A proposed renormalization scheme for non-local QFTs and application to the hierarchy problem

Abstract

We propose a renormalization scheme for non-local Quantum Field Theories (QFTs) with infinite derivatives inspired by string theory. Our Non-locality Renormalization Scheme (NRS) is inspired by Dimensional Regularization (DR) in local QFTs and is shown to significantly improve the UV behavior of non-local QFTs. We illustrate the scheme using simple examples from the ϕ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^{3}$$\\end{document} and ϕ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^{4}$$\\end{document} theories, then we evaluate the viability of NRS-enhanced non-local QFTs to solve the hierarchy problem using a simplified toy model. We find that non-locality protects the mass of a light scalar from receiving large corrections from any UV sector to which it couples, as long as the non-locality scale Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} is sufficiently smaller than the scale of the UV sector. We also find that NRS eliminates any large threshold corrections from the IR sector.