I Evidence of Light-by-light scattering by ATLAS

[mfb]

For centuries, scientists argued whether light was waves or particles. Light scattering with other light would favor the particle concept. Today we know both models are wrong, but quantum electrodynamics also predicts this scattering - just with an incredibly tiny rate, so it has never been observed before. Lead-lead collisions at the LHC allow a search for it: if the nuclei just pass each other without a direct collision, the intense electromagnetic fields around them can lead to photon-photon interactions. Typically electron/positron pairs are produced, but sometimes the product are photons again.

ATLAS searched for events with two photons and nothing else in the detector (meaning the lead nuclei stayed intact). The expected number of background events (other processes looking like the signal) was 2.7, the expected number of signal events was 7.3, and ATLAS saw 13 events. The significance is 4.4 sigma - the probability of getting 13 background events with just 2.7 expected is very small.
As comparison: Those 13 events were the needle in a haystack of a few billion more violent nucleus-nucleus collisions.

If you think the Higgs took long to discover: 60 years is short compared to the centuries needed to see light-by-light scattering.

CMS should have a similar dataset, but no public result yet. Apart from that, improving the measurements will need more lead-lead collisions, currently scheduled for the end of 2018.CERN Courier article
ATLAS note

 

[Vanadium 50]

There is a discussion here that discusses similar points if the mentors don't want to move it.

I don't understand your point about the particle nature of light. LbyL occurs because of a purely quantum effect: vacuum polarization. Strong fields - in this case, 10^25 V/m - polarize the vacuum, and this allows for various non-linear effects. This one, in fact, is among the more difficult to see. Anyway, while the effect does not appear classically, one can add it in by hand to the classical field equations (Jackson does this in chapter 1) and one gets scattering of light waves by light waves.

 

[mfb]

This statement is from a classical, pre-1900 world view. Classical particles can lead to scattering (and if you think of them as "atoms of light", solid objects of finite size, it is unavoidable), classical linear waves cannot. And no one saw nonlinear effects of light back then.

 

[Vanadium 50]

In 1881 (after Heaviside notation was invented) one could have written down the following expression for light:

\vec{D} =\epsilon_0 \left((1+\alpha (E^2-B^2))\vec{E} + \beta(\vec{E} \cdot \vec{B}) \vec{B} \right)

Here α and β are just parameters. In Maxwell's theory they are both zero, but a completely consistent theory of light can be made for other values. (This is essentially the theory of classical light in a classical medium - the word "photon" never appears. To measure α, you would do experiments like measuring the speed of light in an electric or magnetic field. To measure β, you do light by light scattering. As I said before, classically, β=0. In QED,

\beta = 7 \frac{16\pi}{45} \frac{\alpha_{em}^2}{m_e^4}

The ATLAS measurement says that the coefficient 7 has been measured to be something like 10 +/- 5, but zero can be excluded at 4.4 standard deviations.

No photons required. Just 1881 physics.

 

[mfb]

You expect scattering with particles, but with waves you have to add the scattering manually (and make light nonlinear). I did not say waves would be excluded, I said scattering would favor the particle concept.

 

[Vanadium 50]

and make light nonlinear

But that's the beauty of this measurement! Light really is non-linear! The point of this measurement is not to add fuel to the fire in a 300-year old (and now-settled) argument. It's that Maxwell's Equations are not the classical limit of QED, and that we finally have a measurement that shows this. Pretty cool, huh?

 

[RGevo]

Is the observed running of the qed coupling also evidence?

 

[atyy]

I don't understand your point about the particle nature of light. LbyL occurs because of a purely quantum effect: vacuum polarization. Strong fields - in this case, 10^25 V/m - polarize the vacuum, and this allows for various non-linear effects.

But that's the beauty of this measurement! Light really is non-linear! The point of this measurement is not to add fuel to the fire in a 300-year old (and now-settled) argument. It's that Maxwell's Equations are not the classical limit of QED, and that we finally have a measurement that shows this. Pretty cool, huh?

If Maxwell's equations are not the classical limit of QED, then wouldn't LbyL not be a purely quantum effect?

