LUXE-Proc-2021-001

LUXE: A new experiment to study non-perturbative QED in $e^{-}$-laser and
$\gamma$-laser collisions

Ruth Jacobs1$\star$, on behalf of the LUXE collaboration

1 Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany

*<EMAIL_ADDRESS>
Proceedings for the XXVIII International Workshop
on Deep-Inelastic Scattering and Related Subjects,
Stony Brook University, New York, USA, 12-16 April 2021
10.21468/SciPostPhysProc.?

## Abstract

The LUXE experiment (Laser Und XFEL Experiment) is a new experiment in
planning at DESY Hamburg using the electron beam of the European XFEL. LUXE is
intended to study collisions between a high-intensity optical laser and up to
16.5 GeV electrons from the Eu.XFEL electron beam, or, alternatively, high-
energy secondary photons. The physics objective of LUXE are processes of
Quantum Electrodynamics (QED) at the strong-field frontier, where QED is non-
perturbative. This manifests itself in the creation of physical electron-
positron pairs from the QED vacuum. LUXE intends to measure the positron
production rate in a new physics regime at an unprecedented laser intensity.
Parasitically, the high-intensity Compton photon beam of LUXE can be used to
search for physics beyond the Standard Model.

##  1 Introduction

Quantum Electrodynamics (QED) is the most well-tested theory in physics. The
success of QED is based on comparing ultra-precise perturbative calculations
with experimental data. However there exists a regime in which perturbative
calculations of QED break down, namely in the vicinity of a strong background
field. If the field energy (i.e. the work by the field over one Compton
wavelength) is larger than the rest mass of a virtual particle, the vacuum
becomes polarized. In strong-field QED this polarization is expected to
manifest itself in the creation of physical electron-positron pairs from
virtual electron-positron vacuum fluctuations [1]. The critical field
strength, $\mathcal{E}_{\text{crit}}$, required for this process is called the
"Schwinger limit" [2]. For an electrical field, the Schwinger critical field
corresponds to $\mathcal{E}_{\text{crit}}=m_{\text{e}}^{2}c^{3}/e\hbar\approx
1.32\times 10^{18}\;\text{V/m}$. In nature, strong-field QED plays a role, for
example in the gravitational collapse of Black Holes [3], the propagation of
cosmic rays [4], or in processes on the surface of strongly magnetized neutron
stars [5, 6, 7]

The LUXE experiment [8] proposed at DESY and the European XFEL (Eu.XFEL) in
Hamburg and Schenefeld, Germany, is intended to study strong-field QED
processes in collisions of a high-intensity optical laser and the 16.5 GeV
electron beam of the Eu.XFEL, as well as collisions of the high-intensity
optical laser and high-energy secondary photons. The strong background field
is provided by the Terawatt laser-pulse and enhanced by the Lorentz boost of
the electrons. This will allow LUXE to explore a previously uncharted
intensity regime.

This article is structured as follows: Section 2 gives an overview of strong-
field QED processes and parameters. Section 3 introduces the proposed LUXE
experimental setup, including the laser and particle detectors. Section 4
showcases the expected measurement results. Finally, the conclusion is
presented in section 5.

##  2 Strong-field QED processes at LUXE

Two parameters are commonly used when describing processes of non-linear QED:
the so-called classical non-linearity parameter of the laser field,
$\xi=e\mathcal{E}_{L}/m_{e}\omega_{L}$, where $\omega_{L}$ is the laser
frequency, quantifies the coupling of the laser field to the probe charge. In
the regime where $\xi\ll 1$, QED is fully perturbative, while, as $\xi$
approaches 1, an increasing number of higher-order processes contribute, until
for $\xi>1$, the perturbative expansion breaks down and QED becomes non-
perturbative in the coupling to the laser field. The second parameter is the
quantum parameter $\chi_{e}=E^{\star}/\mathcal{E}_{\text{crit}}$ which, in
case of electron-laser interaction, quantifies the ratio of the effective
field strength in the electron rest frame and the critical field. The quantum
parameter $\chi_{\gamma}$ for photon-laser collisions is defined analogously
as $\chi_{\gamma}=(1+\cos\theta)E_{\gamma}/(m_{e}\mathcal{E}_{\text{crit}})$.

(a) Non-linear Compton scattering.

