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The Standard Model
The Standard Model combines the
electromagnetic, weak, and strong
forces (= interactions).
boson
fermion
fermion
Bosons with spin 1 communicate the
force between fermions with spin ½.
Glashow
An extra feature is the
Higgs boson with spin 0.
Salam
Weinberg
Bosons
Three sets of bosons mediate three interactions:
Electromagnetic
photon
Weak
Z, W
Strong
gluons
The principle stays the same, only the players change:
• Bosons communicate interactions between fermions.
• Each interaction has its characteristic set of bosons.
The Higgs boson
• The Higgs boson is unique. There is no other fundamental
particle with spin 0.
• It was concocted by theorists to explain why the Z ,W
bosons have mass while the photon and the gluons don’t.
• It also describes the mass of fermions (electron, quarks).*
• The Higgs particle was observed at the LHC in 2012.
* However, the influence of the Higgs boson on the mass of humans, stars,
and galaxies is negligible. These are made of atoms, whose mass is dominated by the mass of their nucleons. Those consist of quarks and gluons.
The quark mass is < 2% of the nucleon mass (Slide 7) and the gluon mass
is zero. Instead, the nucleon mass is dominated by the kinetic energy of
quarks and gluons, converted to mass using E =m c2.
How the Higgs field creates mass
Mathematically , the mass comes from a clever manipulation of quantum
fields. But it is hard to describe in plain words. The British Science Minister
Waldegrave challenged physicists in 1993 to produce an explanation on a
single sheet of paper. The result can be condensed into a few bullets:
• The Higgs field fills space like molasses, attaching itself to particles.
• When a particle is accelerated, it has to drag the Higgs field along.
That reduces its acceleration a.
• Newton’s F= ma tells us that a smaller acceleration a for the same
force F implies a larger mass m.
The Higgs field is different
The Higgs field oscillates around a non-zero average.
All other fields oscillate around zero , for example the
electric and magnetic field of an electromagnetic wave.
Higgs field
All other fields
0
0
non-zero average
Fermions
Three generations, each consisting of lepton and quark pairs.
light
heavier
heaviest
‘Who ordered that?’ (Isaac Rabi)
Is there a 4th generation ?
The green curve is calculated for 3 neutrino
generations. It fits the
data perfectly.The red
curves for 2 and 4 generations don’t fit.
Number of observed particles
Are there more than three particle generations ? This question can be
answered by measuring the number of particles that originate from the
decay of a Z boson.The Z itself is produced by an electron-positron pair.
Z
boson
Energy (GeV)
Why are there three generations of fermions ?
We are still clueless.
Convergence of the three interactions
The strength of an interaction is determined by its coupling constant .
Inverse coupling constant
Electromagnetic
Coupling ‘constants’ are not constant.
They change with energy. At energies
approaching the Planck energy they
seem to converge to a single, unified
coupling constant.
Weak
This convergence is improved by introducing a new symmetry called supersymmetry, which predicts a new set of
supersymmetric particles with masses
>1TeV.The coupling constants converge
to a value close to the number 1/8 .
Strong
1
Energy (GeV)
TeV
Planck Energy
Caution! This is an extrapolation over 13 orders of magnitude in energy.
The anthropic principle
The Standard Model does extremely well at predicting all
kinds of measurements done by accelerators. But it is not
able to calculate coupling constants.
Some argue that coupling constants cannot be calculated:
Different universes may have different coupling constants.
Our universe has a particular set of coupling constants because otherwise humans would not exist and contemplate
this question. For example, the Sun can’t be too hot or too
cold for life. That would happen with an electromagnetic
coupling constant slightly smaller or larger than 1/137.
This is a slick excuse for our inability to predict the many
numbers that the Standard Model cannot calculate ( 20).