314 CHAPTER 5. ELEMENTARY PARTICLES
5) Free gluons, if there exist, are massless.Remark 5.16.Gluons and photons are massless only in their free states. When they are
confined in mediator clouds around electrons and quarks, they may attain masses. In this
case, massive photons are described by the PID electromagnetic equations as follows:
Vector photons:
(5.5.13) ∂ν(∂νAμ−∂μAν)−eJμ= (∂μ+
e
hc ̄βAμ−1
4
kxμ)φ.Scalar photons:(5.5.14) ∂μ∂μφ−kφ+
e
hc ̄β ∂μ(Aμφ)−1
4
kxμ∂μφ= 0.The masses of bound photons are created in (5.5.13) and (5.5.14) by the spontaneous gauge-
symmetry breaking.
Color charge
In the QCD theory, color quantum numbers are regarded as color charges. Namely, each
quark carries one of the color charges:
(5.5.15)
red charger, green chargeg, blue chargeb,
anti-red charger, anti-green chargeg, anti-blue chargeb.Each gluon is considered to carry a pair of a color charge and an anti-color charge in QCD.
Thus, the three pair of color charges and anti-color chargesin (5.5.15) constitute fundamental
bases ofSU( 3 )andSU( 3 ), and the gluonsgk( 1 ≤k≤ 8 )form an octet of the irreducible
representation
SU( 3 )⊗SU( 3 ) = 8 ⊕ 1 ,
which are expressed as
g^1 =rg,g^2 =br,g^3 =gb,g^4 =1
√
2
(5.5.16) (rr−bb),
(5.5.17) g^5 =gr,g^6 =rb,g^7 =bg,g^8 =g^4.
We remark that the conclusions (5.5.16) and (5.5.17) of QCD for gluons are completely
consistent with those in the weakton model in (5.3.40) and (5.3.41). However, the QCD
version is based on the color charges of (5.5.15), and the version of weakton model is based
on the color quantum number of thew∗-weakton:
w∗r,w∗g,w∗b,w∗r,w∗g,w∗b.Gluon radiation
Based on the Standard Model, quarks can emit and absorb gluons in the same fashion as
electrons emitting and absorbing photons. For example, a redu-quarkuremits anrggluon
grg, thenurbecomes augquark, as shown in Figure5.16.