As it is commonly defined {https://en.wikipedia.org/wiki/R_(cross_section_ratio), the cross section ratio is given by: $$R = \frac{\sigma(e^+e^-\to \mathrm{hadrons})}{\sigma(e^+ e^- \to \mu^+ \mu^-)} $$ Out of curiosity, why is the denominator chosen to be the cross section of the interaction $e^+ e^- \to \mu^+ \mu^-$ and not $e^+ e^- \to \ell^+ \ell^-$ for $\ell$ as another lepton flavour? Thanks guys.

  • $\begingroup$ Can you write down the tree level diagrams involved? Do the electron and positron have to annihilate to a photon in your hypothetical if the product is $e^+e^-$? As for $\tau^+\tau^-$, that lepton was discovered after the popularity of R was established, and has a messier decay and detection. $\endgroup$ Commented Apr 3, 2018 at 0:07

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Two things:

  • First of all, $e^+ + e^- \to e^+ + e^-$ has a very fundamental problem in that you don't know if a reaction we are interested in happened, or if a simple scattering event occurred instead.

  • Secondly muons are experimentally easy. Very, very easy. They are long-lived, highly penetrating, and have distinctive end-states; a combination that makes them about the most easily IDed particle there is.

    Basically, if you can do it with muons it's going to be harder with any other particle.

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    $\begingroup$ Shouldn't you know that something happened by the change in momentum? Unfortunately, that something could involve t-channel exchange of a photon instead of s-channel annihilation followed by pair (re)creation. $\endgroup$ Commented Apr 3, 2018 at 21:24
  • $\begingroup$ @BertBarrois Uhm. Yeah. We don't know if the right reaction occured. $\endgroup$ Commented Apr 4, 2018 at 18:57

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