Guises and Disguises of Quadratic Divergences

TL;DR

This paper offers a new perspective on controlling quadratic divergences in quantum field theory, focusing on the Higgs naturalness problem, by parameterizing UV divergences through basic divergent integrals and illustrating with key examples.

Contribution

It introduces a novel approach to handle quadratic divergences using basic divergent integrals and applies it to important quantum field theory cases.

Findings

Parameterization of UV divergences via basic divergent integrals.

Application to gluon vacuum self energy in QCD.

Analysis of Higgs decay to two photons.

Abstract

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale $\lambda$. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.