Michael, everyone:

> The main barrier to improvement of alphas is the fact that it is difficult to disentangle perturbative and >nonperturbative contributions to event shapes in e+e-.   
...
> If TLEP is built, it will be possible to get high-statistics samples of e+e- event shapes in the same, modern detector at 91 GeV, 250 GeV, and 350 GeV.  Then it should be possible to fit out the 1/Q terms and reach per mil precision in alphas.    

Indeed, with enough luminosity, one can select only the high-pT events in the e+e- event shapes that are less affected by nonperturbative (power-suppressed) effects of order 1/Q or beyond. Then alpha_s can be determined from the data together with the 1/Q nonperturbative correction.  

This is a part of the story, the growing complexity introduces new sources of uncertainty at the per mil level. If we are lucky, including an additional order of alpha_s will reduce the perturbative QCD uncertainty, but this is not guaranteed, as the perturbative QCD series is ultimately asymptotic. At each higher order, the resummed cross sections in the comparisons to the data may contain new structures that were not present at lower orders and may have new nonperturbative degrees of freedom. Higher-order nonperturbative terms (1/Q^2, etc.) may become non-negligible. These are extremely interesting QCD topics, best studied by doing measurements with a variety of colliders and observables. It is not obvious to me that just increasing the luminosity at one collider (TeraZ) will be sufficient for disentangling all contributions.

Best regards,

Pavel
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