1. Introduction
In the paper “On Quarks and Gluons” [1] we have assumed that the gluons and anti-gluons constitute 6 quarks and 6 anti-quarks, respectively. The quarks are
(1)
the anti-quarks are
(2)
where the electric charges of gluons
and anti-gluons
are
(3)
(4)
The spin of every gluon and anti-gluon is 1/4, and their energy
obeys the inequality
. Thus, all of quarks and anti-quarks are fermions with spin1/2, and the charge of every quark or anti-quark equals to the sum of charges of gluons or anti-gluon in it.
It is needed to emphasize that, firstly, since all of gluons are fermions with spin1/4, the same gluons cannot constitute quark, but two different gluons in quark are commutable. Secondly, gluons have no mass, but quarks are massive. In fact, every particle with internal structures is massive, and vice versa.
We know that the mediators of nuclear force are the mesons
and the mediators of weak interaction are the intermediate bosons. Since the intermediate bosons
have the identical decay patterns with the mesons
[2] :
(5)
where
can be electron
or muon
, so the intermediate bosons
should also be composed of a quark and an anti-quark as same as the mesons
, namely both strong and weak interaction should be related to gluons. If the idea that the quark is composed of gluons is extended to other particles, we will see that the number of gluons is conserved in strong interaction but non-conserved in weak interaction, the fermions could be divided into the three generations, the antiparticle of neutrino is itself and why the neutrino oscillation exists.
2. The Gluon Number in Strong Interaction
According to QCD, the mesons are composed of quark and anti-quark, and the baryons are composed of three quarks [3] [4] . So the strong interaction equation
and
can be written as
(6)
If we give the quark number
to each quark and the anti-quark number
to each anti-quark, the quark numbers on both sides of each equation above are equal:
(7)
If we give the gluon number
to each gluon and the anti-gluon number
to each anti-gluon, respectively, using
,
gives
(8)
Obviously, the number of gluons is conserved in strong interaction, and this allows the charge, baryon number and parity to be conserved in strong interaction.
3. The Gluon Number in Weak Interaction
Is the number of gluons conserved in weak interaction? In the paper “On Quarks and Gluons” it is pointed out that the gluon and anti-gluon could annihilate into different particles in different interactional courses when they met. For example,
or
. Using
,
and
,
, considering the spin and charge of the particles gives
(9)
As said previously, since the intermediate bosons
have the identical decay patterns with the mesons
:
, (10)
so there should be
,
. Thus the two other decay patterns of the intermediate bosons
can be written as
(11)
Obviously, the gluon number is conserved in every equation above. But, if the decay
and
of strange particles are written as
(12)
or
(13)
both the quark number and gluon number are non-conserved, this is because of the existence of the decay
and
. So, the reason why the parity is non-conserved in weak interaction is the gluon number is non-conserved.
4. The Formation of Three Generations of Fermions
From Equations ((9) and (11)) we see that the three neutrinos and their antiparticles are composed of gluon
and anti-gluon
, and the three leptons are composed of
. How should this be explained?
As pointed out that in the paper “On Quarks and Gluons”, the binding energy
of two spins
has three values according to the Ising model:
(14)
Therefore, the two gluons
can and can only constitute the three neutrinos in the three different ways, in other words, the three neutrinos are just the three states of the same particle, and the neutrinos’ antiparticle is itself. And since the energy spectrum of lepton in Equations ((9) and (11)) is continuous and tends to be maximal, and the energy spectrum of corresponding neutrino is discrete and tends to be minimal, so the neutrinos can be only composed of the gluons
of minimal energy rather than the gluons of higher energy. Similarly, since the gluon number is conserved in Equations (9) and (11), the three leptons and their antiparticles can be only composed of gluons
and
in the three different ways, respectively.
As shown in Equation (5), the six quarks have only two values of charge. Thus, the six quarks, three leptons and three corresponding neutrinos constitute the three generations of fermions as usually said:
(15)
5. The Reason of Neutrino Oscillation
The static mass of neutrino can be written as (light speed
)
, (16)
where
is the energy of single gluon, and
is the binding energy of two gluons. We know that the mass of three neutrinos
is
. (17)
So their binding energy is
. (18)
As said previously, the three neutrinos are the three states of the same particle. Since the smaller the binding energy is, the state of particle is more unstable, the neutrino state of smaller binding energy is going to decay into the state of greater binding energy, and this is the neutrino oscillation:
(19)
This is consistent with the experiments [5] - [10] .
Using the method from Equations (16) to (19) we can also explain why there are only the decays of
,
and
rather than the reversed decays:
(20)