5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 325
weak repelling radius of the mediators. Consequently, the total numberNof particles in each
layer of mediators satisfies that
(5.5.51) N≤ 4 πr^2 /r^20 ,
whereris the radius of the layer as in (5.5.48). The inequality (5.5.51) means that all particles
on anr-sphere are arranged with distancer 0.
Based on (5.5.51), ifr=kr 0 , thenN≤ 4 πk^2.
3.Spin number of vector photons.An electron refers to the system consisting of the naked
electronνew 1 w 2 and its mediator cloud as shown in (5.5.47). The photon layer contains both
vector and scalar photons. As the total spin of an electron isJ=^12 , both the numberNJ= 1 of
vector photons with spinJ=1 and the numberNJ=− 1 of photons with spinJ=−1 should
be the same, i.e. the vector photons in an electron satisfy
(5.5.52) NJ= 1 =NJ=− 1.
The condition (5.5.52) implies that the emitting and absorbing of vector photons always
in pairs with one spinJ=1 and another spinJ=−1. Scalar photons andν-mediators have
spinJ=0.
In fact, by the Angular Momentum Rule6.14, only bosons withJ=0 can rotate around
a center without the presence of force moment. Hence the photons andν-mediators in the
mediator cloud may all be scalar particles.
Mediator clouds of quarks
Different from the weakton constituents of charged leptons, the weakton constituents of
a quark include aw∗-weakton with a strong charge, leading to different structure of mediator
clouds.
- As a quark curries three weak charges 3gwand a strong chargegs, the mediator cloud
of a quark possesses three layers:
(5.5.53)
gluon layer: vector and scalar gluons,
photon layer: vector and scalar photons,
ν-layer: ν-mediators.- The radii of the 3 layers in (5.5.53) are different:
(5.5.54) rg 6 =rγ, rγ 6 =rν, rν 6 =rg.
Similar to the case for an electron, the particle number in each layer of (5.5.53) satisfies
a relation as (5.5.51).
- The total spin of a quark system is alsoJ=^12. Therefore the vector photons and vector
gluons in the mediator cloud of a quark have to obey the spin number rules as
(5.5.55) NJ= 1 =NJ=− 1 , N ̃J= 1 =N ̃J=− 1 ,
whereNJ= 1 andNJ=− 1 are the numbers of photons with spinsJ=1 andJ=−1, andN ̃J= 1
andN ̃J=− 1 are that of gluons with spinsJ=1 andJ=−1.