Photon-photon (\(\gamma\gamma\)) interactions play an important role in the Standard Model (SM) of particle physics. A prominent example is the Higgs boson discovery at the Large Hadron Collider (LHC), where the \(\gamma\gamma\) channel served as a primary discovery mode.

It is fascinating to realize that \(\gamma\gamma\) interactions, and, in particular, the light-by-light (LbL) scattering, are effects of purely quantum origin. In classical electrodynamics, the linearity of Maxwell's equations precludes such processes from occurring. In the SM, the LbL scattering arises dynamically through the quantum loops of charged particles, as illustrated in the figure below.

A precise calculation of these effects in the SM is, however, not always straightforward - a major obstacle is posed by the non-perturbative nature of the strong interaction, described by quantum chromodynamics (QCD).

In recent years, the need for a detailed understanding of the QCD contribution to LbL scattering has been prompted from different directions:

- The very recent measurement of the
**muon's anomalous magnetic moment**\(a_\mu = \frac{1}{2} (g-2)_\mu\) at Fermilab, which increases the tension between the experimental value and its SM prediction to 4.2 standard deviations, and ongoing further measurements at Fermilab and J-PARC, which call for a higher precision on the hadronic LbL contribution to \((g-2)_\mu\) in order to stringently test the SM calculation, - The recent development of dispersion relations for the computation of the hadronic LbL contribution to \((g-2)_\mu\), which require precision data of
**meson transition form factors**as input and which - in turn - allow for unique probes of hadron structure, - The discovery of
**exotic XYZ states**in the charmonium sector of QCD, and an extraction of their properties through hidden-flavor decays, which hinges upon information coming from γγ-fusion processes in light meson systems, - The first direct observation of
**LbL scattering**at the LHC, opening a new venue for testing the SM and beyond, - The increasingly intensified
**searches for axion-like particles**(ALPs) and**dark sector particles**, stimulated by the mounting evidence from astrophysics and cosmology for physics beyond the SM, and by the possible discovery of a new light boson.

The scientists in this Research Unit (RU) have been playing most visible roles in all of the above-mentioned research directions, either by carrying out precision experiments at various facilities worldwide

(A2@MAMI, BaBar, BESIII, KLOE-2, WASA-at-COSY, ATLAS@LHC), by providing theoretical support for these experiments, or by directly calculating the quantities of interest as for example the hadronic LbL contribution to \((g-2)_\mu\). For these calculations both ab-initio methods such as lattice quantum chromodynamics (lattice QCD) or phenomenological approaches are used.