  A dimensionally continued background-field method makes the rationality of
the 4-loop quenched QED beta function far more reasonable than had previously
appeared. After 33 years of quest, dating from Rosner's discovery of 3-loop
rationality, one finally sees cancellation of zeta values by the trace
structure of individual diagrams. At 4-loops, diagram-by-diagram cancellation
of $\zeta(5)$ does not even rely on the values of integrals at d=4. Rather, it
is a property of the rational functions of $d$ that multiply elements of the
full d-dimensional basis. We prove a lemma: the basis consists of slices of
wheels. We explain the previously mysterious suppression of $\pi^4$ in massless
gauge theory. The 4-loop QED result $\beta_4=-46$ is obtained by setting d=4 in
a precisely defined rational polynomial of d, with degree 11. The other 5
rational functions vanish at d=4.

High Energy Physics - Theory;High Energy Physics - Phenomenology