Subatomic Physics

5.9. Baryon Ground States 105
Japanese theoretical physicist, then suggested in a brilliant paper that a “new sort
of quantum” could be responsible. (25)
Yukawa’s arguments are more mathematical
than we can present here, but the analogy
to the virtual photon exchange permits an estimate
of the mass m of the “new quantum,”
the pion. In Yukawa’s approach, the force between
two hadrons, for instance two neutrons,
is mediated by an unobserved pion, as sketched
in Fig. 5.19.
Figure 5.19: Exchange of a virtual
pion between two neutrons.
The minimum energy of the virtual pion is given by E = mπc 2 and its maximum
velocity by c. With Eq. (5.49), the maximum distance that the virtual pion is
allowed to travel by the uncertainty relation is given by
R ≤ cT = �
≈ 1.4 fm. (5.52)
mπc
The range is therefore at most equal to the Compton wavelength of the pion. Originally,
of course, the argument was turned around, and the mass of the postulated
hadronic quantum was estimated by Yukawa as 100 MeV/c 2 .
Physicists were delighted when a particle with a mass of about 100 MeV/c 2 was
found in 1938. Delight turned to dismay when it was realized that the newcomer, the
muon, did not interact strongly with matter and hence could not be held responsible
for the hadronic force. In 1947, the true Yukawa particle, the pion, was finally
discovered in nuclear emulsions. (26) After 1947, more mesons kept turning up, and
at present the list is long. Some of these new mesons live long enough to be studied
by conventional techniques. Some decay so rapidly that the invariant-mass-spectra
method, discussed in Section 5.3, had to be invented. A list of the known mesons
can be found in PDG.
The fact that the idea of virtual quanta led to the prediction of the existence
of a new particle is important. Even more important, however, is the powerful
concept that forces between elementary particles are caused by the exchange of
virtual particles and we will return to this concept again later.
5.9 Baryon Ground States
The spectrum of baryons is even richer than that of mesons. We begin the survey
by considering nuclear ground states. By about 1920 it was well established that the
25 H. Yukawa, Proc. Math. Soc. Japan 17, 48 (1935). Reprinted in D.M. Brink, Nuclear Forces,
Pergamon, Elmsford, N. Y., 1965. This book also contains a reprint of the articles by G.C. Wick
on which our discussion of the connection between force range and quantum mass is based.
26 C. M. G. Lattes, H. Muirhead, G. P. S. Occhialini, and C. F. Powell, Nature 159, 694 (1947).