= Statistics and symmetry factors of a two-propagator loop
A closed Dirac loop gives a minus sign and a <spinor> <trace>. Replacing it by two distinguishable real scalar species removes both, with no extra interchange factor. One identical real scalar species instead has <Feynman-diagram symmetry factor> two. A cubic interaction $g\phi\chi^2/2$ has vertex $ig$, whereas $g\phi\chi^2$ has vertex $2ig$; those choices give different numerical coefficients even though their drawn loop topology is the same.
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