## Monday, November 1, 2010

### Theory Update 18

Some years ago, when I used to give regular seminars, on information theoretic Koide operators amongst many other things, a common (albeit missing the point entirely) concern was the running of mass in standard quantum field theory. So far, we have mostly neglected the gauge boson masses. It is of course easy to obtain the $(\gamma, W^{+}, W^{-})$ mass triplet, namely $(0,1,1)$, from a Koide matrix. We could for instance take the phase $\theta = i$, and set $r = 1/ \sqrt{3}$. But from a Fermilab review, we see in the graph below the running of the Weinberg parameter with momentum transfer $Q$. This parameter is defined by the ratio

$\cos \theta_{W} = \frac{m_W}{m_Z}$

of W boson and Z boson masses. It would be nice to understand those experimental results. Recall that the twisted Fourier transform recovers the W bosons from the left handed electron and positron, and the photon from a neutrino, whereas the Z boson is more complex. It is therefore tempting to ponder the scenario where $m_W$ is roughly fixed while $m_Z$ runs, although in such a way that we might draw a curve through the data points, ignoring the local electroweak theory.