Mathematical Principles of Theoretical Physics

264 CHAPTER 5. ELEMENTARY PARTICLES

• Meson decays:

(5.1.15)

π+→μ++νμ,

π−→μ−+νμ,

π^0 → 2 γ,

K+→μ++νμ, π++π^0 , π++π++π−,

K−→μ−+νμ, π−+π^0 , π−+π−+π+,

K^0 →π++e−+νe, π++π−, π++π−+π^0 ,

η→ 2 γ, π++π−+π^0 ,

ρ±→π±+π^0 ,

ρ^0 →π++π−,

K∗±→K±+π^0 ,

K∗^0 →K^0 +π^0 ,

ω→π^0 +γ, π++π−+π^0.

5.1.4 Conservation laws

All particle transitions can be expressed in the form:

(5.1.16) A 1 +···+AN→B 1 +···+BK.

They are driven by the three fundamental forces: the electromagnetic, the weak, and the
strong interactions. Particle transitions have to obey certain basic conservation laws in the
sense that for certain conservative quantum numberq, its total values on both sides of (5.1.16)
are the same:

(5.1.17) qA=qB.

In addition, some conservation laws may not be valid for all interactions. For example, parity
is valid only in the strong and the electromagnetic interactions, and is violated in the weak
interaction.
We now introduce the basic conservation laws.

1.Energy conservation.Energy is an additive quantum number. The energy of a particle
is given by the formula

ε=c

√

P^2 +m^2 c^2 ,

wherePis the momentum, andmthe mass. Energy conservation is a law that all transitions
must obey. Namely, for (5.1.16),
N
∑
n= 1

εAn=

K

∑

k= 1

εBk,

whereεAnandεBkare the energies of particlesAnandBk.