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The question is related to
I thought that it won't appear at tree-diagram level. It could appear at higher order loop level (e.g. electron-electron exchange virtual photons, virtual photons exchange virtual quarks, virtual quarks involve strong force), e.g. arxiv.org/pdf/0902.3360v1.pdf Fig 29 (Though it is not precisely e-e interaction)
but someone argues that electron is lepton and hence cannot involve strong force at all.
Which is correct?
When some physicists say electron doesn't participate in strong interaction, they are simply referring to the vertices. On the other hand, if you allow higher orders, then everything in standard model interact with everything else.
Yes, there is some, but it is rather weak (sorry for pun). This "strong interaction" is indirect. Electrons interact directly with hadrons mostly electromagnetically. One can effectively increase the effects of indirect strong interaction with increasing the collision energy.
Quarks with color charge (and composite particles made by quarks like the proton and the neutron) feel the strong force. Electrons are not quarks. The strong force is mediated by gluons. Electrons don't emit/absorb gluons....
Of course quarks have also electromagnetic charge besides color charge and interact with electrons via electromagnetic interactions mediated by photons, so electrons are influenced by strong interaction in this sense. But then everything is influenced by everything else...
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