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

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 nonrelativistic. 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 energydependent 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.

Higgsploding universe

“…It was shown in several independent calculations at leading order [2][3][4][5][6], one-loop resummed [5,7,8] or using a semiclassical approach [9][10][11], that the rate for a transition h à → n × h grows factorially with n. Based on these results it was expected that either the cross section of physical processes, e.g. in proton collisions of pp → n × h, has to grow as well, thereby violating perturbative unitarity in tree-level processes above certain critical values of collision energy and multiplicity and pointing to a validity limit of the standard model of particle physics, or that a nontrivial energy-dependent form factor had to emerge in a strongly coupled perturbation theory or even nonperturbatively.…”

“…[6,9], ultimately providing the foundation of the Higgsplosion phenomenon, as explained in Ref. [1] and analysed further in [11].…”

“…In several independent calculations at leading order [2][3][4][5][6], one-loop resummed [5,7,8] or using a semiclassical approach [9][10][11], it was shown that the rate for a transition h à → n × h grows factorially with n, where the state's total and partial widths are respectively given by…”

“…The details of the derivation of (2.18) and an overview can be found in Ref. [6] and a selection of the earlier fundamental papers on n-point amplitudes in a scalar QFT is [2][3][4][5][7][8][9]15,16].…”

“…The same idea was used previously in the gauge-Higgs system in Refs. [6,17] for computations of amplitudes containing Higgses and vector bosons in the final state. Here we are doing the same for the Higgs-tt system (2.21).…”