Why is tauon not being probed for high accuracy $g-2$ values?

Question

The recent results from LHCb (regarding violation of lepton universality in $B$ meson deacy) and Fermilab (regarding anomalous muon $g-2$ factor) have set the HEP$^1$ community abuzz right now$^0$. In both cases, it seems that the muon isn't just a heavier electron$^2$. Something about the heaviness of the lepton has allowed a probe of all these discrepant effects. For the Fermilab$^3$ result, the hadronic contributions to muon decay seem to be the culprit for the $8^{th}$ decimal onwards, currently $4.2\sigma$, tension b\w theory and expt.

1. Why do similar effects not arise for the electron, albeit at a higher decimal place, or do they?

2. Are similar experimental/theoretical investigations being performed for the even heavier cousin, tauon? Should one expect a more pronounced disagreement in its case? ( I understand that you loose stability as you go up generations but why is strong and top physics probable but taoun's not?)

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$^1$ High Energy Physics
$^2$ I am extrapolating here from Fermilab's insinuation to B's asymmetry titilated by the fact that they both involve the muon and have been published - oh so closely - but the latter may have nothing to do with the former.
$^3$ and BNL
$~$
$^0$ Hurray!

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An excellent summation may be watched at Sixty Symbols.

Answer 1

This part-per-million measurement of the muon's anomalous magnetic moment is a part-per-billion measurement of the muons total magnetic moment. Every part-per-billion measurement is hard. This one is, fundamentally, a measurement of a frequency: the frequency at which the muon's spin precesses in a magnetic field.

In order to measure a frequency with precision, you want to be able to measure it for a long time. If you can't measure it for a long time, you at least want to be able to measure it many times. That suggests, for example, that it should be easier to measure the anomalous magnetic moment for the electron than for the muon. And it is: the electron's $a_e$ is known a thousand times more precisely than the new result for the muon.

The rest-frame lifetime of the muon is about two microseconds. Take a look at the inset to the figure below from the paper you link, the sub-graph with the seven squiggly lines:

That is a histogram: it shows the relationship between the number of decay electrons observed and the amount of time the muon beam has spent in the storage ring, going as many as seven laps around. I count about 140 precession periods on the figure. The result is precise enough to be interesting entirely because that plot is so lovely.

The tau lepton is a factor of ten heavier than the muon, so its magnetic moment is about ten times smaller. However the tau’s lifetime is ten million times shorter than the muon's. This ratio suggests that getting a beam of tau leptons to precess even once before decaying would be a tall order. And the data reflect this challenge: while the new Fermilab result gives $a_\mu$ to about eight significant figures, for $a_\tau$ we have not yet measured the sign, though we predict $a_\tau \approx \alpha/2\pi$ as for the other leptons.

Answer 2

I'm sure someone will give a more detailed answer, but here's a brief one:

1. These effects do occur for the electron, however they are much larger for the muon due to its larger mass.
2. I imagine these sorts of experiments aren't really doable for tau particles due to their extremely short lifetime of $\sim 3\times 10^{-13}$ seconds, in contrast to 2 microseconds for muons.