t, H, W, Z and naturalness

The lightness of the Higgs boson is one of the vexing issues in particle physics today. Why isn't it made heavy by virtual particles?

Meanwhile, on this blog I have chronicled a variety of possible relations among the masses of t, H, W, Z. Perhaps the most impressive of these is the sum rule due to Lopez-Castro and Pestieau (anticipated by Garces Doz, and blogged by Andrew Oh-Willeke 1 2 3).

It has a mild resemblance to the "Veltman condition", a t,H,W,Z relation proposed by Martinus Veltman which would imply that the virtual corrections to the Higgs mass cancel out. In its original form, it implies a Higgs mass greater than 300 GeV, which is wrong.

However, the original form of the Veltman condition is specific to the unadorned standard model. Today, Ernest Ma - one of the few theorists to tackle the Koide formula - has told us what a Veltman condition looks like, in a minor extension of the standard model where neutrinos get their mass from dark matter (the "scotogenic" model; skotos means darkness, thus scotogenic, generated from the dark).

The paper is here. The new conditions are equations 8 and 9. With three new free parameters, it may not look so exciting. But it demonstrates that a naturalness condition can deviate a bit from Veltman's original formula, while still retaining a family likeness. (Further examples may be found here.)

This suggests a new interpretation of the LC&P sum rule (and any other valid tHWZ numerology): as a symptom of an underlying, slightly-beyond-standard-model theory, that is natural.