Mathematical Principles of Theoretical Physics

308 CHAPTER 5. ELEMENTARY PARTICLES

The weakton constituents of this decay is given by

(w∗w 2 w 2 )(w∗w 1 w 1 )(cu)+w∗w∗(gk)+ 2 w 1 w 1 (γ)

→(w∗w 1 w 2 )(w∗w 1 w 1 )(cu)+ (w∗w 1 w 1 )(w∗w 1 w 2 )(ud).

This reaction is due to thec-quark decay

c+gk+ 2 γ→s+u+d,

which is given in the weakton constituents as

(5.4.28) w∗w 2 w 2 (c)+w∗w∗(gk)+ 2 w 1 w 1 (γ)→w∗w 1 w 2 (s)+w∗w 1 w 1 (u)+w∗w 1 w 2 (d).

The reaction (5.4.28) consists of two exchange processes:

(5.4.29) w∗w 2 w 2 (c)+w 1 w 1 (γ)→w∗w 1 w 2 (s)+w 1 w 2 (w−),

and

(5.4.30) w 1 w 2 (W−)+w 1 w 1 (γ)+ (w∗w∗)(gk)→w∗w 1 w 1 (u)+w∗w 1 w 2 (d)

It is clear that both exchanges (5.4.29) and (5.4.30) belong to weak interactions. However,
the final particles in theD^0 -decay areK−andπ+, which are separated by the strong hadron
repelling force. The principle for the quark exchange and hadron separation in theD^0 -decay
process is the same as shown in Figure5.13.

Remark 5.15.In the mechanism of subatomic particle decays and scatterings, the layered
properties of the weak and strong interacting forces play a crucial role. Namely the attract-
ing and repelling radii of weak and strong forces for a particle depend on its radiusρand
interaction constantsAandBor equivalently the parameters

(5.4.31)

A

ρ

in (5.3.11) and

B

ρ

in (5.3.14).

These parameters determine the attracting and repelling regions of the particle. Hence, in the
exchange radius of particles, the weak and strong forces areattracting between weaktons and
quarks, and are repelling between the final particles in decays and scatterings. The reason is
that the parameters in (5.4.31) are different at various levels of subatomic particles.

Mixed decays

The typical mixed decay is theΛ-decay, written as

Λ→p+π−.

The correct form ofΛ-decay should be

(5.4.32) Λ+gk+ 2 γ+γ 0 →p+π−+γ 0.