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A Highest loop order of experimental relevance?

  1. Sep 13, 2017 #26

    Urs Schreiber

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    Isn't it a little more subtle than this makes it sound? Because as the order goes to infinity, the perturbation series is not to be expected to approximate the true physical value, but to be infinitely far from it! The perturbation series of realistic QFTs is expected to be divergent (this goes back to Dyson 52.)

    Now for a general divergent formal power series, even summing up the first few terms makes no particular sense. But since we may assume that the perturbation series is the Taylor expansion of an actual smooth function (namely the non-perturbative theory) it is plausible to expect that it is, even if not convergent, an "asymptotic series". If so, this sort of guarantees that the first few terms (depending on "how small Plnack's constant really is") give a good approximation, but it still means that beyond that the series will diverge arbitrarily far from the desired physical value.
     
    Last edited: Sep 13, 2017
  2. Sep 13, 2017 #27

    Urs Schreiber

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    All right, thanks for finally saying that this is your reasoning!
     
  3. Sep 13, 2017 #28

    Vanadium 50

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    I dunno. It's a counterexample, after all.
     
  4. Sep 13, 2017 #29

    Urs Schreiber

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    Ah, sorry about this, now I see that I misread what you wrote, actually you are saying precisely what I am after. Okay so your hint is:

    Could you point me to a good reference for this?
     
  5. Sep 13, 2017 #30

    Urs Schreiber

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    By the way, the discussion here reminds me of the following quotes from the (very nice) review of asymptotic perturbation series theory in Suslov 05 (please take this in a good spirit, I don't mean to bug anyone):

     
  6. Sep 14, 2017 #31

    Vanadium 50

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    The original NLO paper was (Paulo) Nason, (Sally) Dawson, and (R. Keith) Ellis, around 1989. It builds on a paper a few years earlier by (John) Collins, (Dave) Soper and (Jack) Smith where they derive the relevant factorization theorems. Matteo Cacciari was giving talks about LO, NLO and the state of the art about ten years ago; if you find a conference proceedings by him that references one or both of the above papers, that's probably as good as you are going to get in one place.
     
  7. Sep 14, 2017 #32

    Urs Schreiber

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    Thanks. Maybe slide 12 in
    • Matteo Cacciari: "(Theoretical) review of heavy quark production" BNL 14/12/2005 (pdf)
    has the kind of statement that you are referring to.
     
  8. Sep 14, 2017 #33

    Vanadium 50

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    I think the slides as a whole give a reasonable view of the heavy flavour state of the art. Slide 5 is a motivation for NNLO (and why N3LO may play only a minor role).
     
  9. Sep 14, 2017 #34

    Urs Schreiber

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    Right, sorry, I meant slide 12 (I was pointing somebody else to slide 5 for another reason, and mixed up the numbers when writing here).

    I am trying to pinpoint the statement which you were referring to above when you wrote:

     
  10. Sep 16, 2017 #35

    Vanadium 50

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    I'm sorry, but that's a little unfair. "Here's an article I found - why can't I find a statement you made in it?"

    I think I did a pretty good job of pointing you in the right direction, but it may well be that a single document that has everything you want doesn't exist. But if a literature search needs to be done, I don't think I am the one who needs to do it.
     
  11. Sep 18, 2017 #36

    Urs Schreiber

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    There is some misunderstanding here. But never mind.
     
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