5.4 Mechanisms of Subatomic Decays and Electron Radiations.
There is a probability for these weaktons inAandBto recombine and form new particles.
Then, after the new particles have been formed, in the exchange radiusR, the weak interacting
force between them is governed by the potentials of the new particles, and is repelling, driving
the newly formed particles apart.
For example, in Figure5.10we can clearly see how the weaktons in (5.4.3) undergo the
exchange process. When the randomly moving photons andν-mediators, i.e.w 1 w 1 ,w 2 w 2
andνeνecome into their exchange balls, they recombine to form an electronνew 1 w 2 and
a positronνew 1 w 2 under the weak interaction attracting forces generated by the weakton
potentials (5.4.5). Then, the weak interacting force betweene−=νew 1 w 2 ande+=νew 1 w 2
governed byΦwl in (5.3.15) is repelling, and pushes them apart, leading to the decay process
(5.4.2)
w 1 w ̄ 1w 2 w ̄ 2νe ̄νew (^1) w ̄ 1
w ̄ 2
νe
w ̄ 1 w ̄ 2
ν ̄e
νe
w 1 w 2
γ
γ
ν
w 2
ν ̄e
e+
e−
Figure 5.10
We remark here that in this range the weak repelling force betweene+ande−is much
stronger than the Coulomb attracting force. In fact, by (5.3.29),g^2 w∼ 1030 hc ̄ and the electric
charge squaree^2 = 1371 ̄hc. Hence the weak repelling force in Figure5.10is( 3 gs)^2 /r^2 , much
stronger thane^2 /r^2.
2.Weakton exchanges between leptons and mediators. Theμ-decay reaction formula is
given by
(5.4.6) μ−→e−+νe+νμ.
The complete formula for (5.4.6) is
μ−+ν→e−+νe+νμ,
which is expressed in the weakton components as
(5.4.7) νμw 1 w 2 +νeνe→νew 1 w 2 +νe+νμ.
By the exclusive ruleLeLμ=0, the two particlesνμandνecannot be combined to form a
particle. Hence,νeandνμappear as independent particles, leading to the exchange ofνμ
andνeas in (5.4.7).