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

Valentin V Khoze

doi:10.1007/jhep03(2015)038

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.

Highlights

Leading to the ultimate breakdown of the standard weakly-coupled perturbation theory, as reviewed in [8, 9], see refs. [10,11,12,13,14,15,16,17]
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

Summary

Summing tree graphs on and off the multi-particle threshold

Our approach for computing tree-level high-multiplicity amplitudes in the Gauge-Higgs theory is based on solving recursion relations between the n-point amplitudes involving massive vector and Higgs bosons for different values of n. First made in [16], is that by exponentiating the ordernε contribution, one obtains the expression for the amplitude which solves the original recursion relation (2.3) to all orders in (nε)m in the large-n non-relativistic limit, An(p1 . Solving eq (2.27) by iterations with Mathematica gives the fn coefficients in (2.18), which amounts to the exponentiated form for the amplitude off the multiparticle mass-shell in the non-relativistic limit ε → 0, with nε =fixed,. This is our main result for the tree-level high-multiplicity amplitudes in the scalar theory with SSB in the ε → 0, with nε = fixed limit

Multiparticle production in the gauge-Higgs theory

Recursion relations for amplitudes on the multi-particle threshold

Amplitudes above the threshold

Integrating over the phase space

Conclusions

A Unbroken φ4 theory