Lightbylight scattering in a photon–photon collider
Abstract
We studied the feasibility of observing lightbylight scattering in a photon–photon collider based on an existing accelerator complex and a commercially available laser system. We investigated the statistical significance of the signal over the QED backgrounds through a Monte Carlo simulation with a detector model. The study showed that lightbylight scattering can be observed with a statistical significance of eight to ten sigma in a year of operation, depending on the operating conditions.
1 Introduction
Quantum electrodynamics (QED) is one of the most successful theories that describe electromagnetic interaction and has been tested with great precision. Although QED is a wellvalidated theory that underwent many experimental verifications, not all of its predictions have been observed to date. One of such areas is the interaction between real photons. Although the interactions between photons have been tested with great precision, all or a part of the photons involved in these interactions have been virtual photons. For example, electronpositron pair creation caused by a photon impinged on the media, which is one of the most famous and welltested processes in QED, is an interaction between a real photon and electric fields in the media, characterizing a virtual photon. The only experimental observation of pair creation by real photons was obtained through nonlinear QED interaction, performed by the E144 experiment in SLAC [1]. Another phenomenon of interest is lightbylight scattering. A higherorder perturbation of QED predicts an elastic scattering between two photons. This phenomenon has been known since the conception of QED and the crosssection was calculated approximately 50 years ago [2, 3].
While several attempts to observe this phenomenon have been performed, no observation has been reported to date [4, 5]. An experimental observation of this process in heavyion collisions at the LHC has been reported by the ATLAS experiment in 2017 [6, 7]; however, the direct observation in collisions of real photons still remains to be reported.
In this article, we report on the feasibility of observation of lightbylight scattering through a Monte Carlo simulation study considering most of the issues, such as background processes, a detector model and design of a photon–photon collider based on the Beijing Electron Positron Collider (BEPC) accelerator complex in IHEP, China.
2 Photon–photon collider
The concept of a photonphoton collider based on backward Compton scattering was first discussed in [10, 11, 12, 13]. Since then, it has been mainly discussed as an option for high energy electron–positron colliders [14, 15, 16].
Laser and electron beam parameters for the proposed \(\gamma \gamma \) collider
Laser  Electron  

Wave length (\(\upmu \)m)  1.054  Energy (MeV)  245 
Size at focus (\(\upmu \)m)  5  Bunch charge (nC)  2 (0.4) 
Rayleigh Range (\(\upmu \)m)  300  Size of IP (\(\upmu \) m)  2 
Pulse energy (J)  2 (0.4)  Emittance (nm)  5.2 
Pulse Length (ps)  2  Beta* at IP (mm)  727 
Repetition (Hz)  100  Bunch length (mm)  0.6 
Angle (mr) to ebeam  167  Repetition (Hz)  100 
IPCP distance (\(\upmu \)m)  383  Crossing angle (mr)  0 
Nonlinear parameter  0.3 (2 J) 
2.1 The interaction region and detector
We assumed a final focus system which consists of three permanent magnets, similar to that discussed in the reference [8]. The final focus magnet is placed 10 cm from the IP. The inner and the outer radius of the magnet are 3 mm and 50 mm, respectively. To introduce laser pulses to the electron beam, the magnets have holes of 137 mr in an angular aperture centered at 78 mr with respect to the beam axis and pointing to the IP. The angular aperture of the holes is approximately \(\pm 4 \sigma \) of the angular divergence of the laser wave to ensure good focusing property of the laser pulse at the CP. The beam pipe, made of 1mmthick beryllium, has an inner radius of 50 mm so that the final focus magnets are placed within the beam pipe.
3 Event rate and monte carlo event generation

\(\gamma \gamma \rightarrow {e^ + }{e^  }\) Breit–Wheeler process,

\(\gamma \gamma \rightarrow {e^ + }{e^  }\gamma \) and \(\gamma \gamma \rightarrow {e^ + }{e^  }\gamma \gamma \) BreitWheeler process with the final state radiations,

\({e^  } \gamma \rightarrow {e^  } \gamma \) Compton scattering of a Compton photon and a beam electron,

\({e^  } \gamma \rightarrow {e^ + }{e^  }{e^  }\) trident process with a Compton photon and a beam electron,

\( {e^  }{e^  } \rightarrow {e^  }{e^  }\) Moller scattering of beam electrons.
4 Event pileups
In order to ensure proper detector operation and subsequent data analysis, we must suppress the event pileups in a bunch collision below a reasonable level. In general, the acceptable rate of the pileups depends on the details of data analysis and the probability of the pileups and total (integrated) luminosity depend on the laser and electron beam parameters.

When changing the electron bunch charge, the ratios of the number of events for the signal and backgrounds are the same as the estimation with 2nC/bunch and 2 J/pulse case, since bunch luminosities of all combinations, \(L_b^{\gamma \gamma }\), \(L_b^{e^ \gamma }\), \(L_b^{e^ e^}\), have the same charge dependence, i.e, approximately proportional to the square of the electron bunch charge.

