Fair enough, obviously these symmetries were trying
to tell us something about the composition of hadrons. What?
Well, needless to say, Gell-Mann did not immediately
come up with a simple nuts-and-bolts assembly manual;
instead, they developed an abstract mathematical description
called analogous to the description of spin
for electrons,
. [If you're interested, the
acronym stands for Simple Unitary group of order 2 or 3.]
I won't attempt to elaborate, but you can see why something
like this was needed - as for the
component of
spin, the projections of the three
operators
along God-only-knows what axes in God-only-knows what
dimensions
cannot have a continuum of possible values but only a fixed
number of discrete or quantized values.
What is actually refers to is totally unknown.
Or, more properly, it refers to just what it says; if that
means nothing to us, well, that's just because our empirical
personal experience of the space of
is so limited
that we don't relate to it very well. What do ``normal''
space and time actually refer to?
Anyway, someone inevitably formulated a simpler instruction manual
for assembling hadrons. This was to give the requisite properties
to three (there are more now, but hold off on that) really
fundamental component particles called
`` quarks.''
All mesons are composed of a quark-antiquark pair
whereas baryons are composed of three quarks
held together by a `` superstrong'' force mediated by
a new type of intermediary called `` gluons'' (g)
[more cuteness, but who can argue...].
Table:
The known (or suspected) ``generations'' of quarks
All quarks have a ``baryon number''
as well as fractional electric charge
because it takes 3 to make one baryon.
The ``hypercharge''
of any particle is the sum of
its baryon number and its strangeness:
.
For each quark there corresponds an antiquark
of the same mass, spin, parity and isospin,
but with opposite values of electric charge, strangeness,
baryon number and hypercharge.
Figure:
Upper left: the three lowest-mass quarks.
Lower left: the corresponding antiquarks.
Right: the spin- baryons.
The
(strangeness -3) was predicted by
a ``quark content'' analysis and later found experimentally,
convincing everyone that the
model was correct.