Evidence of Light-by-light scattering by ATLAS

[mfb]

Maxwell's equations are not the only Lorentz-invariant field equations. They are the classical limit for low field strength.

 

[RockyMarciano]

Maxwell's equations are not the only Lorentz-invariant field equations.

Sure but they have some relevance in their quantum form for QED. What other equations are you thinking of that are relevant here?

They are the classical limit for low field strength.

But that's like saying Lorentz-invariance is only important for the theory at low field strength. Is this what you mean?

 

[mfb]

Sure but they have some relevance in their quantum form for QED.

Yes, they are the classical limit of QED for low field strength, as I said already. See the discussion in the first few posts for classical limits which include light-by-light scattering.

But that's like saying Lorentz-invariance is only important for the theory at low field strength.

No, and I have no idea how you got that idea.

 

[RockyMarciano]

Yes, they are the classical limit of QED for low field strength, as I said already. See the discussion in the first few posts for classical limits which include light-by-light scattering.
No, and I have no idea how you got that idea.

Ok. Here is my reasoning, it seems to me that given that we are talking about a global anomaly that appears also non-perturbatively(the measure of the path integral cannot be defined globally, the symmetry in the classical action is not a symmetry of the integral measure), using the perturbative heuristic of classical limit only at zero loop(low field strength) is not so convincing, because non-perturbatively the idea is that there is no classical electrodynamics limit, period.

And I don't know how to recover the global symmetries of the theory without the classical limit, so how is this sorted out in practice?

 

[atyy]

And I don't know how to recover the global symmetries of the theory without the classical limit, so how is this sorted out in practice?

Maxwell's equations are the classical limit of QED - not just at low energies - the light by light scattering appears at one loop (see my discussion with Vanadium 50 about the same point you are raising, and his answer in post #13).

 

[DrDu]

Shouldn't this effect be even clearer when elementary particles are used instead of nuclei, e.g. in electron electron scattering, as electrons, being point particles, cannot really collide with each other?

 

[RockyMarciano]

Shouldn't this effect be even clearer when elementary particles are used instead of nuclei, e.g. in electron electron scattering, as electrons, being point particles, cannot really collide with each other?

I guess you actually meant something else when you wrote about particles "not really colliding"(what were particles doing in the LEP collider if not colliding?) ;) But yes with elementary particles the results are in a sense "cleaner" and therefore "clearer", the issue here is more to do with energy(lighter particles means less energy in the collisions) and that's why the results have been first obtained in the hadron collider.

 

[DrDu]

I guess you actually meant something else when you wrote about particles "not really colliding"(what were particles doing in the LEP collider if not colliding?) ;) But yes with elementary particles the results are in a sense "cleaner" and therefore "clearer", the issue here is more to do with energy(lighter particles means less energy in the collisions) and that's why the results have been first obtained in the hadron collider.

Personally, I have problems to talk of a collision of point particles like electrons but not to imagine a collision of extended objects as nuclei. But maybe this is a question of definition.

 

[RockyMarciano]

Maxwell's equations are the classical limit of QED

Here you are saying the opposite of what Vanadium wrote in #6 and #10

- not just at low energies -

And here you are doing the same with mfb.

the light by light scattering appears at one loop (see my discussion with Vanadium 50 about the same point you are raising, and his answer in post #13).

I've mentioned the fact that the effect is predicted at first loop already in my first post so I don't know how that answers anything. Did you read that this can be analysed non-perturbatevely?

 

[RockyMarciano]

Personally, I have problems to talk of a collision of point particles like electrons but not to imagine a collision of extended objects as nuclei. But maybe this is a question of definition.

Discussing this would take us far into a philosophical debate of what a particle is and what it means to collide for objects without classical properties, etc..
Such discussions seem to not be allowed in this site so I won't say more.

 

[atyy]

Here you are saying the opposite of what Vanadium wrote in #6 and #10

And here you are doing the same with mfb.

Yes, I don't think what they said is correct if one uses the usual definition of classical limit. I believe Vanadium 50 agrees (ie. he agrees that LbyL is a quantum effect obtained at one loop, not an effect that can be obtained in the classical limit of QED), I'm not sure why mfb put in the restriction to low energies.

 

[Vanadium 50]

Shouldn't this effect be even clearer when elementary particles are used instead of nuclei

This is a non-linear effect, so it goes as Q^4. 82^4 is 45 million. That's a heck of a head start.

 

[RockyMarciano]

Yes, I don't think what they said is correct if one uses the usual definition of classical limit. I believe Vanadium 50 agrees (ie. he agrees that LbyL is a quantum effect obtained at one loop, not an effect that can be obtained in the classical limit of QED), I'm not sure why mfb put in the restriction to low energies.

I suppose you are simply using a different definition of classical limit from mine (and apparently from Vanadium's and mfb's), you seem to be referring to the possibility of recovering the classical result(this is the definition in wikipedia), in this case at the tree level, that is of course a necessary condition for a theory in terms of consistency, the problem is that in quantum theory (as described for example in the first pages of Landau/Lifshitz vol.3) this recovery also implies dependency of the classical theory, which is a bad thing for a theory that tries to generalize classical mechanics.
While I'm using a less trivial meaning of classical limit, more related to the concept of global anomaly in quantum field theory, related to how classical symmetries are broken by quantum effects(regardless of the regularization method). I was highlighting the fact that this is not a perturbative effect as it is present non-perturbatively in the path integral approach too so there is a discontinuity between the physical symmetries at tree level and renormalized QED at one-loop order that is obviously not physical.

Now from Vanadium discussion in post #4 he means still a different thing for the sentence "Maxwell's equations are not the classical limit of QED" if I get him right he is saying that one can have a different classical limit than specifically the Maxwell's equations, but apparently he doesn't care that this alternative classical limit with alpha different than 0 would not be Lorentz invariant.

 

[mfb]

This post is aimed at the general audience, I won't tell V50 anything new here:

This is a non-linear effect, so it goes as Q^4. 82^4 is 45 million. That's a heck of a head start.

That alone is not sufficient. The analysis uses 480/µb at 5 TeV nucleus-nucleus cms energy. Scaling it to proton-proton, we get the same events in 20/fb pp collisions at the same energy. We had more than that at a higher energy in run 1 (2011+2012) already.

The problem with proton-proton collisions: a similar number of events has to be found in 50 million times more overall collisions. Many of them will produce two photons without light-by-light scattering, so the process is harder to observe. To make it worse: To handle the huge collision rates, the experiments have to throw away most events in the trigger system - in particular, nearly all low-energetic events are discarded. For events with two photons, typically both photons need ~20 GeV to store the event.
Another issue is pileup - while the lead-lead collisions happen isolated, up to 50 proton pairs collide at the same time in the detectors. That makes the events messy, and it gets challenging to figure out where photons came from.

Protons are smaller than lead nuclei, the maximal energy of the events is higher, but higher energies means even lower production rates.