Mathematical Principles of Theoretical Physics

284 CHAPTER 5. ELEMENTARY PARTICLES

Y

K+(pΛ) ̄

π+( ̄np)

I 3

K−( ̄pΛ) K ̄^0 ( ̄nΛ)

π−(np ̄) η π^0

K^0 (n ̄Λ)

Figure 5.6

Table 5.6

Sakataons I I 3 Q S B

p 1 / 2 + 1 / 2 +1 0 +1

n 1 / 2 − 1 / 2 0 0 +1

Λ 0 0 0 -1 +1

In addition, from the quantum numbers of the three particles(5.2.63) , we can deduce the
quantum numbers for the eight mesons in (5.2.65); see Table5.6and5.7.

In Table5.7,Jis the spin andπis the parity. HenceJπ= 0 −represents that spinJ= 0
and parityπ=−1.

The Sakata model explains the mesons well. However, it encounters difficulties if we
use this model to describe baryons. In fact, if we use the three sakataons to form a baryon,
then the baryon numberB=3 for a baryon. Hence, we have to use two sakataons and one
anti-sakataon to form a baryon to ensureB=1. Unfortunately those combinations do not
agree with experiments.

5.2.6 Gell-Mann-Zweig’s quark model

Based on the Eightfold Way, as shown in Figures5.2-5.5, the hadrons are classified as fol-
lows:

{

Mesons(J= 0 ): 8 particles,

Mesons(J= 1 ): 8 particles,







Baryons(J=

1

2

): 8 particles,

Baryons(J= 3 / 2 ): 10 particles.