(b) Non-linear Breit-Wheeler pair production.

Figure 1: Feynman diagrams of strong-field QED processes at LUXE [8].

In electron-laser collisions, the process of interest for the LUXE experiment
are non-linear Compton scattering (see figure 1(a)) and subsequent non-linear
Breit-Wheeler pair production (see figure 1(b)). In non-linear Compton
scattering, the incident photon absorbs multiple laser photons, emitting a
single Compton photon. This Compton photon undergoes non-linear Breit-Wheeler
pair creation by absorbing multiple laser photons and creating an electron-
positron pair. The combined process $e^{-}+n\gamma_{L}\rightarrow
e^{-}+e^{+}+e^{-}$, known also as the Trident process can in general take
place as a "one-step" process with an off-shell virtual photon, or as "two
step" process with a real photon. In the LUXE parameter regime, the two-step
process is dominant, whereas the one-step process is negligible. In photon-
laser collisions, the incident high-energy Bremsstrahlung photons undergo non-
linear Breit-Wheeler pair production (figure 1(b)) directly, in the reaction
$\gamma_{B}+n\gamma_{L}\rightarrow e^{+}+e^{-}$ [9].

The main experimental goal of LUXE is to measure the positron rate of the
Trident process and the direct Breit-Wheeler pair production as a function of
the laser intensity parameters $\chi$ and $\xi$.

##  3 LUXE experimental setup

The LUXE experiment will be located at the end of the Eu.XFEL electron
accelerator. A dedicated beam-line was designed to extract one single electron
bunch out of 2500 bunches per Eu.XFEL train to be guided to the LUXE
experimental area at a repetition rate of $10\,\text{Hz}$ [10]. The laser will
operate at a $1\,\text{Hz}$ repetition rate, enabling in-situ background and
calibration data-taking. This design allows LUXE to collect a large sample of
precision data while being transparent to the Eu.XFEL photon science
programme.

The field strength of the high-intensity laser in the laboratory frame,
$\mathcal{E}_{L}$, with current state-of-the-art lasers, is three orders of
magnitude below the Schwinger limit. However, the Lorentz boost of the 16.5
GeV incoming electrons leads to an enhancement of the field $E^{\star}$
experienced by the electrons in their rest frame:

$E^{\star}=\gamma_{\text{e}}\mathcal{E}_{L}(1+cos{\theta}),$ (1)

where $\gamma_{\text{e}}\sim 10^{4}$ is the electron Lorentz factor and
$\theta=17.2^{\circ}$ is the foreseen crossing angle between the electron beam
and the optical laser pulse in LUXE. As a result, field strengths above the
Schwinger limit are accessible at LUXE with current laser technologies.

###  3.1 The Laser

The laser intended for the LUXE experiment is a femtosecond-pulsed Titanium-
Sapphire optical laser ($\lambda_{L}=800\,\text{nm}$) using the chirped-pulse-
amplification technique [11]. A staged approach is foreseen, where for phase-0
the existing, well-characterized Jenaer Titan:Saphir $40\,\text{TW}$ Laser
System (JETI40) will be used, which for phase-1 of LUXE will be replaced by an
upgraded $350\,\text{TW}$ laser system. The laser intensity parameter $\xi$ is
varied by changing the laser focal spot size in the interaction point, with
the highest $\xi\sim 7.9(23.6)$ in phase-0 (phase-1) achieved with a $3\,\mu
m$ spot size. The maximum quantum parameter $\chi_{e}$ achievable is
$\chi_{e}=1.5(4.45)$ with the phase-0 (phase-1) setup. Among the most
important characteristics of the laser system is its precise shot-to-shot
stability. This will be ensured by several redundant diagnostics measurements
both on the unperturbed outgoing laser beam itself, as well as by precision
determination of particle spectra after the interaction points.

###  3.2 Particle detectors

Figure 2 shows a schematic drawing of the particle detectors for the electron-
laser and the photon-laser setup. Both setups employ a magnetic dipole
spectrometer (B=1.5T) to measure the energy spectrum of electrons and
positrons after the interaction point. For every detection area, two redundant
detector technologies are foreseen, to enable cross-calibration and reduction
of systematic uncertainties. One of the biggest challenge of the LUXE
experiment are the vastly different particle rates in different detection
areas of the setup. The detector technologies have been specifically adapted
for the conditions in which they need to operate in LUXE:

(a) Electron-laser setup.

