From Veltman's conditions to Finite Unification

TL;DR

This paper reviews Veltman's approach to the naturalness problem, discusses the role of supersymmetry in finite theories, and highlights a specific finite unified theory's predictions for particle masses and future experimental tests.

Contribution

It connects Veltman's conditions with the development of all-loop finite supersymmetric theories and presents a specific model with testable predictions.

Findings

Predicted top and Higgs masses consistent with observations

Finite unified theory achieved through reduction of couplings

Future collider experiments can test the model's predictions

Abstract

First we review Veltman's suggestion to attack the naturalness problem in the Standard model by requiring absence of quadratic divergences and the resulting mass formula. Then we emphasise the influence of Veltman's suggestion in strengthening the belief that supersymmetry is the natural playground for solving the problem of quadratic divergences. Going further, we recall few sporadic suggestions concerning the cancellation of the logarithmic divergences too, which in the framework of supersymmetry has led to the construction of all-loop Finite Theories with the use of the idea of reduction of couplings. Eventually, we concentrate on a specific Finite Unified Theory and its successful predictions for the top and Higgs mass, among others, and the prospects of its final justification in future collider searches.