Effective field theories for low-energy reactions

Quantum-mechanical reactions can be used to probe the nature of composite particles if relations between reaction and structure observables are known. Such correlations are, however, often hard to obtain theoretically, especially when constituent particles participate in the reaction or when interactions involve many parameters. Effective field theories (EFTs) provide a promising way to reduce the number of relevant particles and interaction parameters in the low-energy limit. At the same time, EFT correlations come along with quantitative uncertainty estimates and can be improved systematically if needed. We exemplify this approach at the example of three systems in hadron, nuclear, and atomic physics. The first system is the exotic charmonium state X(3872). Its mass lies less than 200 keV away from the D⁰D̄⁰* threshold, reinforcing its interpretation as a loosely bound dimeson. To confirm this picture, the mass has to be measured with a high precision, for example in the B± → K± + X(3872) → K± + D⁰D̄⁰π⁰ decay reaction. Threshold effects, however, are known to disguise the true pole position in this process. For this reason, we propose a novel EFT to extract the mass and width of the X(3872) from its line shape. The theory uses Galilean-invariant contact interactions among D⁰, D̄⁰, and π⁰ fields. The D⁰* enters as a D⁰π⁰ p-wave resonance, allowing for a systematization of pion interactions. The second part is a pilot study exploring the potential of halo effective field theory to describe nuclear (d, p) reactions. As a test case, we use the neutron transfer reaction ¹⁰Be(d, p)¹¹Be. The relevant degrees of freedom for this process are the ¹⁰Be core nucleus, the neutron, and the proton, which we treat as point-like particles. In contrast, the halo nucleus ¹¹Be and the deuteron are generated by contact interactions using experimental and ab initio input. As opposed to the X(3872) system, Coulomb repulsion occurs in addition to strong interactions in the ¹⁰Be-proton sector. The leading photon exchange diagrams are identified in a scaling analysis and iterated in a Faddeev equation. In the third part, we investigate loss effects in an ultracold polarized ⁶Li Fermi gas due to three-body recombination 3⁶Li → ⁶Li₂(d) + ⁶Li into deeply bound molecules. This process is enhanced in the presence of a p-wave Feshbach resonance. In leading order, atom-atom interactions can then be described by the large scattering volume and the initially unknown p-wave effective range only. By fitting our leading-order theory to data for the loss coefficient at nonzero temperature, we predict a value for the p-wave effective range. Moreover, our results suggest the existence of a low-energy three-body state