We investigate a method to extract response functions (dynamical polarisabilities) directly from a bound-state approach applied to calculations of perturbation-induced reactions. The use of a square-integrable basis leads to a response in the form of a sum of delta functions. We integrate this over energy and fit a smooth function to the resulting stepwise-continuous one. Its derivative gives the final approximation to the physical response function. We show that the method reproduces analytical results where known, and analyse the details for a variety of models. We apply it to some simple models, using the stochastic variational method as the numerical method. Albeit we find that this approach, and other numerical techniques, have some difficulties with the threshold behavior in coupled-channel problems with multiple thresholds, its stochastic nature allows us to extract robust results even for such cases.

The vast bulk of visible mass emerges from nonperturbative dynamics within quantum chromodynamics (QCD) -the strong interaction sector of the Standard Model. The past decade has revealed the three pillars that support this emergent hadron mass (EHM); namely, a nonzero gluon mass-scale, a process-independent effective charge, and dressed-quarks with constituent-like masses. Theory is now working to expose their manifold and diverse expressions in hadron observables and highlighting the types of measurements that can be made in order to validate the paradigm. In sketching some of these developments, this discussion stresses the role of EHM in forming nucleon electroweak structure and the wave functions of excited baryons through the generation of dynamical diquark correlations; producing and constraining the dilation of the leading-twist pion distribution amplitude; shaping pion and nucleon parton distribution functions -valence, glue and sea, including the antisymmetry of antimatter; and moulding pion and proton charge and mass distributions.