Mathematical Principles of Theoretical Physics

5.1. BASIC KNOWLEDGE OF PARTICLE PHYSICS 265

2.Momentum conservation.Momentum is vectorial additive. For two particlesA 1 and
A 2 , their total momentumP= (P 1 ,P 2 ,P 3 )equals to

Pk=PkA^1 +PkA^2 , 1 ≤k≤ 3 ,

wherePA^1 andPA^2 are the momentums ofA 1 andA 2.
Momentum conservation is a universal conservation law, andfor (5.1.16) the following
equality holds true:
N
∑
n= 1

PAjn=

K

∑

k= 1

PBjk, 1 ≤j≤ 3.

3.Angular momentum conservation.This quantum number is vectorial additive. The
angular momentum~Jof a particle consists of the orbital angular momentumLand spin~S:

~J=~L+~S, ~L=~r×P, Pis the momentum.

Angular momentum conservation law is also a universal conservation law, and for (5.1.16),

N

∑

n= 1

~JAn=

K

∑

k= 1

~JBk.

4.Other universal conservation laws.In particle physics, the following quantum numbers
are additive and conservative in all interactions: the electric chargeQe, the lepton numbers
Le,Lμ,Lτ, and the baryon numberB.
Table5.1lists the conservation or non-conservation properties of quantum numbers for
the three interactions.

Remark 5.2.CPcombines charge conjugationCand parityP, andCPTcombinesCPand
time reversalT.
CombinedCPTconservation was proved by G. L ̈uders and W. Pauli independently in
1954, calledCPTtheorem. TheCPTconservation is an important result in quantum physics.
Based onCPTtheorem, we can deduce that particles and antiparticles have the same masses
and lifetimes, and their magnetic moments are reversal withthe same magnitudes.

5.1.5 Basic data of particles

Here, we list the basic data for leptons, quarks, and hadronsin Tables5.2-5.5. The units are:
mass in MeV/c^2 , lifetime in seconds, and electric charge in the unit of proton charge.
Note that the quantum numberQwin Table5.2represents the weak charge number. Here
the values ofQware based on the weakton model in Section5.3.
Also, all neutrinos possess left-hand spin withJ=−^12 , and antineutrinos possess right-

hand spin withJ=^12. Namely, neutrinos move at the speed of light.
In addition, the data ofW±,Z,H^0 are given as follows.
W±:m= 80 .4 GeV/c^2 , Qe=± 1 , τ= 3. 11 × 10 −^25 ,
Z:m= 91 .2 GeV/c^2 , Qe= 0 , τ= 2. 67 × 10 −^25 ,
H^0 :m=126 GeV/c^2 , Qe= 0 , τ= 10 −^21.