sees less Weak charge.
Grand Unified Theories
Mass Energy
Strength of
Interaction
One thing we know about the Strong, Weak and EM interactions is
that their strength converges at energies ~ 1015 GeV
GUT predicts decay of proton
Through processes such as these the proton is expected to decay:
p  e 

0
i.e. to a positron plus a neutral pion. The SU5 theory predicts
that the proton’s half life should be between 1030 and 1033 years.
But Super-Kamiokande data put the half life as more than 1035
years. Simple SU5 now seems unlikely to be true.
[The life-time of the universe is only 1.5 x 1011years]