140 The very early universe
This color combination would only occur if the unit matrix were among theλ
matrices. But the unit matrix was excluded when we decided to restrict ourselves
to theSU( 3 )group instead of theU( 3 )group. TheU( 3 )group would have an extra
U( 1 )gauge boson decoupled from the other gluons. This boson would induce long
range interactions between all hadrons regardless of electrical charge, in obvious
contradiction with experiments.
In contrast to photons, gluons interact with each other. The Lagrangian for non-
Abelian gauge fields contains third and fourth powers in the field strengthAand
the corresponding interaction vertices have three and four legs respectively.
Conservation laws are easily determined from the elementary vertices. First of
all, we see that quark flavor does not change in strong interactions and this leads to
numerous flavor conservation laws. The total number of quarks minus the number of
antiquarks also remains unchanged, and hence the total baryon number is conserved
(by convention a quark has baryon number 1/3 and an antiquark− 1 /3). In addition,
there is a color conservation law which is analogous to electric charge conservation
in electrodynamics.
At first glance, the number of quarks (6 flavors×3 colors=18 quarks) seems
too large to give an elegant explanation of the “Periodic Table of the hadrons”:
the Periodic Table of chemical elements is built out of only two elementary con-
stituents−protons and neutrons. However, one should not forget that unlike the
chemical elements, which can be composed from an arbitrary number of protons
and neutrons, the few hundred hadrons consist only of quark–antiquark pairs or of
three quarks. To be precise, all mesons are composed of quark–antiquark pairs and
all baryons consist of three quarks. For instance, the lightest baryons, the proton
and the neutron, are composed ofuudanduddquarks respectively. The lightest
meson,π+,is made of auquark and ad ̄antiquark.
There is a deep reason why two or four quark bound systems do not exist as
free “particles.”Every naturally occurring particle should be a color singlet. This
statement is known as theconfinementhypothesis, according to which colored par-
ticles, irrespective of whether they are elementary or composite, cannot be observed
below the confinement scale. In particular, quarks are always bound within mesons
and baryons.
As we have seen, the colorless gluon state (rr ̄+bb ̄+gg ̄) does not enter the
fundamental Lagrangian (4.19). Therefore, it is natural to assume that the appro-
priate colorless composite particles are “neutral” with respect to strong interaction
and can exist at any energy scale. The above color singlet can be built only as a
quark–antiquark pair and corresponds to mesons. Another possible color singlet is
a three-quark combination:(rbg−rgb+grb−gbr+bgr−brg),and it corre-
sponds to baryons. All other colorless states can be interpreted as describing few
mesons or baryons.