Speaker
Description
Many hadronic resonances, including the most intriguing ones (Roper, $\pi_1(1600)$, or $T_{cc}^+(3872)$), decay into three or more particles. To determine their masses and widths from Lattice QCD, one has to supply existing three-body formalisms with amplitude analysis techniques. In particular, one has to analytically continue reaction amplitudes extracted from the finite-volume calculation to the complex energy plane.
In the talk, I will present a study of the analytic continuation of relativistic three-particle integral equations for a system composed of three identical scalar bosons. As an illustration, I will consider a scattering process in which a bound state forms in the two-body sub-channel. After discussing the analytic properties of the scattering amplitude, I will show the solution procedure involving analytic continuation via the integration contour deformation and present the resulting three-body scattering amplitudes for complex energies in the physical and unphysical Riemann sheets. In particular, I will present evidence for three-particle bound states in the system under study that agrees with previous work utilizing relativistic finite-volume formalism.
Finally, I will also comment on the obtained numerical evidence of the breakdown of the two-body finite-volume formalism in the vicinity of left-hand cuts.