Is it true that Maxwell's equations are not the classical limit of QED? I guess classical limit means $\hbar \rightarrow 0$?

 

[atyy]

For centuries, scientists argued whether light was waves or particles. Light scattering with other light would favor the particle concept.

Couldn't LbyL be described by nonlinear waves?

 

[Vanadium 50]

If Maxwell's equations are not the classical limit of QED, then wouldn't LbyL not be a purely quantum effect?

We can spend a lot of time discussing words that describe the equations, but the reality is the equations. The effect is purely quantum mechanical, yes, but it ends up appearing on a macroscopic scale. Like I wrote in post #4, one can write down a general expression for the classical polarization tensor, and you get different predictions from the QED classical limit than you do from Maxwell. Now this difference is visible.

 

[atyy]

We can spend a lot of time discussing words that describe the equations, but the reality is the equations. The effect is purely quantum mechanical, yes, but it ends up appearing on a macroscopic scale. Like I wrote in post #4, one can write down a general expression for the classical polarization tensor, and you get different predictions from the QED classical limit than you do from Maxwell. Now this difference is visible.

By quantum, is it right to say that LbyL appears at loop level in the QED expansion (ie. not at tree level, which in QED is typically the classical term)?

 

[mfb]

Sure.

Couldn't LbyL be described by nonlinear waves?

Yes, see posts 2-5 for a discussion.

 

[Vanadium 50]

LbyL appears at loop level in the QED expansion

Yes, it appears at one loop.

 

[vanhees71]

Yes, at leading order the four-photon vertex, describing scattering of light by light, is a set of box diagrams of order $e^4$. There is no renormalizable four-photon vertex at tree level. That's why it doesn't occur in the fundamental QED Lagrangian (assuming that QED should be a renormalizable QFT). Power counting shows that each box diagram is logarithmically divergent, which smells like desaster, because since there's no renormalizable gauge invariant four-photon term to put as counter term it seems as if QED is inconsistent. However, gauge symmetry comes to a rescue. If you take all the box diagrams together, as you must do to be consistent at the one-loop order (i.e., the order $\hbar$ in the loop expansion of the proper vertex functions), the result turns out to be finite due to a Ward-Takahashi identity that follows from electromagnetic gauge invariance. So the scattering of light by light is a clear prediction of a pure quantum effect in renormalizable QED.

Historically, it's also a result of one of the first calculations of an effective low-energy QFT by Euler and Heisenberg (1936). In modern terms it's "integrating out the electrons". The Euler-Heisenberg Lagrangian provides the higher-order non-renormalizable terms in the quantum action (which is the pendant of the classical action, including quantum effects and is in fact the generating functional for proper vertex functions), leading to non-linear field equations. Effectively that means to contract the boxes to a point, which is possible at very low scattering energies of photons by photons (the "high-energy" scale in this approach is the electron mass).

https://en.wikipedia.org/wiki/Euler–Heisenberg_Lagrangian

 

[mfb]

Effectively that means to contract the boxes to a point, which is possible at very low scattering energies of photons by photons (the "high-energy" scale in this approach is the electron mass).

At low energies the process hasn't been observed yet - the ATLAS study looks for multi-GeV-photons., 4 orders of magnitude above the electron mass.

 

[vanhees71]

Sure, it's amazing that ATLAS could do it at the high photon energies. For ultrasoft photons (with energies at the order of below 511 keV) I'm pretty sure there's no chance.

 

[mfb]

At very low energies, the cross section is $\displaystyle \frac{\alpha^4 s^3}{m_e^8}$, with red lasers (800 nm) we get s=(3 eV)^2, and a cross section of the order of 10^-64 m² = 10^-20 fb (a few million times the Planck area).

Slide 13 in this presentation shows that ~1PW lasers should be sufficient to get scattering (without saying anything about the focusing). There are a few lasers with such a power, but the extreme light infrastructure plans to get much more powerful lasers, with a peak power of 10+ PW, later up to 200 PW (http://www.eli-beams.eu/science/lasers/ ). This is more than the total power of sunlight hitting the Earth - but the laser has this just for a femtosecond every 10 seconds. That power should be sufficient to get many scattering pairs.

