Michael, 

I should also mention that typically at very high pT in e+e- hadroproduction, Z production, etc., one can neglect the resummed contributions fully, but need to include one higher order in the fixed-order contribution to reduce the scale dependence.  At moderately high pT, the scale dependence is smaller and one does not need to include one higher order to reach comparable accuracy, but the resummed effects become important. So in practice it is 
beneficial to include the data from both moderate pT and high pT to cross check various uncertainties. 

Pavel
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Pavel Nadolsky
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________________________________________
From: [log in to unmask] [[log in to unmask]] on behalf of Nadolsky, Pavel
Sent: Friday, April 19, 2013 9:31 AM
To: Peskin, Michael E.; Ashutosh Kotwal; Michael Schmitt
Cc: Sven Heinemeyer; snowmass-electroweak; [log in to unmask]
Subject: Re: [SNOWMASS-ELECTROWEAK] question from the Capabilities group

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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