Multiple Deligne values: a data mine with empirically tamed denominators

Understand

Multiple Deligne values (MDVs) are iterated integrals on the interval $x\in[0,1]$ of the differential forms $A=d\log(x)$, $B=-d\log(1-x)$ and $D=-d\log(1-\lambda x)$, where $\lambda$ is a primitive sixth root of unity.

• MDVs of weight 11 enter the renormalization of the standard model of particle physics at 7 loops, via a counterterm for the self-coupling of the Higgs boson.
• A recent evaluation by Erik Panzer exhibited the alarming primes 50909 and 121577 in the denominators of rational coefficients that reduce this counterterm to a Lyndon basis suggested by ideas from Pierre Deligne.
• Oliver Schnetz has studied this problem, using a method from Francis Brown.