226 CHAPTER 4. UNIFIED FIELD THEORY
4.5.3 Quark confinement
Quark model was confirmed by lots of experiments. However, noany single quark is found
ever. This fact suggests that the quarks were permanently bound inside a hadron, which is
called the quark confinement. Up to now, no other theories cansuccessfully describe the
quark confinement phenomena. The direct reason is that all current theories for interactions
fail to provide a successful strong interaction potential to explain the various level strong
interactions.
Now, we can derive the quark confinement by using the layered strong interaction poten-
tials (4.5.41).
The strong interaction bound energyEfor two particles is given by (4.5.43). In particular,
for two same particles we have
(4.5.45)
E=g^2 s(ρ)[
1
r−
A
ρ( 1 +kr)e−kr]
,
gs(ρ) =(
ρw
ρ) 3
gs.The quark confinement can be well explained from the viewpoint of the strong quark
bound energyEqand the nucleon bound energyEn. In fact, by (4.5.45) we have
(4.5.46)
Eq
En⋍
Aq
An(
ρn
ρq) 7
.
According to the physical observation fact,
(4.5.47) ρn⋍ 10 −^16 cm, ρq⋍ 10 −^19 cm.
Then, by (4.5.46) we derive that
Eq
En
⋍ 1021
Aq
An.
PhysicallyAq/Anis no small, and we assume thatAq/An⋍ 10 −^1. Then we have
(4.5.48) Eq= 1020 En.
It is known that the bound energy of nucleons is about
En∼ 10 −^2 GeV.Thus, we obtain by (4.5.48) that
Eq∼ 1018 GeV,
which is at the Planck level. This clearly shows that the quarks is confined in hadrons, and
no free quarks can be found.
Remark 4.19. The magnitude order (4.5.42) and (4.5.47) are not accurate, but they are
enough precisely to explain the important physical problems as the quark confinement and