Photon-photon elastic scattering is a very rare phenomenon in which two real photons interact producing a new real photon pair. The direct observation of this process at high energy, impossible during decades, was done by ATLAS  and CMS  experiment at CERN between 2016 and 2019. These successes have led the two collaborations to strengthen their involvement in this new field, leading to a new measurement, currently being published by the ATLAS experiment . Presented for the first time at the LHCP conference in May 2020, the new idea is to use photon collisions to search for a hypothetical axion-like particle. As with the first publications on the subject, IRFU members are at the origin of the ideas at work in the analyses carried out at CERN.
Particle of light in collision
The elastic collision of real photons is a very rare phenomenon in which two real photons interact, producing another pair of real photons. Direct observation of this high-energy process proved difficult for decades, until it was observed by the ATLAS and CMS experiments at CERN between 2016 and 2019 . Let us recall that this phenomenon is predicted by the Standard Model of Particle Physics, it is a process of a quantum nature. However, in classical electromagnetism, if we add to Maxwell's equations a current density vector proportional to a power of the electric field present in the medium, then the collision of two photons becomes possible. For more precision, one can rely on exercise 5 of a collection of exercises proposed at X oral exams. Thus, the theoretical origin of the effect lies in the non-linear nature of the equations describing this phenomenon in the standard model. This phenomenon is a natural consequence of quantum mechanics in the standard model, but can also be seen as an extension of elementary physics in the sense described above.
The result  opens a new field of exploration at the frontier between heavy ion physics and quantum electrodynamics. Thus, the research theme has flourished with more data accumulated and more personnel involved. This effort has led quite rapidly to a new measurement, which is being published by the ATLAS experiment . It was first presented at the LHCP conference in May 2020. This time, the new idea is to use photon collisions (induced during heavy ion collisions) to search for an unknown particle, which would behave like a scalar field (thus a bit like the Higgs-Brout-Englert boson field) and which is commonly called Axion. This idea had been exposed in a more general way in an article preceding that of the ATLAS experiment and which was used as a reference for the study . The idea, once again, finds its most complete expression in the Standard Model, but it can also be understood in elementary physics, as can be seen with exercise 2 of the collection cited above. Finally, it is once again with an almost intuitive approach that one can understand practically everything on this research topic, identify the simplest possible ideas and consequently propose a new measure.
Experimental context of photon-photon collisions
Let us recall the context. Lead ion (Pb) collisions (with a +82 charge) at the Large Hadron Collider (LHC) at CERN provide the ideal environment to study photon-photon scattering . Indeed, when Pb ions accelerate to near-light speed, a huge flow of photons is generated by these positively charged ultra-relativistic ions. Equivalent to this, an extremely intense electric field of about 1025 V/m is generated in the immediate environment of each Pb ion. It is understandable why with such field values, standard electromagnetism is not applicable and non-linear effects have to be included. Therefore, when two Pb ions from beams propagating in opposite directions pass side by side, remaining at a small but non-zero distance from each other, of the order of 10 femto-meters (fm), photons accompanying the Pb ions may interact. This is how photon-photon elastic collision is possible in practice.
Moreover, because Pb ions lose only a tiny fraction of their energy in this process, the outgoing ions continue their path around the LHC ring. This leads to a clear characterization of the events, with two photons observed in the ATLAS central detector and no other activity in this detector. In addition, Pb ions are observed almost intact in their beamlines several tens of meters from the central detector. If an event is observed with these characteristics, it is said to be a candidate event.
New results recently presented by the ATLAS collaboration include the LHC Run-2 heavy ion (Pb-Pb) collision data set . Out of more than one hundred billion collisions in which Pb ions remain at a distance of the order of 10 fm, 97 candidate events have been identified, while 27 events are expected from background processes. The figure below shows this observation converted into the measurement of the two-photon elastic collision cross-section. In particular, the figure on the left shows the result as a function of the invariant mass of the two emitted photons, expressed in GeV/c2, thus in GeV with natural units. At present, this is the best result.
Differential cross-section of the elastic collision of two photons in Pb-Pb collisions (with an energy of 5.02 TeV per nucleon pair) as a function of the invariant mass of the photon-photon pair and the cosine of the scattering angle in the center of mass of the photon-photon pair. The red curve corresponds to the theoretical prediction (called SuperChic) which includes a calculation of the elastic collision of photons in the standard model. Note that it approximatively describes the data but it is far from being perfect. This shows us that there are still elements to improve theoretically.
The hypothetical axions under constraint
As mentioned above, the measurement of the cross-section of the photon-photon elastic collision is sensitive to processes beyond the standard model. Thus, the presence or absence of a scalar axion-like particle can change the cross-section of the standard model photon-photon interaction [3, 4]. The new analysis of the ATLAS experiment places limits on the production rate of these particles, the best existing limits to date in the considered measurement range. To do better, it will be necessary to take up some of the ideas outlined in  but this cannot be done immediately.
Recall that the axion-like particles (called simply "axions" hereafter) are hypothetical spinless (i.e. scalar) particles with an odd parity quantum number and weak interactions with standard model particles. In particular, these particles are good candidates to be part of the so-called dark matter in astrophysics. The new result discussed here is based on the idea that if the pairs of interacting photons produce axions, this could occur via the following successive reactions: photon-photon → axion → photon-photon. This is why there would then be an excess of events for a mass of the observed photon-photon pair equal to the mass of the axion, which is called a resonance. The results are presented in the figure below, which shows exclusion zones in the plane axion-photon-photon coupling intensity (1/Λ) versus axion mass. The couplings that remain possible after this study (within the statistical limits of this kind of analysis) have a value below the coloured zones.
Note that only a possible resonance effect with a high quality factor can reveal hypothetical axions. This was the difficulty of the task: we know how to use Pb ion beams as pulsed laser sources, but we have to identify within the photon collision process in the ATLAS experiment the equivalent of a cavity with a large quality factor. This is what we have produced here.
A prosperous future for photon collisions
In conclusion, it is understandable that such tenuous phenomena should be re-examined with more refined analyses or new ideas. In particular, in  we have introduced many ideas that still remain to be explored. For example, there is an important interest to study collisions with oxygen or argon ions and even to consider unsymmetrical collisions of a heavy ion with a proton and to conduct the same kind of experimental study as described here. There is therefore a whole programme still pending for LHC Run-3.
 Previous highlight
 Evidence for light-by-light scattering and searches for axion-like particles in ultraperipheral PbPb collisions at √SNN = 5.02 TeV
 Measurement of light-by-light scattering and search for axion-like particles with 2.2/nb of Pb+Pb data with the ATLAS detector, ATLAS-CONF-2020-010
 Extending the constraint for axion-like particles as resonances at the LHC and laser beam experiments, S. Hassani, L. Schoeffel et al., Phys. Lett. B 795 (2019) 339-345.
Contact: Laurent Schoeffel