To a second approximation, the afore-mentioned cancellation can be made
very exact by giving each particle a partner which exactly balances its
contribution (or words to that effect). These are the "superpartners", and
give a fermion for each known boson and vice versa. Since fermions and
bosons have opposite effects in renormalisation, these could be made to
cancel out exactly if these were identical apart from their spins. But
since these superpartners haven't been observed they must have a greater
mass than their mundane partners, this being a broke symmetry. However they
can still cancel to high precision...

...unless I am still barking up the wrong branch of the Feynman diagram, of
course.

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