#StudentSeminar: Three-Body Unitarity with Isobars

por Julian Andres Sanchez Muñoz (Instituto de Física Corpuscular (IFIC))

viernes 16 oct. 2026 15:00 → 16:30 Europe/Madrid

1001-Primera-1-1-1 - Paterna. Seminario (Universe)

Abstract: We present a pedagogical derivation and exploration of a three-body unitarization framework formulated in terms of isobar–spectator degrees of freedom. Our approach provides an alternative perspective to conventional Faddeev and Khuri–Treiman methods. In particular, we show how the topologies generated by a Bethe–Salpeter-like ansatz can be matched to the standard connected and disconnected topologies of three-body scattering.
We consider the relativistic 3 → 3 scattering amplitude for spinless particles, organized as an effective 2 + 1 isobar–spectator system. Starting from the unitarity relations, we derive a relativistic three-dimensional integral equation that manifestly satisfies three-body unitarity while consistently incorporating two-body-unitary subamplitudes.
Finally, we illustrate the framework through successful applications to the dynamical generation of resonances in the axial-vector Jᴾ = 1⁺ and pseudoscalar Jᴾ = 0⁻ sectors, focusing on the a₁(1260) and K(1460), respectively. We also briefly discuss triangle singularities and their role in producing resonance-like structures, with particular emphasis on the a₁(1420).