Mass spectrum from stochastic Levy-Schroedinger relativistic equations: possible qualitative predictions in QCD

TL;DR

This paper links Levy-Schroedinger stochastic processes to relativistic quantum equations, proposing a mass spectrum model that offers qualitative insights into quark and lepton families in QCD.

Contribution

It introduces a novel connection between stochastic Levy processes and relativistic quantum field theories, leading to a new approach for understanding particle mass spectra.

Findings

Derives a relation between Levy processes and renormalizable field theories.

Proposes a phenomenological mass spectrum consistent with quark and lepton families.

Suggests a natural cutoff in perturbative diagrams from Levy process properties.

Abstract

Starting from the relation between the kinetic energy of a free Levy-Schroedinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cut-off in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model.