302 CHAPTER 5. ELEMENTARY PARTICLES
3.Weakton exchanges between quarks and mediators. Thed-quark decay in (5.3.2) is
written as
(5.4.8) d→u+e−+νe.
The correct formula for (5.4.8) is
d+γ+ν→u+e−+νe,which, in the weakton components, is given by
(5.4.9) w∗w 1 w 2 +w 1 w 1 +νeνe→w∗w 1 w 1 +νew 1 w 2 +νe.
In (5.4.9), the weakton pairw 2 andw 1 is exchanged, andνeis captured by the new doublet
w 1 w 2 , which is the vector bosonW−, to form an electronνew 1 w 2.
5.4.2 Conservation laws
The weakton exchanges must obey certain conservation laws,which are listed in the follow-
ing.
1.Conservation of weakton numbers. The weaktons given in (5.3.18) are elementary
particles, which cannot undergo any decay. Also, thew-weaktons cannot be converted be-
tween each other. Although the neutrino oscillation, whichis unconfirmed, may convert one
flavour of neutrino to another, for a particle decay or scattering, the neutrino number is still
conserved. Namely, the lepton numbersLe,Lμ,Lτare conserved.
Therefore, for any particle reaction:
(5.4.10) A 1 +···+AN→B 1 +···+BK,
the number of each weakton type is invariant. Namely, for anytype of weaktonw ̃, its number
is conserved in (5.4.10):
NAw ̃=NwB ̃,
whereNwA ̃andNw ̃Bare the numbers of thew ̃weaktons in both sides of (5.4.10).
2.Spin conservation.The spin of each weakton is invariant. The conservation of weakton
number implies that the spin is also conserved:
JA 1 +···+JAN=JB 1 +···+JBK,whereJAis the spin of particleA.
In classical particle theories, the spin is not considered as a conserved quantity. The
reason for the non-conservation of spin is due to the incompleteness of the reaction formulas
given in Section5.1.3. Hence, spin conservation can also be considered as an evidence for
the incompleteness of those reaction formulas. The incomplete decay reaction formulas can
be made complete by supplementing some massless mediators,so that the spin becomes a