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I know that electron and positrons can annihilate via a Z boson or a photon and produce a bottom quark-antiquark pair. But why can't this happened through in addition the strong nuclear force via a gluon ? Thanks

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    $\begingroup$ Because the electron is not charged under the strong force and so doesn't interact with gluons, you would have to collide quarks to do this (hence why top pairs are produced at LHC) $\endgroup$
    – Triatticus
    May 19, 2018 at 22:42

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Electrons and positrons (and more generally leptons in Standard Model) are not charged under colour $SU(3)$, meaning that they do not directly couple to gluons (at least at tree level).

Stated in another way, there is no gluon-electron-positron vertex.

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