  We explore the analytic structure of the non-perturbative S-matrix in
arguably the simplest family of massive non-integrable quantum field theories:
the Ising field theory (IFT) in two dimensions, which may be viewed as the
Ising CFT deformed by its two relevant operators, or equivalently, the scaling
limit of the Ising model in a magnetic field. Our strategy is that of collider
physics: we employ Hamiltonian truncation method (TFFSA) to extract the
scattering phase of the lightest particles in the elastic regime, and combine
it with S-matrix bootstrap methods based on unitarity and analyticity
assumptions to determine the analytic continuation of the 2 to 2 S-matrix
element to the complex s-plane. Focusing primarily on the "high temperature"
regime in which the IFT interpolates between that of a weakly coupled massive
fermion and the E8 affine Toda theory, we will numerically determine 3-particle
amplitudes, follow the evolution of poles and certain resonances of the
S-matrix, and exclude the possibility of unknown wide resonances up to
reasonably high energies.
