Perturbative growth of high-multiplicity W, Z and Higgs production processes at high energies

TL;DR

This paper calculates high-multiplicity scattering amplitudes in a broken gauge theory, revealing factorial growth and potential perturbation breakdown at high energies, with implications for future collider experiments.

Contribution

It extends known amplitude expressions to non-relativistic kinematics and demonstrates factorial growth in spontaneously broken gauge theories at high multiplicities.

Findings

Amplitudes grow factorially with particle number.

Cross sections grow exponentially at multi-TeV energies.

Perturbation theory breaks down at high multiplicities.

Abstract

Using the classical recursion relations we compute scattering amplitudes in a spontaneously broken Gauge-Higgs theory into final states involving high multiplicities of massive vector bosons and Higgs bosons. These amplitudes are computed in the kinematic regime where the number of external particles n is >> 1 and their momenta are non-relativistic. Our results generalise the previously known expressions for the amplitudes on the multi-particle thresholds to a more non-trivial kinematic domain. We find that the amplitudes in spontaneously broken gauge theories grow factorially with the numbers of particles produced, and that this factorial growth is only mildly affected by the energy-dependent formfactor computed in the non-relativistic limit. This is reminiscent of the behaviour previously found in massive scalar theories. Cross sections are obtained by integrating the amplitudes squared over the non-relativistic phase-space and found to grow exponentially at energy scales in a few hundred TeV range if we use the non-relativistic high multiplicity limit. This signals a breakdown of perturbation theory and indicates that the weak sector of the Standard Model becomes effectively strongly coupled at these multiplicities. There are interesting implications for the next generation of hadron colliders both for searches of new physics phenomena beyond and within the Standard Model.