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# Probing non-perturbative QED and new physics with a LUXE-type experiment at
the ILC.

Adrián Irles1 1IFIC, Universitat de València and CSIC, C./ Catedrático José
Beltrán 2, E-46980 Paterna, Spain  on behalf of the LUXE collaboration  1IFIC,
Universitat de València and CSIC, C./ Catedrático José Beltrán 2, E-46980
Paterna, Spain

###### Abstract

The proposed LUXE experiment (LASER Und XFEL Experiment) at DESY, Hamburg,
using the 16.5 GeV electron beam from the European XFEL, aims to probe QED in
the non-perturbative regime created in collisions between high-intensity laser
pulses and high-energy electron or photon beams. In this strong-field regime,
where the electromagnetic field of the laser is above the Schwinger limit,
physical electron-positron pairs will be created from the QED vacuum, similar
to Hawking radiation from black holes. LUXE intends to measure the positron
production rate in an unprecedented intensity regime, in and beyond the regime
expected in the beam-beam interaction of future electron-positron colliders.
This setup also provides a unique opportunity to probe physics beyond the
standard model by leveraging the large photon flux generated at LUXE, probing
axion-like particles (ALPs) at a reach comparable to FASER2 and NA62. In this
contribution, we will give an overview of the LUXE experimental setup and its
challenges and explore the sensitivity of a LUXE-type experiment using the
ILC’s or another future Higgs factory’s electron beam instead of the EU.XFEL
one.

LUXE-PROC-2023-003

Talk presented at the International Workshop on Future Linear Colliders (LCWS
2023), 15-19 May 2023. C23-05-15.3.

##  1 LUXE and the study of strong-field QED

The LUXE (Laser Und XFEL Experiment) aims to study Quantum Electrodynamics,
QED, in uncharted regimes with very strong fields above the critical QED field
strength, also known as the Schwinger limit (in case of an electric field
$E_{\text{cr}}=m^{2}_{e}c^{3}/(e\hbar)\approx 1.32\times
10^{18}\,\text{V/m}$)111Here, $m_{e}$ denotes the electron mass, $c$ the speed
of light in vacuum, $e$ the electron charge and $\hbar$ the reduced Planck
constant. [1]. For a recent review of strong-field QED, SFQED, processes and
effects, see [2]. Two key parameters for LUXE and the study of SFQED are the
classical non-linearity parameter or laser intensity parameter, $\xi$, and the
quantum non-linearity parameter, $\chi$. The former measures the work done by
the EM field over an electron Compton wavelength ($\lambdabar=\hbar/(m_{e}c)$)
in units of the laser photon energy $\hbar\omega$. Whenever it is larger than
unity, calculating processes at any given order in the QED coupling, $\alpha$,
requires a resummation at all orders of $\xi$. The quantum non-linearity
parameter characterises the field strength experienced by an electron in its
rest frame and the recoil experienced by the electron-emitting a photon. Both
parameters222The field intensity parameter is defined as
$\xi=\frac{m_{e}\mathcal{E}_{L}}{\omega_{L}\mathcal{E}_{crit}}$ where
$\omega_{L}$ is the laser wavelength and $\mathcal{E}_{L}$ is the laser
electromagnetic field strength. The quantum non-linearity parameter is defined
as $\chi=\frac{e\mathcal{E}_{L}\lambdabar}{m_{e}c^{2}}$. are dependent on the
beam and laser parameters.

Figure 1: LUXE main Strong Field QED candidate processes.

LUXE main goal is the study of the SFQED, particularly the study of non-linear
Compton scattering and non-linear Breit-Wheeler and non-linear trident pair
production (diagrams shown in Fig. 1. Non-linear Compton scattering refers to
the absorption of multiple laser photons by an electron, which results in the
emission of a single energetic photon. This process is examined by measuring
the displacement of the Compton edge as the laser intensity parameter changes.
On the other hand, the Breit-Wheeler process involves a high-energy photon
absorbing multiple laser photons and producing an electron-positron pair. The
scaling of this process with laser intensity is direct evidence of the
transition from perturbative to non-perturbative QED and has no classical
equivalent.

Figure 2: Quantum parameter $\chi$ as a function of the intensity parameter
$\xi$ for LUXE and a selection of experiments and facilities. Figure extracted
from the LUXE Conceptual Design Report [3]

.

