Subatomic Physics

7.6. Additive Quantum Numbers of Quarks 215
Table 7.1: Baryon Number A, Strangeness S,
Hypercharge Y , and Average Value of the
Charge Number Nq = q/e.
Particle A S Y 〈Nq〉
Photon γ 0 0 0 0
Pion π + π0π− 0 0 0 0
Kaon K + K0 0 1 1
1
2
Nucleon
Lambda
pn
Λ
1 0 1
1
2
0 1 −1 0 0
Sigma Σ + Σ0Σ− 1 −1 0 0
Cascade Ξ−Ξ0 1 −2 −1 − 1
Omega Ω
2
− 1 −3 −2 −1
particles, baryons and mesons. The principles become much more transparent,
however, if we assign additive quantum numbers to the quarks, which are the counterparts
to the leptons. Recall that a baryon is composed of three quarks, (qqq), a
meson of a quark and antiquark, (qq). Each quark has a specific individual additive
flavor quantum number, which distinguishes it from the others and is conserved in
hadronic and electromagnetic interactions. By assigning additive quantum numbers
to each quark, we easily find the quantum numbers of any hadron as the sum of
those of its component quarks. In order to agree with the values assigned by early
experiments, it is necessary to assign strangeness −1 tothes quark. Then the K + ,
composed of (us), has the assigned strangeness of +1; the Λ 0 ,composedof(uds),
has the desired strangeness −1; values of S for other hadrons are readily obtained.
These assignments also explain why baryons can have strangeness S ranging from 0
to −3, with the Ω − being composed of all s quarks (sss), whereas mesons only can
have strangeness S =0,and±1. The additive quantum number S, connected to the
quark s and the antiquark s, can appear in a covert or overt way: (ss) containstwo
strange objects, a strange quark and strange antiquark, but appears to the outside
as nonstrange. On the other hand, (us) contains one strange object, and exhibits
strangeness explicitly.
By 1964, three quarks had been introduced, but four leptons were known. Suggestions
for the existence of a fourth quark were made, for instance, by Bjorken and
Glashow, (28) who described the hypothetical quark by the additive quantum number
“charm.” In 1970, Glashow, Iliopoulos, and Maiani (29) introduced a model that
included the fourth quark, charm, showed quark–lepton symmetry, and explained
one unsolved problem, the strong suppression or absence of decays like K 0 → µ + µ −
and K ± → π ± e + e − (see Section11.4). The major breakthrough occurred with the
“November revolution” in 1974. Ting and his group at Brookhaven (30) and Richter
28 J. D. Bjorken and S. L. Glashow, Phys. Lett. 11, 255 (1964).
29 S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2, 1285 (1970).
30 J. J. Aubert et al., Phys. Rev. Lett. 33, 1404 (1974).