Multiparticle Higgs and Vector Boson Amplitudes at Threshold

Understand

In a spontaneously broken gauge theory we consider (sub)-processes in which one virtual intermediate state (it can be a Higgs or a gauge field) produces many on-shell Higgses and massive vector bosons.

• In the kinematic regime where all final states are produced on their mass threshold, we show how to compute iteratively all tree-level amplitudes ${\cal A}_{1\to n+m}$ involving an arbitrary number $n$ of Higgs bosons and $m$ of longitudinal vector bosons in the final state, and list the amplitudes coefficients for up to $n=32$ and $m=32$.
• We find that these amplitudes exhibit factorial growth not only in the number of scalar fields, but also in the number of longitudinal gauge fields, ${\cal A}_{1\to n+m} \sim n! \,m!$.
• This growth is not expected to disappear at loop-level in the fixed-order perturbation theory.