Mathematical Principles of Theoretical Physics

(Rick Simeone) #1

304 CHAPTER 5. ELEMENTARY PARTICLES


With the weakton model, all decays are carried out by exchanging weaktons. Hence decay
types can be fully classified into three types: the weak type,the strong type, and the mixed
type, based on the type of forces acting on the final particlesafter the weakton exchange
process.
For example, the reactions


(5.4.13)


νμ+e− → μ−+νe,
n → p+e−+νe,
π^0 → γ+γ.

are weak decays,


(5.4.14) ∆++→p++π+


is a strong decay, and


(5.4.15) Λ→p++π− (i.e.Λ+gk+ 3 γ→p++π−+γ)


is a mixed decay.
In view of (5.4.13)-(5.4.15), the final particles contain at most one hadron in a weak decay,
contain no leptons and no mediators in a strong decay, and contain at least two hadrons and a
lepton or a mediator in a mixed decay.
In summary, we give the criteria for decay types based on the particles appearing in the
final step of the decay process:


(5.4.16)


weak decay: at most one hadron,
strong decay: no leptons and no mediators,
mixed decay: others.

Remark 5.14.The new classification is easy to understand, and the criterion (5.4.16) pro-
vides a convenient method for us to distinguish the different types of decays and scatterings.
In fact, this classification truly reflects the roles of interactions in particle reaction processes.


5.4.4 Decays and scatterings


Decays and non-elastic scatterings are caused by weakton exchanges. The massless mediators


(5.4.17) γ,gk,γ 0 ,gk 0 ,ν,


spread over the space or around the charged leptons and quarks at various energy levels, and
most of them are at low energy states. It is these random mediators in (5.4.17) entering the
exchange radius of matter particles that generate decays. In the following we shall discuss
these reaction processes for various types of decays and scatterings.


Weak types



  1. First we consider thee-μscattering


νμ+e−→μ−+νe,
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