326 CHAPTER 5. ELEMENTARY PARTICLES
We remark that two scalar mediators can be transformed into apair of vector particles
withJ=1 andJ=−1 respectively.
- By Assertion 2) of Theorem5.21, the color indices of a quark systemqand an anti-
quark systemq, carrying gluon clouds, must take the values as follows
(5.5.56)
Indc(q) =r,g,b,
Indc(q) =r,g,b.- The gluons in the cloud layers of quarks are confined in a hadron. However, gluons
between quarks in a hadron can be exchanged. The gluon exchange process between quarks
in a hadron is called gluon radiation. In fact, a quark can emit gluons which will be absorbed
by other quarks in the hadron. - Consider a quarkq 1 , which is transformed toq 3 after emitting a gluong 0 , and consider
a quarkq 2 , which is transformed toq 4 after absorbing the gluong 0. The exchange process is
expressed as
q 1 →q 3 +g 0 , q 2 +g 0 →q 4.
Equivalently,
q 1 +q 2 →q 3 +q 4.
The corresponding color transformation is given by
Indc(q 1 ) =Indc(q 3 )Indc(g 0 ),
Indc(q 4 ) =Indc(q 2 )Indc(g 0 ),which lead to
(5.5.57) Indc(q 1 +q 2 ) =Indc(q 3 +q 4 ).
The relations (5.5.53)-(5.5.57) provide the basic properties of mediator clouds of quarks.
Further discussion will be given in the next chapter.
Gluon clouds of hadrons
Different from electrons and quarks, there is no photon andν-mediator cloud layer around
a hadron, due to the fact that the radius of a naked hadronρHis greater than the range of the
weak interaction:
ρH≥ 10 −^16 cm.
Namely, a hadron can only have a strong attraction to vector and scalar gluons, forming a
gluon cloud with radius about the same as the radius of a hadron:
rH∼ 10 −^16 ∼ 10 −^14 cm.Also, hadrons are colorless. For a baryonBand a mesonMgiven by (5.5.42), we have that
Indc(M) =ciciIndc(π) =w
Indc(B) =cicjckIndc(π) =w, 1 ≤i,j,k≤ 3.