What does next to next leading order calculations mean?

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Discussion Overview

The discussion revolves around the concept of "next to next leading order calculations" within the context of the standard model in particle physics. Participants explore the implications of loop corrections and the ambiguity in defining order based on different criteria.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants explain that next to next leading order calculations refer to the inclusion of two-loop corrections to the lowest order diagram for a given process.
  • Others argue that the definition of order can depend on whether one counts loop-order (L) or coupling-constant-order (N), suggesting that both perspectives can lead to different interpretations.
  • A later reply notes that the ambiguity in discussing "the order" arises unless it is specified whether it pertains to the number of vertices or the number of loops.
  • Some participants mention that the context of infrared effects complicates the discussion, as low energy particles may not be observed, affecting the interpretation of diagrams.

    • Areas of Agreement / Disagreement

    Participants express differing views on the criteria for defining order in calculations, indicating that multiple competing perspectives remain without a consensus.

    Contextual Notes

    Limitations include the dependence on definitions of loop-order and coupling-constant-order, as well as the context of infrared effects which may influence the interpretation of diagrams.

lavster
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me again... what are next to next leading order calculations in the standard model?
 
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lavster said:
me again... what are next to next leading order calculations in the standard model?

That just means the two loops corrections to the lowest order diagram you can draw for a given process. So you consider a certain process and draw the diagram with the fewest number of loops possible; this is your leading order diagram (this leading order diagram could be a tree level diagram but it may also contain loops since some processes are only possible with loops). Then you consider all the diagrams containing two extra loops relative to the leading order diagram. These are the next to next leading order corrections.
 
It depends if you count loop-order L or coupling-constant-order N. You can add vertices increasing N keeping L fixed.
 
tom.stoer said:
It depends if you count loop-order L or coupling-constant-order N. You can add vertices increasing N keeping L fixed.

Good point. But this possibility arises only in the context of infrared effects, where we do not observe the low energy particles (for example photons). Otherwise, having a differenr number of coupling constant does not give the same diagram as the lowest order diagram (the asymptotic particle content is different).
 
Yes, I agree.

All what I say is that talking about "the order" is ambiguous unless you specify whether it is the number of verices or the number of loops.
 
It's right that if you count loop-order L or coupling-constant-order N.
 

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