To correctly calculate scattering amplitudes in nonabelian gauge theory, one must include Feynman diagrams with internal Faddeev-Popov ghosts (fictitious fermionic scalars that only appear internally in loop diagrams, not as external legs). I've seen many different talks by high-energy experimentalists and particle phenomenologists, which have included plenty of complicated loop Feynman diagrams involving strong and weak interaction scattering processes (e.g. here and here). But I've never, ever seen any experimentalist ever show a Feynman diagram containing an internal FP ghost propagator. Why can they get away with neglecting the FP ghosts?
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5$\begingroup$ "Why can they get away with neglecting the FP ghosts?" They can't. In a talk you can omit irrelevant stuff to keep it simple. In the full computation, you must include the FP ghosts (or use a ghost-free formalism, which in general is more cumbersome). $\endgroup$– AccidentalFourierTransformJan 14, 2018 at 21:37
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2$\begingroup$ @AccidentalFourierTransform Can you point me to an experimental or phenomenological paper containing a Feynman diagram with a FP ghost that illustrates a physically realistic scattering process? $\endgroup$– tparkerJan 14, 2018 at 21:41
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OP is asking how can phenomenologists get away with neglecting the FP ghosts. The answer is that they can't. In a talk you can omit irrelevant stuff to keep things simple. In the full computation, you must include the FP ghosts (or use a ghost-free formalism, which in general is much more cumbersome; e.g., the axial or unitary gauge).
For an explicit example of a paper from this week (from the phenomenology section on arXiv), see Dynamical Symmetry Breaking by SU(2) Gauge Bosons. In particular, in the appendix you will find an explicit computation that requires ghosts (although the relevant diagrams are not shown, but referred to an older paper). See also The method of global R* and its applications. For an example from last month, see Evidence of ghost suppression in gluon mass dynamics. There are countless examples. It couldn't be otherwise: you do need ghosts to have gauge-invariant results. If you did not, why would people introduce them at all?
Perhaps OP does not usually find ghost loops in phenomenological papers because the latter tend to use results from other papers instead of calculating them themselves. For example, the beta function of a QFT is an indispensable object that is used all the time in phenomenological papers; but these papers tend to quote the formula from theoretical papers where it was first computed. No need to compute it again. Needless to say, when a theoretician calculated it, they did use ghosts. The phenomenologists simply shows the result, so you won't see the ghosts there. But, like the real ghosts, they are there, whether you see them or not.
Alternatively, another reason is that many phenomenological papers are usually more concerned about the qualitative description of the system than the quantitative details. Therefore, tree-level computations usually suffice. And as ghosts only appear in loops, they are irrelevant for the tree-level result, and may therefore be neglected. But as soon as you want to include loops, make sure to bring them back, or otherwise your calculations will be wrong.
answered Jan 19, 2018 at 22:18
AccidentalFourierTransformAccidentalFourierTransform
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$\begingroup$ For more examples, you can use arxiv.org:443/find/hep-ph/1/abs:+AND+ghost+feynman/0/1/0/all/0/… $\endgroup$ Jan 19, 2018 at 22:34
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$\begingroup$ I believe these examples all consider pure Yang-Mills theory, so they don't really get at what I was looking for. Certainly the standard treatment of pure Yang-Mills uses ghosts; that's how they're introduced in all the standard textbooks. My question is whether as a practical matter, they're relevant for qualitatively understanding more realistic physical processes involving the full matter fields of the Standard Model - the kind of Feynman diagrams that experimentalists use. E.g. do we need ghosts to explain any of the processes we see in the LHC? $\endgroup$– tparkerJan 20, 2018 at 0:06
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$\begingroup$ There are no ghosts at tree-level, if that's what you mean. For perturbative theories, the tree-level result is usually very good as far as the overall qualitative description is concerned. In this sense, qualitative descriptions do not really need ghosts. But the LHC most certainly can see loops, so you do need ghosts. As I said, the beta function of the coupling constants of the SM all require ghosts for their calculation. And the running of, say, the strong c.c. is one of the major topics of experimental and phenomenological physics. $\endgroup$ Jan 20, 2018 at 0:11
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2$\begingroup$ In a general sense, you can say that ghost loops are nothing but a correction (to account for the over-counting of d.o.f.) to gauge loops. Therefore, they are of the same order of magnitude, but slightly smaller. If you only care about the order of magnitude, you may neglect ghosts and estimate only the gauge contribution. Matter, on the other hand, is typically much smaller in magnitude, so you can safety neglect it (this can be seen from the large $N$ limit, which suggests that $\text{gauge}\gtrsim\text{ghost}\gg \text{matter}$). $\endgroup$ Jan 21, 2018 at 15:26
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2$\begingroup$ Yeah, that makes sense, I just haven’t seen that perspective before — I learned ghosts as just a magic thing that pop out of doing a weird determinant. $\endgroup$– knzhouJan 21, 2018 at 21:31
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Perturbative QCD computations can be done in ghost-free gauges, such as the axial gauge. As far as I understand, this is customary for the computations revolving around the parton density functions in the proton, or in the pion. As well as for the final state equivalent, the parton fragmentation functions. Combined, this makes for a rather large section of QCD phenomenology I think. This might be one reason explaining your experience.
