Description
Axion-like-particles (ALPs) are among the most well motivated extensions of the Standard Model. In many scenarios, they are understood as the (pseudo) Nambu-Goldstone bosons of sponteneously broken U(1) symmetries and are thus (approximately) invariant under shift-symmetry. In this talk we investigate the origin of the shift-symmetry by directly studying the physical properties of amplitudes involving ALPs and matter particles. To do this, we use on-shell methods, that allows us to write the amplitudes without the need of fields and Lagrangians. With these methods we can characterise all shift-symmetric interactions of ALPs and easily construct a non-redundant basis for higher-order amplitudes. We show how such higher-order interactions can be relevant and even surpass the effects of dimension 5 operators at future lepton colliders.
