Mathematical Principles of Theoretical Physics

5.4. MECHANISMS OF SUBATOMIC DECAYS AND ELECTRON RADIATIONS 307

It is clear that the final particles are the protonpand mesonπ+. Hence by the criterion
(5.4.16), the∆++decay is a strong type. Recalling the weakton constituents in (5.3.19) and
the quark constituents of hadrons in Section5.1.1, the first reaction formula in (5.4.24) is
rewritten as

(5.4.25) 3 w∗w 1 w 1 (∆++)+w∗w∗(g 0 k)+w 1 w 1 (γ 0 )+w 2 w 2 (γ 0 )

→( 2 w∗w 1 w 1 )(w∗w 1 w 2 )(p)+ (w∗w 1 w 1 )(w∗w 1 w 2 )(π+).

This reaction process in (5.4.25) consists of two steps:

(5.4.26) weakton exchanges: gk 0 + 2 γ 0 →d+d,

(5.4.27) quark exchanges: uuu+dd→uud+ud.

The exchange mechanism of (5.4.26) was discussed in (5.4.22), which is a weak interaction,
and the quark exchange (5.4.27) is both weak and strong interaction types. But, the final
particlespandπ+are driven apart by the strong hadron repelling force.
After the weakton exchange to yieldd-quark pair in (5.4.26), the mechanism of the quark
exchange and decay in (5.4.27) can be interpreted as follows:

1) When the quark pairddis formed in the exchange radiusRof∆++, the strong and

weak interactions between the quarksd,dandu,u,uin∆++are governed byΦsqin

(5.3.12) andΦwqin (5.3.15), which are attracting and recombine these quarks to form

two new hadronspandπ+, as shown in Figure5.13(a); and

2) the two newly formed hadronspandπ+are controlled by the strong interaction poten-

tialΦnfor hadrons, which is repulsive in the exchange radiusRand pushes them apart;

see Figure5.13(b).

u u u

d d ̄

u u

ud ̄

d

(a)

u u

ud ̄

d

u u

ud ̄

d

(b)

Figure 5.13

2.D^0 -decay.Let us discuss theD^0 -decay, which is considered as the weak interacting
type in the classical theory, because it violates the strange number conservation. But in our
classification it belongs to strong type of interactions. TheD^0 -decay is written as

D^0 →K−+π+.

The complete formula is
D^0 +gk+ 2 γ→K−+π+.