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Since muon colliders are in the road map of future colliders, one could ask why not to use another superheavy particle to accelerate. Of course, some challenges to solve are:

  1. Lifetime of the tau particle and its decay into hadrons.
  2. Continuous or almost continuous supply of such an unstable particle, just the same problem we found in rare isotope facilities used to production of superheavy elements.
  3. Issues concerning radiation of tau particles at high energies.

If solved, what could be the advantages of tau particle colliders (if any), with respect to muon or electron colliders?

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It's not what you want to hear, but even the first 'challenge' you mention is a showstopper at this time: the project simply isn't possible with current or envisioned technology.

Consider how far (hah!) a $1.7\,\mathrm{TeV}$ $\tau$ beam could travel in the particles lifetime: \begin{align} \text{range} &= \gamma c \tau \\ &= 1000 \, (3.0 \times 10^8\,\mathrm{m/s}) \, (3 \times 10^{-13}\,\mathrm{s})\\ &= 10^{-1} \,\mathrm{m}. \end{align} What are you going to do with $10\,\mathrm{cm}$? You can't filter the other junk much less focus the resulting beam or add any meaningful further acceleration. And thinking about cooling the beam is a joke.

For comparison the range of muons in the g-2 experiment is about 18 kilometers, and in the proposed muon colliders it would be much longer than that.

And the range you get only scales up linearly with the beam energy because the particle is already ultra-relativistic, so the only factor that changes is $\gamma = T_\text{beam}/(m_\tau c^2)$.


Now the two advantages of using muons are

  • Get the 'clean' physics of QED rather than the messy physics of QCD at the production vertex.
  • The higher mass of a muon compared to an electron means lower Bremsstrahlung lasses and thus higher beam energy.

A tau beam would partake of the former to some degree and have even more advantage from the latter.

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