When changing the laser pulse energy, \(L_b^{\gamma \gamma }\) is approximately proportional to the square of the laser pulse energy, \(L_b^{e^ \gamma }\) is linearly proportional to the laser pulse energy and \(L_b^{e^ e^}\) is independent of the laser pulse energy. The number of events were estimated accordingly.
5 Data analysis
5.1 Analysis overview
In order to discriminate the background photons from the beam pipe, and the signal from the IP, we increase the radius of the beam pipe to 50 mm so that these two processes can be discriminated from one another by defining proper observables, as described in Sect. 5.2.
5.2 Event analysis
 1.
\({E_j} \equiv \left {{{\mathbf {P}}_j}} \right \); Energy of each jet;
 2.
\(E = \sum {{E_j}} \); total energy deposition of an event;
 3.
\(\cos \,{\theta _{{P_1}}}\)
 4.
\(\cos \,{\theta _{{P_2}}}\)
 5.
\(\,{\theta _{acl}} \equiv \pi  {\mathbf {P}_1}\angle {\mathbf {P}_2}\); acollinearity angle
 6.
\(\,{\theta _{acp}} \equiv \pi  P_1^ \bot \angle P_2^ \bot \) ; acoplanarity angle
 7.
\(E_1^{psc}\); Energy deposition on the plastic scintillator of \({\mathbf {P}_{1}}\)
 8.
\(E_2^{psc}\); Energy deposition on the plastic scintillator of \({\mathbf {P}_{2}}\)
Expected number of signals and backgrounds with 1 year (\(10^7\) s) of operation at the maximum statistical significance (BDT output = 0.295)
\(\gamma \gamma \rightarrow \gamma \gamma \)  \(\gamma \gamma \rightarrow {e^ + }{e^  }\)  \(\gamma \gamma \rightarrow {e^ + }{e^  } \gamma \)  \(\gamma \gamma \rightarrow {e^ + }{e^  } \gamma \gamma \)  \({e^  } \gamma \rightarrow {e^  }\gamma \)  \({e^  } \gamma \rightarrow {e^ + }{e^  }{e^  } \)  \({e^  } {e^  } \rightarrow {e^  }{e^  } \)  bg total 

383.1 ± 2.8  530 ± 150  15 ± 10  6.5 ± 4.6  < 32  131 ± 36  < 0.25  680 ± 160 
364.0 ± 2.6  510 ± 150  14 ± 10  6.2 ± 4.4  < 160  620 ± 170  < 6  1150 ± 270 

\(E < 2.5\) GeV

\(E_1^{psc} = E_2^{psc} = 0 \)

\(\,{\theta _{acp}} < 0.15 \)
To optimize event selection, we used the Boosted Decision Tree (BDT) implemented in the Toolkit for MultiVariable Analysis (TMVA) in ROOT [26]. For each signal and background event, 100 k events were used to train the BDT and remaining events were used to test the performance of the event selection. The outputs from the BDT analysis are shown in Fig. 8.
6 Conclusion
We demonstrated the feasibility of observing lightbylight scattering in a photonphoton collider based on a design with existing facility and feasible technology. An expected statistical significance to observe the signal has been investigated for the first time with a realistic luminosity distribution estimated using an accelerator lattice and laser optics, a detector model that can be constructed using reasonable resources, and a Monte Carlo data analysis considering most of the possible background processes. The results showed that lightbylight scattering can be observed with a statistical significance of eight to ten sigma after 1 year of operation depending on the operating conditions, which is well above the level of discovery.
In this study, we have shown that lightbylight scattering can, in principle, be measured with a gammagamma collider at the CMS energy around 1 MeV. We can, however, consider further developments and optimizations toward the construction of the experimental facility. Methods to manage pileup events must be studied in detail. The number of pileup events depends both on the laser pulse energy and the electron bunch charge, while the acceptable rate of the pileups must be investigated quantitatively by detector simulation. A comprehensive study closely related with hardware design is necessary. The measurement of luminosity is another issue. It is necessary to measure the luminosities not only for \(\gamma \gamma \) collision but also for \(e^{} \gamma \) and \(e^ e^\) collisions. In the analysis we report in this paper, we trained the BDT to maximize \(\gamma \gamma \rightarrow \gamma \gamma \) signal over the background. It is straightforward to train the BDT to enhance other processes such as \(\gamma \gamma \rightarrow e^+ e^\) or \(e^ \gamma \rightarrow e^ \gamma \) or \(e^ \gamma \rightarrow e^ e^ e^+\) or \(e^ e^ \rightarrow e^ e^\) to monitor the luminosity. It is also possible to turn on/off the laser pulses to measure each collision separately. As for the detector system, further R&D, including the machine detector interface, laser optics, readout electronics and data acquisition system, is necessary. The necessity of a tacking detector and/or a solenoid magnet are important issues to be discussed, since they could significantly improve the detector performance.
In addition to the observation of lightbylight scattering, we note that the Breit–Wheeler process has not been observed by the collision of real photons. Furthermore, the proposed photon–photon collision system can be realized as a facility to observe nonlinear effect in QED, such as a shift in the high energy peak and/or multiple photon absorption in Compton scattering.
Notes
Acknowledgements
This work is supported by National Natural Science Foundation of China (11655003), Innovation Project of IHEP (542017IHEPZZBS11820), and in part by the CAS Center for Excellence in Particle Physics (CCEPP).
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