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What is the highest loop order in standard model scattering computations that still contributes a measurable effect seen in past and present particle collider experiments?

In other words, to which order are loop corrections necessary for accounting for observed high energy physics?

I expect it's order-1 for most computations and order-2 in some rare cases, and not higher. Or are there notable exceptions? What would be a good reference to check this?

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    $\begingroup$ AFAIK, the electron anomaly is measurable up to the fifth order in QED (and to second order in EW plus hadronic corrections). The precision of the experiment is expected to improve in the next couple of years, and the EW+hadronic corrections are under study, so the sixth order in QED should be measurable around 2020, if everything goes as planned. I am not posting this as an answer because I don't have the time right now to look up for references to support my claims (and I could be misremembering something), but perhaps you look could it up yourself. $\endgroup$ – AccidentalFourierTransform Sep 9 '17 at 12:19
  • $\begingroup$ @AccidentalFourierTransform Thanks! I took the liberty of asking my question also on PhysicsForums, and user "mfb" there exactly agrees with your answer, and points to references: physicsforums.com/threads/… $\endgroup$ – Urs Schreiber Sep 11 '17 at 12:16
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    $\begingroup$ BTW: I collected some examples of higher order loops here: physics.stackexchange.com/q/383135/84967 I'll add more if I anything comes to mind. I don't know if you're still interested in this, but if you do you may find it useful. Cheers! $\endgroup$ – AccidentalFourierTransform Jan 31 '18 at 22:34

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