###  1.1 Experimental setup

SFQED fields will be reached at LUXE by creating electron-laser and photon-
laser interactions with the 16.5 GeV electron beam of the European XFEL and a
laser beam with a power of up to 350 TW. A staged approach is planned, using
an upgradable laser system, which will deliver a power of $40\,\text{TW}$ in
phase-0 ($\xi_{\text{max}}=7.9,\>\chi_{\text{max}}=1.5$) and subsequently will
be upgraded to $350\,\text{TW}$ for phase-1
($\xi_{\text{max}}=23.6,\>\chi_{\text{max}}=4.45$). During the data-taking in
LUXE, $\xi$ and $\chi$ are varied by de-focusing and re-focusing the laser
pulse at the interaction point. The reach of LUXE at different stages of its
operation is compared with the other present, past or future experiments in
Fig. 2.

LUXE will run in two modes of operation: the $e$-laser mode, in which the
intense laser collides directly with the electron beam, and the $\gamma$-laser
mode, in which the laser interacts with secondary photons generated by the
electron beam in a high-Z target upstream of the interaction point. These two
operation modes are shown in Fig. 3. In these interactions, a broad range of
fluxes of electrons, positrons and photons will be produced: the expected
ranges are $10^{-3}$ to $10^{9}$ per 1 Hz bunch crossing, depending on the
laser power and focus.

In addition, low-energy high radiation backgrounds will be present at LUXE. To
overcome such challenges and study the SFQED in uncharted regimes with
precision, LUXE foresees the use of dedicated physics-driven detectors at
specific locations downstream of the interaction point.

Saludos,Providing a detailed description of these systems is out of the scope
of this contribution. For a more comprehensive picture, we refer the reader to
the Conceptual Design report of LUXE [3] and the Technical Design report of
LUXE, which will soon appear.

|
---|---
Figure 3: Sketch of the LUXE experimental setups.

##  2 LUXE-NPOD: new physics searches with an optical dump at LUXE

The LUXE experiment will provide an intense secondary beam of hard photons
through the interaction between the high-energy electron beam and the laser
pulses as optical dump. This dump behaves as thick target for the incoming
electron, through non-linear Compton scattering but with negligible
interaction with the photon beam. Fig. 4 shows a schematic illustration of the
optical dump. Therefore, the intense and collimated hard photon beam flux can
be efficiently used for specific new physics searches beyond the Standard
Model, BSM. LUXE plans to use this beam to search for weakly interacting new
particles that couple to photons. In particular, LUXE will provide access to
direct searches of new spin-0 (scalar or pseudo-scalar) particles with
coupling to photons, as the axion-like particles (ALPs). This proposal is
denoted as LUXE-NPOD: New Physics at Optical Dump.

---
Figure 4: Schematic illustration of the optical dump.

The most relevant production mechanism for these new physics particles, NP, is
the so-called secondary NP production. In this case, the photons produced in
the electron-beam and laser pulse collisions freely propagate through the beam
pipe until they reach a sizeable thick dump made of heavy nuclei. These NP are
produced via the Primakoff production mechanism during the photon-nuclei
interaction. The other production mode is the primary NP production, in which
the NP is produced directly in the electron-laser interaction region via
electron coupling. This latter mode of production is considerably suppressed
compared with the secondary NP production, and it allows the inspection of
only low mass NP $\mathcal{O}(keV)$ instead of $\mathcal{O}(GeV)$. These
production mechanisms and their kinematics are schematically represented in
Fig. 5.

---
Figure 5: An illustration of the LUXE-NPOD concept and the different search
modes. Shown are schematics of the secondary (top) and primary (middle)
production mechanisms realisation in the experimental setup. The relevant
background topologies are also shown (bottom). The charged particles are
deflected by a magnet placed right after the interaction chamber.
---
Figure 6: The emitted photon spectrum for phase-0 (1) in blue (black) compared
to the perturbative Bremsstrahlung spectrum with $E_{e^{-}}=16.5$ GeV and
target length of $0.01\leavevmode\nobreak\ X_{0}$ in red.

The number of NP produced and decayed in front of the calorimeter, $N_{X}$,
depends directly on effective luminosity ($\mathcal{L}_{eff}$), the Primakoff
production cross section ($\sigma_{X}$), the energy spectrum of the photon
beam $\frac{dN_{\gamma}}{dE_{\gamma}}$ and the acceptance $\mathcal{A}$ and
geometrical characteristics of the setup and detector:

$N_{X}\simeq\mathcal{L}_{eff}\int
dE_{\gamma}\frac{dN_{\gamma}}{dE_{\gamma}}\sigma_{X}(E_{\gamma})(e^{-\frac{L_{D}}{L_{DX}}}-e^{-\frac{L_{V}+L_{D}}{L_{DX}}})\mathcal{A}$
(1)

