This section uses units where (Planck's constant)/2p
and the speed of light = 1. This choice of units is called natural
units. With this choice, mass has units of inverse length,
and vice versa. The
This section uses units where (Planck's constant)/2p
and the speed of light = 1. This choice of units is called natural
units. With this choice, mass has units of inverse length,
and vice versa. The conversion factor is 2x10-7 eV = 1/meter.
Unification and group theory
The success of spontaneous symmetry breaking in explaining
electroweak physics led physicis to wonder whether the three particle
theories of the SU(3)xSU(2)xU(1) model
could be the spontaneously broken version of a higher unified theory
at some higher energy scale, a single theory with only one gauge group
and one coupling constant. This type of theory is called a Grand
Unified Theory, or GUT for short.
The quantum behavior of the known particle coupling
constants supports the idea of Grand Unification. Because of renormalization,
the electromagnetic coupling constant grows larger
at high energies, whereas the coupling constants for the weak and strong
nuclear interactions grow smaller at
higher energies. At the mass scale
the three coupling constants become equal. Therefore, this ought to
be the mass scale where the single gauge symmetry of a Grand Unified
Theory would become spontaneously broken into the three distinct gauge
symmetries of the SU(3)xSU(2)xU(1) model.
The single gauge group of a GUT has to be mathematically
capable of containing the group product SU(3)xSU(2)xU(1)
of the three gauge groups relevant to low energy particle physcs. The
best candidate for such a theory is unitary group SU(5),
which would give 24 gauge bosons mediating the single unified force,
but there are also other GUT models based on other groups, such as the
orthogonal group SO(10), which would
give 45 gauge bosons and contain the SU(5) theory as a subgroup.
The problem with Grand Unification is that the unified
gauge bosons allow quarks to couple to leptons in such a way that two
quarks can be converted into an antiquark and an antilepton. For example,
two up quarks would be allowed to turn into a positron and and a down
A proton consists of two up quarks and and down quark.
A neutral pion consists of a down quark and a down antiquark. Therefore
the unified gauge boson in a GUT could mediate proton decay by the interaction
and other related decays.
The proton lifetime predicted in a GUT is about
whereas the current best measurement of the proton lifetime is
It's important to note here that proton decay can happen through radiative
corrections even in the Standard Model, so we don't expect the proton
lifetime to be infinite.
However, it seems that the proton doesn't decay as
quickly as predicted by a GUT. This situtation is improved when supersymmetry
is added to the GUT, and this will be explained in next section.
What about gravity?
Einstein's elegant and experimentally tested theory
of gravity called General
Relativity is not a normal gauge theory like electromagnetism.
The symmetry is not a unitary group symmetry like U(1)
or SU(3), but instead a symmetry under
general coordinate transformations in
four spacetime dimensions. This does not lead to a renormalizable quantum
field theory, and so gravity cannot be unified with the other three
known physical forces in the context of a Grand(er) Unified Theory.
But string theory claims to be