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I have seen examples of other particles that decay into gluons but do gluons themselves ever decay. Since gluons are not composed of anything else I assume they are fundamental.

On there other hand some fundamental particles decay and some do not i.e the photon. But on the other other hand some non fundamental particles do not decay either. i.e proton.

Maybe I am getting tangled up in semantics. Instead of decay would transformation be a better description.

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    $\begingroup$ Decay is a terminology that is usually only used for free particles, which the gluon is not. Of course there is some notion of decays of virtual gluons. And it is not clear if the proton is absolutely stable either. $\endgroup$
    – user178876
    Aug 5 '18 at 21:27
  • $\begingroup$ Particles decay not because they are not "fundamental" or rather elementary. Being elementary or composite has nothing to do with decaying or not. Particles decay, if a transition to a lower energy state is allowed by conservation laws. For example, the muon is elementary, but decays into the electron, muon neutrino, and electron antineutrino, all three also elementary. Although, hypothetically, if you imagine the muon as "consisting" of a muon neutrino and W-boson and the electron "consisting" of the electron neutrino and W-boson, then this decay becomes very intuitive with a pair production. $\endgroup$
    – safesphere
    Aug 6 '18 at 5:12
  • $\begingroup$ There are three and four gluon vertices in QCD, so from that you could presumably have a process where a gluon turns into two gluons with the same overall colour charge/anticharge. $\endgroup$ Aug 6 '18 at 5:50
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In the standard model of particle physics zero mass elementary particles, of which the gluon is one if you look at the table, cannot decay. This is because the standard model is formulated on fourvectors of special relativity, and has to obey basic quantum mechanical conservation laws, as energy and momentum conservation.

If a zero mass particle were to decay within this framework, the decay products (as an example two particles) would have as an invariant mass, the length of the added four vectors, . This would contradict energy and momentum conservation , as the before (gluon four vector ) and after decay(summed four vector of the two decay products) four vectors should be the same .

The gluon plays the same role as the photon for the strong interactions.

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A gluon does not decay in a standard sense. There are a number of reasons, but the simplest is to consider the decay of any massless particle. The energy-momentum vector for a massless particle is $(E,~\vec pc)$ which with $E~=~\hbar\omega$ means $$ P^\mu~=~\hbar\left(\omega,~\omega~\hat n\right). $$ Here $\hat n$ is a unit vector along the motion of the massless particle. Since the photon is massless $P^\mu P_\mu~=~$ $E^2~-(pc)^2~=$ $\omega^2~-~\omega^2~=~0$. This is an invariant, so what ever decay happens it must be the case this is upheld. It is clear the massless particle can't decay into massive particles for such particles obey $P^\mu P_\mu~=~(mc^2)^2$. Clearly this massless particle can't decay into two massless particles that have momenta in different directions.

Let us consider a gluon that transforms into two gluons. A gluon is a state $g^{cc'}$, where the color indices $c$ and $c'$ define the QCD state of the gluon. Now suppose we have $g^{cc'}~\rightarrow~g^{cc"}~+~g^{c\bar c"}$. Here the color indices $c"$ and $\bar c"$ correspond to a color and its opposite. We then have the requirement the frequency of the original gluon is conserved with $\nu~=~\nu_1~+~\nu_2$. In effect this is a QCD version of the parametric down shift of a photon in quantum optics. I am not sure how this can occur in QCD, or if it has been considered. I see nothing impossible about this.

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    $\begingroup$ The last part of your answer is unclear. Are you saying a free gluon can decay into two gluons just like a photon can decay into two photons double the wavelength? The photon does not decay though. Could you please clarify? $\endgroup$
    – safesphere
    Aug 6 '18 at 4:57
  • $\begingroup$ This is not decay. It is parametric downshift or amplification. A photon of a given frequency is converted into two photons with different frequencies that sum to the original frequency. The two photons are entangled states. It requires that a unit of spin be transferred from the lattice. Look up squeezed states of light. In principle it is not impossible for something analogous to occur with gluons. $\endgroup$ Aug 6 '18 at 12:54
  • $\begingroup$ A photon split is a result of interaction with a crystal, not a spontaneous decay. It is still unclear what this has to do with the question about a decay. If the same can happen to gluons, it would not mean they can decay, would it? And if so, then how does this relate to the question? $\endgroup$
    – safesphere
    Aug 6 '18 at 15:36
  • $\begingroup$ Also the gluon could turn into a pair of quarks(quark and antiquark). Just like a photon could turn into a pair of leptons(electron positron pair) in a process called pair production. $\endgroup$ May 20 '20 at 1:31

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