Neutrino phenomenology

Sheppeard’s first phenomenology paper in several years has appeared. I would put it in context as follows:

She is aiming at a theory in which physics is standard model all the way up to the quantum gravity scale, and in which quantities like the mass matrices of the standard model are ultimately determined by what happens at that high scale. Various generalized Koide relations among fermion masses are the big clue we have about the details of that.

So here she begins with a model of neutrino mixing from noncommutative geometry (reference 1) – to be amended so that the deformation parameter θ appears directly as a mixing angle. In conventional terms we could say that this is an effective theory.

Then we have some algebraic speculations about where the Koide relations come from. For example, that the Brannen-Koide angle for the down quarks, of 4/27 radians (see page 17 of Sheppeard 2010), derives from the 2/9 radians angle for the charged leptons, acted on by a triality transformation of the exceptional Jordan algebra, which should play a role in quantum gravity.

To place this in context again, I think it helps to remember some of her other ideas – that Bilson-Thompson’s mapping of braids to standard-model fermions applies in some categorical way (in which braids are morphisms), that the dark sector is made of mirror braids and that mass originates in a kind of cohomological inner product of braids and their mirrors.

For the neutrino masses, she uses a Koide-like ansatz due to Brannen (a modification of his own rewrite of the original Koide formula), then changes a sign to get mirror neutrino masses, and claims a connection with the (current!) CMB temperature. To make sense, that last step is going to require some seriously nonstandard cosmology.

So, when it comes to specifics, there are a lot of details and I am not on board with most of them. But the criticality of the electroweak vacuum suggests that it really might be standard model all the way to the Planck scale, so the overall concept of getting Koide numerology from quantum gravity is a logical one. And a pioneering concrete proposal tends to inspire the construction of others.


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