Theory Update 23

Many thanks to kneemo for pointing me to this 2008 paper by Stanford's Zhang et al. They suggest that magnetic monopoles hide in topological insulators, like a mirror image of an electric charge sitting near the outside of the surface.

For reasons that we shall discuss later, we consider an adjustment of the Koide rule for the charged lepton masses, as follows. Instead of the usual eigenvalues, with parameters $r = \sqrt{2}$ and $\theta = 2/9$, we will consider eigenvalues

$\lambda_{i} = 1 + \sqrt{2} \cos (2/9 + \pi + \omega_i)$

for $\omega_i$ the usual cubed roots of unity. At the charged lepton mass scale, this gives us a candidate triplet of masses: $45.2$, $632.6$ and $1205$ MeV. This kind of monopole has not yet been well studied in the laboratory, but there is great interest in these materials.