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Some processes can not happen at the tree level, but it happen via loops, like for Higgs decay to pair of glouns or pair of photons, (h -> gg), (h -> y y) . For instance, effectively h -> gg written as ##~ h~ G^a_{\mu\nu} G_a^{\mu\nu}~ ## which is Lorentz and gauge invariant ..

Now if we considered instead of SM- h, a coloured triplet scalar, T= (3,2), then on the loop level i could mediate this decay ## T^0 \to yy ## by a loop of charged SU(3) triplet scalars ## T^\pm ## such that the coluor will be conserved in that process, but still effectively there is no an operator as ## T^a B_{\mu\nu} B^{\mu\nu} ## (where a is the SU(3) index) because it is not gauge invariant,

The question can this process happen or no ?

In short, is it a condition for a process to be allowed on the loop level to has an effective operator or it's just sufficient that for this process to conserve colour or charge via loop mediator ?

Best.

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# Effective operator and allowed loop level interactions

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