(b) Photon-laser setup.

Figure 2: Sketch of the LUXE experimental setups [8].

  * •

positron detectors: The positron rates for the Breit-Wheeler and Trident
process vary between $10^{-3}-10^{4}e^{+}/\text{shot}$. The foreseen detector
system consists of four layers of Silicon pixel tracking detectors using the
ALPIDE sensor technology, as well as a high-granularity Tungsten-Silicon
electromagnetic calorimeter. The main objectives are a high signal efficiency
and good background rejection.

  * •

electron detectors: For the electron-laser setup the rate of Compton-scattered
electrons is of the order of $10^{9}/\text{shot}$, therefore the detectors
must be tolerant of such high rates. Foreseen are segmented Argon-filled
Cherenkov detectors, measuring the particle rate as a function of deflection
by the magnetic field, as well as a Scintillator screen that is read out by an
optical camera. The Scintillator provides excellent position resolution, while
the Cherenkov detector helps to reject photons and low-energy backgrounds due
to the Cherenkov threshold of $\sim 20\,\text{MeV}$. In case of the photon-
laser setup, the particle rates between electron and positron side are
comparable. In this case the detector system on the electron side will consist
also of a Tracker and Calorimeter.

  * •

photon detectors: In both electron- and photon-laser setups there is a large
flux of photons. The photon energy and flux are characterized by several
systems, namely by studying the conversion into electron-positron pairs on a
target, as well as directly profiling the photon beam angular distribution
using Sapphire strips. Finally, the photon flux is determined by measuring
backscattering from the photon beam dump in a crystal calorimeter.

###  3.3 Parasitical BSM search

In both the electron-laser and the photon-laser setup, the LUXE experiment
produces a high-intensity beam of GeV photons, in the former case via Compton-
scattering and in the latter, via Bremsstrahlung. A photon beam dump is
foreseen at the end of the LUXE setup. One of the possible scenarios for
Beyond-the-Standard Model physics in LUXE is the production of axion-like
particles (ALPs) in the photon beam dump material (see figure 3), which decay
into a pair of photons behind the dump and get detected by a photon detector
at the end of the LUXE experimental setup. With a $1\times 1m^{2}$ detector
area, the expected sensitivity of LUXE to axion-like particles in the
lifetime-mass plane is comparable with that of other ongoing and future
experiments [12].

Figure 3: Possible production modes of long-lived BSM particles in LUXE [8].

##  4 Expected results

The main goal of the LUXE experiment is to measure the positron rate from
vacuum polarization as a function of the laser intensity parameter $\xi$ and
the quantum parameter $\chi$ and to compare it to theoretical predictions from
strong-field QED. In strong-field QED, the probability to create an electron-
positron pair via Breit-Wheeler pair production, $P$, is expected to have a
tunneling-like dependence
$P\propto\chi_{\gamma}\exp\left(-\frac{8}{3\chi_{\gamma}}\right)$, for $\xi\gg
1$. At low $\xi\ll 1$, the behavior can be approximated by a power law
$P\propto\xi^{2n}$, however the perturbative expansion breaks down for values
of $\xi>1$.

Figure 4(a) shows the expected probability of Breit-Wheeler pair production as
a function of the laser intensity parameter $\xi$ and the quantum parameter
$\chi$. It is clearly visible how the rate predicted by strong-field QED
departs from the power-law expectation from perturbative calculation in the
parameter regime that will be reached by LUXE. It is expected that the main
source of uncertainty on the positron rate originates from the uncertainty of
the laser intensity parameter $\xi$. The goal is to achieve an uncertainty on
$\xi$ of $5\%$, which results in an uncertainty of about $40\%$ on the
positron production rate. Several complementary measurements of $\xi$ are
foreseen in the LUXE setup to ensure that $\xi$ is determined with sufficient
precision.

(a) Predicted probability of Breit-Wheeler pair production for the LUXE
experiment [8].

(b) LUXE and other strong-field QED experiments in the strong-field QED
parameter space [8].