 

[Vanadium 50]

How good is the vacuum in these systems? The problem with these very low cross-sections is that a single atom in the area of convergence can produce many times as much scattering. (Put another way, a single atom changes the properties of the medium more than the quantum corrections do). One advantage of working at the GeV scale is that atomic effects are much smaller.

The question of whether ATLAS could see 1/2 MeV photons came up. The answer is no. ATLAS wasn't even designed to do this measurement. One could certainly design an experiment that would do this - the challenge would be to maintain this level of performance when also blasted a billion times by energetic lead-lead collisions. But why? If you're interested in vacuum polarization, there are much better ways to do this: lepton magnetic moments, for example. The measurement is neat - it shows directly at low precision what we knew indirectly at high precision - but it is sort of a dead end scientifically.

If you like, it tells us that the LQP - the lightest charged particle - is the electron. Nice, but it closes the book on that line of speculation.

 

[vanhees71]

Well, sure, the evidence for the correctness of QED at the many-loop level is in precision experiments like the anomalous magnetic moment of the electron and muon or the Lamb shift. Nevertheless it's fascinating that you also can also directly measure the light-by-light scattering process directly.

 

[mfb]

Scattering with an atom should produce a different angular distribution, and you have to subtract background anyway (also from scattering at material elsewhere).
If they can make the spectrum narrow enough (=>pulse length has to go up) while keeping a reasonable intensity, they can also cross the lasers at an angle, and observe scattered photons at different energies depending on their direction.

Sure, electron g-2 experiments test the same vertices, but measuring something in a new way is always nice.

 

[Vanadium 50]

. Nevertheless it's fascinating that you also can also directly measure the light-by-light scattering process directly.

I agree. But I don't think you learn anything with 1000 events that you didn't learn with 13.

 

[mfb]

You get better limits on deviations from QED at this particular process. In addition, the energy range the LHC probes is different from g-2 experiments.

As a random other example, the LHC experiments also look for H->eµ although muon decay experiments set much more sensitive limits on it already. Why? Because we might not understand how BSM physics works.

 

[fluidistic]

Apparently this experiment is not the first to show an evidence of light-by-light scattering. http://physics.stackexchange.com/a/1364/75916

 

[mfb]

The SLAC experiment had light producing electron plus positron (something the LHC also saw years ago if I remember correctly). The recent LHC result is the first measurement of light->light scattering.

 

[Vanadium 50]

You get better limits on deviations from QED at this particular process. In addition, the energy range the LHC probes is different from g-2 experiments.

Up to a challenge? Can you write down a Lagrangian that shows an observable deviation in LbyL at the LHC but leaves the fermion magnetic moments consistent with their measured values? I don't think this is possible - at least not without a multiway conspiracy of cancellations.

 

[mfb]

I cannot, but I have seen theorists writing down things for superluminal neutrinos. If the LHC would find a deviation, I'm sure theorists would find something within days.

 

[MathematicalPhysicist]

I cannot, but I have seen theorists writing down things for superluminal neutrinos. If the LHC would find a deviation, I'm sure theorists would find something within days.

:-D LOL
It makes you think how much does their work have any merits on experiments... :-D

 

[atyy]

You get better limits on deviations from QED at this particular process. In addition, the energy range the LHC probes is different from g-2 experiments.

As a random other example, the LHC experiments also look for H->eµ although muon decay experiments set much more sensitive limits on it already. Why? Because we might not understand how BSM physics works.

How about LbyL versus muon g-2?

 

[RockyMarciano]

We can spend a lot of time discussing words that describe the equations, but the reality is the equations. The effect is purely quantum mechanical, yes, but it ends up appearing on a macroscopic scale. Like I wrote in post #4, one can write down a general expression for the classical polarization tensor, and you get different predictions from the QED classical limit than you do from Maxwell. Now this difference is visible.

