How to prove gluon has this quantum number assignment?

[BuckeyePhysicist]

[URGENT]How to prove gluon has this quantum number assignment?

From PDG booklet, for gluon, I^G(J^{PC}) = 0(1^-).

My questions are:

1. How to prove its P=-1?

2. Why C parity and therefore G parity are not well-defined for a gluon?
Is it because gluon have nothing to do with electromagnetic interaction so it do not have well-defined properties associated with (electric) charge conjugation transformation?

3. I=0 can be understood that gluon must be flavor singlet and have no charm, no strangeness, no bottomness and no topness. Right?

 

[Meir Achuz]

1. The gluon is a theoretical particle that is believed (in QCD) to be only virtual, so its parity can't be "measured" as can that of the photon.
In QCD, it is hypothesized as a vector gauge particle, which means spin 1 and negatve intrinsic parity. A gauge particle must have the same parity (-) as a spatial derivative.

2. Gluons have color charge which means they can't be eigenstates of C.

3. Right.

 

[sir-pinski]

To prove that gluon has a P=-1 assignment, we can look at the properties of gluon as described in the PDG booklet. Gluons are the carriers of the strong nuclear force, which is responsible for holding quarks together in a nucleus. This force is known to be a spin-1 force, meaning that gluons have a spin of 1. According to the rules of quantum mechanics, particles with spin 1 must have a parity of -1. Therefore, based on the known properties of gluons, we can conclude that they have a P=-1 assignment.

As for the question about C and G parity, it is true that gluons do not have a well-defined charge conjugation or G parity. This is because they do not interact with the electromagnetic force, which is responsible for charge conjugation and G parity transformations. Gluons only interact with the strong force, which does not have any well-defined properties associated with these transformations. Therefore, it is not meaningful to assign C or G parity to gluons.

Finally, the statement about I=0 for gluons is correct. Since gluons are the carriers of the strong force, they must be flavor singlets in order to interact with all types of quarks equally. This means that they cannot have any specific flavor, such as charm, strangeness, bottomness, or topness. Therefore, I=0 is a result of gluons being flavor singlets.