The expected $\frac{dN_{\gamma}}{dE_{\gamma}}$ distribution for LUXE operating
in different modes are shown in Fig. 6. The physical dump (or photon dump) at
the end of the beamline is made of a block of tungsten with a length of
$L_{D}=1$ m in the baseline design, and it is positioned at 13 m of the
interaction point. The NP produced in the photon-dump interaction are long-
lived. Therefore, an empty distance $L_{V}=2.5$ m (baseline design) is left
between the physical dump and the detector. $L_{X}$ is the propagation length
of the $X$ particle. The detector should consist of an electromagnetic
calorimeter with good energy and spatial resolution. It must be able to
separate photon showers to reconstruct the $\gamma\gamma$ vertex and the two
photons’ invariant mass with precision. In addition, it should feature photon-
neutron discrimination capabilities and timing of $\mathcal{O}(0.1)$ ns for
the background rejection. The detailed design and technological choice are
still under discussion. The effective luminosity is directly proportional to
the density and radiation length of the physical dump and to the
multiplication of the number of electrons per bunch and total bunches
collected. With these ingredients and assuming one year of data taking and a
negligible amount of backgrounds, the LUXE collaboration has estimated the
projected reach of LUXE-NPOD for the direct searches of new physics. The reach
of LUXE in the plane of the NP mass, $m_{X}$, versus the effective coupling,
$1/\Lambda_{X}$, is shown in Fig. 7 and compared with other existing or coming
experiments. More details on this plot can be found in [4]. This figure shows
that already in the phase-0 LUXE will probe a never reached parameter space in
the mass range of 50 MeV $\lesssim m_{X}\lesssim 250$ MeV and
$1/\Lambda_{X}>4\times 10^{-6}$ GeV-1. For the phase-1, the parameter space is
increased up to 40 MeV $\lesssim m_{X}\lesssim 350$ MeV and
$1/\Lambda_{X}>2\times 10^{-6}$ reaching the naturalness limit for the scalar
model.

---
Figure 7: The projected reach of LUXE-NPOD phase-0 (1) in a solid blue (black)
compared to the currently existing bounds (gray regions) and projections
(dotted) on ALPs-couplings from other experiments. Details on this plot and
references are to be found in [4] .

##  3  LUXE-type experiment at Higgs Factories

In this contribution, we focus on the prospects of having a LUXE-like
experiment at the International Linear Collider (ILC), as studied in [5]. The
ILC and Eu.XFEL beams feature similar characteristics, being both based on 1.3
GHz superconducting radio-frequency cavities producing pulsed electron and
positron beams. However, the ILC and all other Higgs Factories proposals will
operate electron and positron beams of the order of 120 GeV in their baseline
operation modes. This is one order of magnitude larger than what is foreseen
at LUXE with the EU.XFEL electron beam. With this energy, the Lorentz boost of
the photon in the reference system of the accelerated electron will be more
than ten times larger than at the EU.XFEL, resulting in a reach for $\chi$ of
about 40 times more than LUXE. The tentative timeline of the ILC expects
collisions in the mid-2030s. It is realistic to assume that at that time, 100
PW lasers at wavelengths of 1µwill be on reach. Assuming a pulses size of 1µin
diameter, and a pulses length of 120µm, we would expect values of the SFQED
quantum non-linearity parameter of $\chi\sim 250$, which is 40 times larger
than at LUXE in EU.XFEL. Moreover, the combined usage of such powerful laser
and energetic electron beams will allow us to study SFQED phenomena
unreachable until now as can be the creation and dynamics of coherent and
incoherent $e^{+}e^{-}$ plasma.

The direct searches of new scalar or pseudo-scalar particles will also benefit
from the higher beam energy and higher luminosity foreseen at Higgs Factories.
The most critical beam parameters for a LUXE experiment at Higgs Factories are
summarised in Table 1333Compiled by F. Meloni, J. List and F. Zimmerman for
the $1^{st}$ ECFA Workshop on $e^{+}e^{-}$ Higgs/EW/Top Factories, including
prospects for linear and circular Higgs factories proposals. The table assumes
the baseline designs of four different accelerator scenarios and $10^{7}$
seconds of data taking per year. Of course, for ILC or FCC-ee, the beams can
only be used for a LUXE-type experiment once they have been used for their
main purpose (high energy $e^{+}e^{-}$ collisions). For the ILC, this study
assumes the usage of all spent beams, which have a larger energy spectrum than
the primary ones. For FCC-ee, two cases have been considered: the usage of the
dump beams (3 times per day) or the usage of dedicated FCC-ee booster cycles
for a beam dump every 10 seconds. In all cases, the same laser as in phase-0
for LUXE is assumed. The last row shows the enhancement of the signal yield
for ALPs production.