Figure 4:

Figure 4(b) shows the region in parameter space that is accessible by the LUXE
experiment, in comparison to a selection of past and future strong-field QED
experiments. The $\chi$ and $\xi$ values accessible with LUXE depend on the
power of the laser system as well as on the laser spot size. With the foreseen
upgrade to a $350\,\text{TW}$ laser power in connection with a small spot size
($3\,\mu\text{m}$), LUXE is expected to reach well into the non-perturbative
regime of $\chi>1$ and $\xi>1$. Compared to the previous E144 experiment [13,
14], the LUXE phase-1 setup will attain a factor of 20 higher $\chi$ and a
factor of 60 higher $\xi$. This improvement is mainly due to the higher laser
intensity of the LUXE laser. Another novelty of the LUXE experiment compared
to previous strong-field QED experiments are the foreseen collisions between
real, externally produced GeV photons with the laser.

##  5 Conclusion

The LUXE experiment aims to explore a previously uncharted regime of Quantum
electrodynamics by studying electron-laser and photon-laser interactions, with
the potential of being the first to enter the non-perturbative Schwinger
regime of QED. Using one bunch per train of the $16.5\,\text{GeV}$ electron
beam of the European XFEL, a state-of the art optical Terawatt laser system
and specifically optimized detector technologies, LUXE aims to collect a large
dataset of electron- and photon-laser collisions in order to perform precision
measurements of strong-field QED. The Compton photon beam of LUXE impinging on
a beam dump can be used to search for signs of physics beyond the Standard
Model, with the BSM detector running at the same time as the photon- or
electron-laser collision data-taking.

## Acknowledgements

This work was in part funded by the Deutsche Forschungsgemeinschaft under
Germany’s Excellence Strategy – EXC 2121 “Quantum Universe" – 390833306.

## References

  * [1] W. Heisenberg and H. Euler,  _Consequences of Dirac’s theory of positrons_ ,  Z. Phys. 98, 714 (1936),  arXiv:physics/0605038.
  * [2] J. Schwinger,  _On Gauge Invariance and Vacuum Polarization_ ,  Phys. Rev. 82, 664 (1951).
  * [3] R. Ruffini, G. Vereshchagin and S.-S. Xue,  _Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes_ ,  Phys. Rept. 487, 1 (2010),  10.1016/j.physrep.2009.10.004,  arXiv:0910.0974.
  * [4] A. I. Nishikov,  _Absorption of high-energy photons in the universe_ ,  Sov. Phys. JETP 14, 393 (1962).
  * [5] C. Kouveliotou _et al._ ,  _An X-ray pulsar with a superstrong magnetic field in the soft gamma-ray repeater SGR 1806-20._ ,  Nature 393, 235 (1998).
  * [6] R. Turolla, S. Zane and A. Watts,  _Magnetars: the physics behind observations. A review_ ,  Rept. Prog. Phys. 78, 116901 (2015),  10.1088/0034-4885/78/11/116901,  arXiv:1507.02924.
  * [7] V. M. Kaspi and A. M. Beloborodov,  _Magnetars_ ,  Annual Review of Astronomy and Astrophysics 55, 261 (2017),  10.1146/annurev-astro-081915-023329.
  * [8] LUXE collaboration,  _Conceptual Design Report for the LUXE Experiment_ (2021), arXiv:2102.02032.
  * [9] H. R. Reiss,  _Production of electron pairs from a zero-mass state_ ,  Phys. Rev. Lett. 26, 1072 (1971),  10.1103/PhysRevLett.26.1072.
  * [10] F. Burkart and W. Decking,  _Extraction and XTD20 Transfer Line: Conceptual Design Report_.
  * [11] D. Strickland and G. Mourou,  _Compression of amplified chirped optical pulses_ ,  Opt. Commun. 55, 447 (1985),  [Erratum: Opt. Commun. 56 (1985) 219].
  * [12] Z. Bai, O. Davidi, A. Hartin, T. Ma, G. Perez, Y. Soreq, A. Santra and N. Tal Hod,  _in progress_ .
  * [13] C. Bula _et al._ ,  _Observation of nonlinear effects in Compton scattering_ ,  Phys. Rev. Lett. 76, 3116 (1996).
  * [14] D. L. Burke _et al._ ,  _Positron production in multi - photon light by light scattering_ ,  Phys. Rev. Lett. 79, 1626 (1997).