One-Loop Integrals for Purely Virtual Particles

TL;DR

This paper develops modified one-loop scalar integrals for quantum field theories with fakeons, enabling phenomenological studies of models with purely virtual particles and analyzing their impact on amplitudes and decay processes.

Contribution

It introduces new functions for one-loop integrals with fakeons, compatible with existing reduction methods, facilitating their use in phenomenological analyses.

Findings

Modified integrals differ from standard ones in specific energy ranges.

Differences are characterized by additional nonanalyticities.

Fakeons can alter cross sections and decay widths in toy models.

Abstract

Quantum field theories with purely virtual particles, or fakeons, require suitable modifications in one-loop integrals. We provide the expressions for the modified scalar integrals in the case of the bubble, triangle and box diagrams. The new functions are defined by means of their difference with the `t Hooft-Veltman scalar integrals. The modifications do not affect the derivation of the Passarino-Veltman reduction and one-loop integrals with nontrivial numerators can be decomposed in the same fashion. Therefore, the new functions can be directly used to study the phenomenology of any models with standard particles and fakeons. We compare our results with standard amplitudes and show that the largest differences are often localized in relatively small energy ranges and are characterized by additional nonanalyticities. Finally, we give explicit examples in the context of a toy model, where cross sections and decay widths of standard particles are modified by the presence of fakeons.