Properties of hadrons in external magnetic fields and polarisabilities from lattice QCD

The properties of QCD matter when exposed to strong (external) magnetic fields are potentially important for a number of different physical systems, such as noncentral heavy-ion collisions, magnetars, and the evolution of the early universe. One of the characteristics of the magnetic field is its effect on the hadron spectrum, which has an impact on all of the aforementioned systems. Related to this field induced change of the spectrum are magnetic moments and polarisabilities of hadrons, which are important quantities to probe their inner structure. Compared to the effects on the phase diagram, the knowledge from first principles QCD about the spectrum in external magnetic fields and the associated magnetic polarisabilities is rather limited. We determine the continuum extrapolated light meson spectrum in the presence of an external magnetic field using Wilson fermions in the quenched approximation. The continuum extrapolation is facilitated by adding a novel magnetic field-dependent improvement term to the additive quark mass renormalization, leading to a strong reduction of lattice artefacts. We also present first results with dynamical quarks in the electromagnetic-quenched setup. The external field also affects decay rates, which can have an impact on the cooling mechanism and the stability of neutron stars and the products of neutron star mergers, for instance. We present the first computation of the leptonic decay of charged pions in a magnetic field. In this case new fundamental decay constants appear, which we compute in the continuum limit using both the quenched Wilson fermion and dynamical staggered fermion setups.