A common feature of all such Feynman diagrams is the
virtual particle(s) being exchanged
[created on one side and annihilated on the other]
between the interacting particles. They are called
``virtual'' because they never manifest themselves directly
outside the scattering region; of course, in most cases
the same sorts of particles can be ``knocked clear''
of the collision by appropriate combinations of momenta,
but then the diagram has a different topology.
For instance, in Fig. 2
the right-hand diagram involves a simple rotation of the
left-hand diagram by 90
- so it describes in some sense
``the same physics'' - but the process depicted, in which a
positron and an electron ``temporarily annihilate'' into a photon
and then that photon immediately converts into a new 
pair,
is nominally quite different from the electron-electron scattering
in the left diagram. Any 
adept would automatically think of
both as being more or less the same thing.
Figure:
Left: Feynman diagram for electron-electron scattering
by single photon exchange.
Right: ``Crossing symmetry'' diagram for electron-positron
scattering in the ``s-channel'' by virtual photon annihilation and
pair production.
How is it possible to create a particle ``out of nothing''
as pictured in these diagrams? Only by virtue of the
time-energy version of Heisenberg's uncertainty principle,
which says that you can ``cheat'' energy conservation by
an uncertainty 
, but only for a short time
such that
The bigger the ``cheat,'' the shorter the time.
For photons, with no rest mass, a minimum of energy has to be ``embezzled'' from the ``energy bank'' to create a virtual photon; as a result it can travel as far as it needs to find another charged particle to absorb [annihilate] it. A heavier particle, on the other hand, cannot live for long without either being reabsorbed by the emitting particle or finding a receiver to annihilate it; otherwise the uncertainty principle is violated. This brings us back to Yukawa.
Around Yukawa's time every physicist knew that atomic nuclei were composed of nucleons (protons and neutrons) confined to an extremely small volume. The problem with this picture is that the protons are all positively charged and the neutrons are (as the name suggests) neutral, so that such a nucleus entails keeping positive charges very close to each other - something that Coulomb repulsion would rather they didn't do! Therefore (reasoned Yukawa) there must be a ``strong'' attractive force between nucleons that was able to overpower the electrostatic repulsion.
But if the strong force were long-range (like the electromagnetic force), then all nucleons everywhere would ``reach out to someone'' and fall together into one gigantic nucleus! This appears not to be the case, luckily for us. Therefore (reasoned Yukawa) the strong force must be short-range.
Now, we have just finished describing what would make a force
have a short range - namely, the uncertainty principle:
if the virtual quanta (particles) mediating the force
are moderately massive [ ``mesons''] then
they require a big ``cheat'' of energy conservation to be
created in the first place, and must be annihilated again
very soon to have existed at all. Yukawa compared the known
size of nuclei (about 
m) with the uncertainty
principle, assuming propagation at roughly the speed of light,
and deduced that the mesons mediating the strong force
must have a mass of about 130 MeV
.
Figure:
Left: Feynman diagram for proton-proton scattering
by single pion exchange.
Right: ``Crossing symmetry'' diagram for proton-antiproton
scattering in the ``s-channel'' by virtual annihilation into a 
followed by proton pair production. Note the similarity with the
Feynman diagrams for 
, where the pion's role is played by a photon.
A few years later, muons were discovered in high-energy
cosmic rays,
and the physics world was quick to acclaim them as Yukawa's
mesons. Unfortunately, they were wrong; the muon is a
lepton, like the electron or the neutral neutrinos,
which accounts for its penetration through the atmosphere
(leptons do not interact strongly).
This quickly became clear,
and shortly thereafter the true ``nuclear glue'' meson, the
pion, was discovered in very high-altitude cosmic
ray experiments and at the 184 inch Cyclotron in Berkeley.
Then high energy physics began in earnest.
