Mathematical Principles of Theoretical Physics

262 CHAPTER 5. ELEMENTARY PARTICLES

Here are a few important scatterings in the history of quantum physics:

Compton scattering: γ+e−→γ+e−,

Pair annihilation: e++e−→γ+γ,

Pair creation: γ+γ→e++e−,

Moller scattering: e−+e−→e−+e−,

Bhahba scattering: e−+e+→e−+e+.

Deep inelastic scattering : e−+p→e−+p+π^0.

3.Radiations. Radiations include the electromagnetic radiation and the gluon radiation.
The first one is that electrons emit photons:

(5.1.9) e−→e−+γ,

and the second one is that quarks emit gluons

(5.1.10) q→q+gk,

Electromagnetic radiations are caused in two scenaries:

1) As an electron changes its velocity, it emits photons. This radiation is called the

bremsstrahlung. The radiation energy in unit time can be expressed by the formula:

W=

2

3

e^2

c^3

a^2 withabeing the average acceleration.

2) As an electron at a higher energy levelE 1 undergoes a transition to a lower energy

levelE 0 <E 1 , it emits photons. The energyεof the emitting photons equals to the

difference of energy levels:

ε=E 1 −E 0.

In summary, there are three types of particle transitions: decays, scatterings, and radia-
tions. They are the main dynamic behavior for micro-particles, and reveal the interior struc-
ture of particles, and provide crucial information about the three interactions associated with
the electromagnetic, the weak, and the strong forces.
Here we list some principal decay forms:

• Lepton decays:

(5.1.11)

μ−→e−+νe+νμ,

μ+→e++νe+νμ,

τ−→e−+νe+ντ,

τ−→μ−+νμ+ντ,

τ−→π−+ντ,

τ−→ρ−+ντ,

τ−→K−+ντ.