# FeaturedI Evidence of Light-by-light scattering by ATLAS

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1. Nov 12, 2016

### Staff: Mentor

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

2. Nov 12, 2016

Staff Emeritus
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.

3. Nov 12, 2016

### Staff: Mentor

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.

4. Nov 12, 2016

Staff Emeritus
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.

5. Nov 12, 2016

### Staff: Mentor

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.

6. Nov 12, 2016

Staff Emeritus
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?

7. Nov 12, 2016

### RGevo

Is the observed running of the qed coupling also evidence?

8. Nov 12, 2016

### atyy

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 $\hbar \rightarrow 0$?

9. Nov 12, 2016

### atyy

Couldn't LbyL be described by nonlinear waves?

10. Nov 12, 2016

Staff Emeritus
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.

11. Nov 13, 2016

### atyy

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)?

12. Nov 13, 2016

### Staff: Mentor

Sure.
Yes, see posts 2-5 for a discussion.

13. Nov 13, 2016

Staff Emeritus
Yes, it appears at one loop.

14. Nov 14, 2016

### 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

15. Nov 14, 2016

### Staff: Mentor

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.

16. Nov 14, 2016

### 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.

17. Nov 14, 2016

### Staff: Mentor

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/ [Broken]). 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.

Last edited by a moderator: May 8, 2017
18. Nov 14, 2016

Staff Emeritus
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.

19. Nov 14, 2016

### 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.

20. Nov 14, 2016

### Staff: Mentor

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.