Mathematical Principles of Theoretical Physics

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306 CHAPTER 5. ELEMENTARY PARTICLES


w 1 w 2

νμ

w 1 w 2
νe

w 1 w 2

νe

νe

νμ

νμ

e−
μ−

Figure 5.12:e-μscattering.

They are rewritten in the weakton constituent forms as


(5.4.21) w∗w∗⇈(gk)+w 1 w 1 ↓↑(γ 0 )+w 1 w(γ)


→w∗w 1 w 1 ↑↓↑(u)+w∗w 1 w 1 ↑(u),

(5.4.22) w∗w∗↑↓(gk 0 )+w 1 w 1 ↑↓(γ 0 )+w 2 w 2 ↓↑(γ 0 )


→w∗w∗↑↓(gk 0 )+w 1 w 2 ↑↓(H−)+w 1 w 2 ↓↑(H+)
→w∗w 1 w 2 ⇈↓(d)+w∗w 1 w 2 ↑(d).

In (5.4.21),w∗andw∗in a gluon are captured by a scalar photonγ 0 and a photonγto create
a pairuandu. In (5.4.21),w 1 andw 2 in the two scalar photonsγ 0 are exchanged to form a
pair of charged HiggsH+andH−, thenH+andH−capturew∗andw∗respectively to create
a pair ofdandd.


4.Lepton decays.The lepton decays

μ−+ν→e−+νe+νμ,
τ−+ν→μ−+νμ+ντ,

are rewritten in the weakton constituents as


(5.4.23)


νμw 1 w 2 +νeνe → νew 1 w 2 +νe+νμ,
ντw 1 w 2 +νμνμ → νμw 1 w 2 +νμ+ντ.

Here the neutrino exchanges form leptons in the lower energystates and a pair of neutrino
and antineutrino with different lepton numbers. By the exclusive ruleLiLj= 0 (i 6 =j), the
generated neutrino and antineutino cannot be combined together, and are separated by the
weak interaction repelling force.


Strong types


1.∆++-decay.Consider the following decay

∆++→p+π+.

The complete decay process should be


(5.4.24)


∆+++gk 0 + 2 γ 0 →p+π+,
∆+++gk+ 2 γ→p+π+.
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