So, either a field medal or an interesting failure. I don't have the time to go deep into this, and probably the level of math is way above me, but feel free to follow up the story. For some reasons, I thought the Todd function was related to toads... but was wrong (thanks to @dexterdev's document, now I know better: no tadpoles here ;)
It would be a tad strange if tadpoles were involved :P
Tadpoles are usual stuff when loop corrections in quantum field theory are what we talk about. Therefore, I clearly made a too hasty mental-connection :D