Subatomic Physics

214 Additive Conservation Laws
determines the strangeness of the K 0 as positive. This assignment raises a question.
We have
S(K + )=1, S(K − )=−1
S(K 0 )=1, ?
Something is missing: We have two kaons with S = 1 and only one with S = −1.
Gell-Mann therefore suggested that K 0 should also have an antiparticle, K 0 ,with
S = −1. This antiparticle was found; it can, for instance, be produced in the
reaction.
pπ + −→ pK + K 0 .
The existence of the two neutral kaons, different only in their strangeness but in no
other quantum number, gives rise to truly beautiful quantum mechanical interference
effects; they will be discussed in Chapter 9. These effects are the subatomic
analog to the inversion spectrum of ammonia.
For some discussions it has become customary to use the hypercharge Y rather
than strangeness for ordinary and strange particles; the hypercharge Y is defined by
Y = A + S. (7.48)
In Table 7.1 we list the values of baryon number, strangeness, and hypercharge for
some hadrons. In the last column we give the average value of the charge number
of the particles listed in the relevant row. This quantity will be used later.
Table 7.1 provides considerable food for thought, and a few remarkable facts
stand out. Some of these we shall be able to explain later. First we note that
the number of particles in each row varies. There are three pions, two kaons,
two nucleons, one lambda, and so forth. Why? We shall give an explanation in
Chapter 8. Second, we remark that all antiparticles exist and have been found.
In some cases the set of antiparticles is identical to the set of particles. When
can this happen? Equation (5.64) states that a particle can be identical to its
antiparticle only if all additive quantum numbers vanish. The only particles in
Table 7.1 satisfying this condition are the photon and the neutral pion. The pion
set is identical to its own antiset, and the positive pion is the antiparticle of the
negative one. All other entries in Table 7.1 are different from their antiparticles.
Third, we note that for physical particles
�
q
�
Y =2〈Nq〉 =2 , (7.49)
e
and this relation will be used later.
7.6 Additive Quantum Numbers of Quarks
The additive quantum numbers listed in Table 7.1 are not complete; additional ones
have been discovered. Before discussing the newer ones, we change the basic style
of assignments. Up to now we have discussed the quantum numbers of the observed