Unitarity, analyticity, dispersion relations and resonances in strongly interacting $W_L W_L$, $Z_L Z_L$ and $hh$ scattering

Understand

If the Electroweak Symmetry Breaking Sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity (where the perturbative expansion breaks down).

• This is achieved by dispersion relations, whose subtraction constants and left cut contribution can be approximately obtained in different ways giving rise to different unitarization procedures.
• We illustrate the ideas with the Inverse Amplitude Method, one version of the N/D method and another improved version of the K-matrix.
• In the three cases we get partial waves which are unitary, analytical with the proper left and right cuts and in some cases poles in the second Riemann sheet that can be understood as dynamically generated resonances.