Yes the difference is visible, making the reality of the equations evident. Let's reflect on what this means. Here we don't simply have a quantum correction that gives you different decimals in a calculation. This is showing how the inexistent 0-loop interaction between 2 photons happens to become an existent interaction with enough energy at one loop. A supposedly purely perturbative effect(that is usually depicted graphically with the appearance of inexistent virtual pairs) is giving us a certainly non-perturbative visible effect.
Theorists will mention things like external/global anomalies but how does an experimentalist explain this to avoid mentioning lack of unitarily equivalence between 0-loop and one-loop?

Yes, at leading order the four-photon vertex, describing scattering of light by light, is a set of box diagrams of order $e^4$. There is no renormalizable four-photon vertex at tree level. That's why it doesn't occur in the fundamental QED Lagrangian (assuming that QED should be a renormalizable QFT). Power counting shows that each box diagram is logarithmically divergent, which smells like desaster, because since there's no renormalizable gauge invariant four-photon term to put as counter term it seems as if QED is inconsistent. However, gauge symmetry comes to a rescue. If you take all the box diagrams together, as you must do to be consistent at the one-loop order (i.e., the order $\hbar$ in the loop expansion of the proper vertex functions), the result turns out to be finite due to a Ward-Takahashi identity that follows from electromagnetic gauge invariance. So the scattering of light by light is a clear prediction of a pure quantum effect in renormalizable QED.

Of course gauge invariance is enforced at the relevant order. But could you elaborate on the importance of the fact that al these nice consistency checks (unitarity and lorentz invariance, gauge invariance) are only valid up to loop order in the renormalized theory and how this is relevant or irrelevant for the symmetries of the S-matrix Dyson-Wick's expansion as a whole?

 

[vanhees71]

I cannot, but I have seen theorists writing down things for superluminal neutrinos. If the LHC would find a deviation, I'm sure theorists would find something within days.

Well, but what was written about superluminal neutrinos during the OPERA hype was more embarassing for theorists than anything else .

 

[DrDu]

Hurray, we don't need crystals any more to do nonlinear optics!

 

[Vanadium 50]

Hurray, we don't need crystals any more to do nonlinear optics!

Just patience. Lots and lots of patience.

 

[Vanadium 50]

Rocky, this is far from the 1st time this has been seen. The decay pi0 --> gamma gamma occurs through a process that does not exist at all classically. You may have heard the term "anomaly", which refers to a classical symmetry that is not present quantum mechanically.

 

[mfb]

:-D LOL
It makes you think how much does their work have any merits on experiments... :-D

There is a lot of useful work, but I don't trust "I found a Lagrangian for that", because experience shows that people find Lagrangians for everything.

How about LbyL versus muon g-2?

See the post you quoted. I said "g-2" because it applies to both electron and muon g-2.

@RockyMarciano: Processes that don't have tree-level diagrams are not new. Neutral meson mixing, flavor-changing neutral currents, Higgs to photon decays, gluon fusion as dominant Higgs production mode, ...

 

[RockyMarciano]

@RockyMarciano: Processes that don't have tree-level diagrams are not new. Neutral meson mixing, flavor-changing neutral currents, Higgs to photon decays, gluon fusion as dominant Higgs production mode, ...

Rocky, this is far from the 1st time this has been seen. The decay pi0 --> gamma gamma occurs through a process that does not exist at all classically. You may have heard the term "anomaly", which refers to a classical symmetry that is not present quantum mechanically.

Yes, that is what I meant when I wrote that theorists refer to these as global anomalies. I'm not saying this is new conceptually. I could have asked the same question about any of those processes but this thread happens to be about gamma-gamma scattering and it is nice to get to see it (not that anyone was expecting otherwise).
But Vanadium you wrote: "The point of this measurement is [...] that Maxwell's Equations are not the classical limit of QED, and that we finally have a measurement that shows this. Pretty cool, huh?". And with my question I was trying to get you to comment on that coolness ;)
Because the usual argument is that QED classical limit should be Maxwell's equations, as the symmetry of classical electrodynamics is the group leaving the Minkowski spacetime invariant and we are still using Minkowski spacetime as background in QED last I heard.

 

[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.