Speaker
Description
We investigate the determination of the $s$-wave scattering length in the $O(4)$ $\phi^4$ theory in the symmetry-broken phase. The theory is simulated on a four-dimensional lattice in the strong-coupling limit with a small external symmetry-breaking term. This model provides a controlled setting for testing methods used to extract low-energy scattering observables from lattice simulations.
We focus on the isospin-$0$ and isospin-$2$ two-pion channels and compare perturbation theory, the finite-volume formalism of Lüscher, and the Euclidean correlator approach of Maiani and Testa for the extraction of the scattering length. Particular attention is paid to the the signal-to-nosie problem of the Maiani-Testa approach and its impact on the practical determination of scattering observables.