2-, 3- and 4-Body Decays in the Constructive Standard Model

TL;DR

This paper advances the constructive theory of the Standard Model to compute decay amplitudes more simply and efficiently, showing agreement with Feynman diagram results and potential benefits for numerical stability and computational speed.

Contribution

It extends the massive constructive theory to include various decay processes and demonstrates its advantages over traditional Feynman diagram calculations.

Findings

Constructive theory results match Feynman diagram calculations.

Amplitudes are significantly simpler in the constructive approach.

Potential for faster, more stable matrix-element computations.

Abstract

We further develop the massive constructive theory of the Standard Model and use it to calculate the amplitude and squared amplitude for all two-body decays, a collection of weak three-body decays, as well as Higgs decay to four neutrinos. We compare our results with those from Feynman diagrams and find complete agreement. We show that in all the cases considered here, the amplitudes of massive constructive theories are significantly simpler than those resulting from Feynman diagrams. In fact, a naive counting of the number of calculations required for a matrix-element generator to compute a phase-space point is orders-of-magnitude smaller for the result coming from the constructive method suggesting that these generators might benefit from this method in the future, even in the case of massive weak amplitudes. We also anticipate that our simpler expressions will produce numerically more stable expressions.