| Accelerators
---|---
Beam parameters | Eu.XFEL | ILC250 | FCC-ee | FCC-ee (booster)
Electron beam energy [GeV] | 16.5 | 125 | 120 | 120
Number of electrons per bunch | $1.5\times 10^{9}$ | $2\times 10^{10}$ | $1.8\times 10^{11}$ | $0.5\times 10^{10}$
Number of bunches in one year | $10^{7}$ | $6.6\times 10^{10}$ | $1.1\times 10^{5}$ | $3.3\times 10^{8}$
Signal Yield (w.r.t. Eu.XFEL) | 1 | $8.8\times 10^{4}$ | 1.3 | $3.3\times 10^{8}$
Table 1: Beam parameters for four accelerator scenarios.

A very important aspect, granted by the higher beam energy, is the harder
photon beam spectrum obtained in the laser-beam interaction, with an average
$E_{\gamma}$ of 40 GeV, in contrast with the expected at LUXE. This is shown
in Fig. 8 and is to be compared with Fig. 6. This alone, without an upgrade of
the laser setup, will allow access to the production of larger masses for the
ALPs.

---
Figure 8: The emitted photon spectrum for a LUXE-like experiment at the ILC.
For comparison, in blue, we show the LUXE phase-0 spectrum. In red is the
perturbative Bremsstrahlung spectrum at ILC. In orange, the expected spectrum
with $E_{e^{-}}=125$ GeV. in red.

The study presented in Section 2 has been extended to the ILC case. Similarly
to the LUXE case, we assumed a background-free scenario but doubled the depth
of the physical dump. The same laser setup as in LUXE phase-0 is assumed, and
only secondary production by the Primakoff process. This leads to an
enhancement of the reach in direct searches of NP, up to masses of 0.5 GeV.
The result of this study is summarised in Fig. 9

Another exciting possibility is to use the photon beam generated by the ILC
positron source to produce and detect the non-standard scalar or pseudo-scalar
particles through the concept of ”light-shining-through-the-wall”. This idea
and that described above are under investigation by the LUXE and ILC
collaborations [5].

---
Figure 9: The projected reach of a LUXE-NPOD proposal operating with ILC
beams. This plot is an update of Fig. 7 with the addition of the study
performed in [5] .

##  4 Conclusion

The main objective of the LUXE experiment is to explore the realm of Strong
Field Quantum Electrodynamics. This will be achieved by analyzing the
collisions between a high-energy photon beam or electron beam and a high-
intensity optical laser. The experiment will be conducted in a continuous
data-taking mode, enabling the measurement of strong-field QED processes such
as non-linear Compton scattering and Breit-Wheeler pair creation with high
precision. The laser system and particle detectors in LUXE are explicitly
designed to cater to the physics requirements of the experiment. LUXE is
poised to become the first experiment to venture into the uncharted territory
of QED under conditions free from external interference, making it a
significant milestone for the scientific community. Additionally, with the
$\gamma$-laser setup LUXE will be the first experiment to investigate
collisions between high-intensity laser and real high-energy gamma photons.

The LUXE-NPOD extension is a novel approach to detecting feebly interacting
spin-0 scalar or pseudoscalar particles. This proposal has the potential to
explore a challenging region of parameter space. It will use an intense GeV
photon beam generated through the interactions between high-energy electrons,
and a highly intense laser pulse, which can be directed towards a target dump
to create new BSM states through the Primakoff process. The produced non-
standard particles would have a lifetime long enough to traverse the target
dump; they can decay into photon pairs that a calorimeter system can detect in
an experiment that is effectively free of background noise. This experiment
could help exclude new scalar or pseudoscalar states with masses ranging
between 40 MeV and 350 MeV for an effective coupling of $1/\Lambda_{X}>2\times
10^{-6}$.

Finally, we presented first studies of the promising prospects of LUXE and
LUXE-NPOD types of experiments using $\mathcal{O}(100$GeV$)$ electron beams
from a future Higgs Factory as the International Linear Collider.

## Acknowledgements

We thank the DESY technical staff for continuous assistance and the DESY
directorate for their strong support and the hospitality they extend to the
non-DESY members of the collaboration. This work has benefited from computing
services provided by the German National Analysis Facility (NAF) and the
Swedish National Infrastructure for Computing (SNIC). AI is funded by the
Generalitat Valenciana (Spain) under the grant number CIDEGENT/2020/21. AI
also acknowledges the financial support from the MCIN with funding from the
European Union NextGenerationEU and Generalitat Valenciana in the call
Programa de Planes Complementarios de I+D+i (PRTR 2022), reference
ASFAE$/2022/015$

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