The Price of Tiny Kinetic Mixing

TL;DR

This paper investigates the smallness of gauge kinetic mixing parameters in particle physics, analyzing both bottom-up and top-down theoretical approaches to explain how such mixings can be suppressed below naive estimates.

Contribution

It provides a detailed analysis of mechanisms that suppress gauge kinetic mixing, including multi-loop effects and grand-unification embeddings, highlighting scenarios consistent with experimental constraints.

Findings

Kinetic mixing via gravity alone requires at least six loops.

Gravity-induced kinetic mixing could be as small as ~10^{-13}.

Embedding in grand-unified theories can influence kinetic mixing levels.

Abstract

We consider both "bottom-up" and "top-down" approaches to the origin of gauge kinetic mixing. We focus on the possibilities for obtaining kinetic mixings $\epsilon$ which are consistent with experimental constraints and are much smaller than the naive estimates ($\epsilon \sim 10^{-2} - 10^{-1}$) at the one-loop level. In the bottom-up approach, we consider the possible suppression from multi-loop processes. Indeed we argue that kinetic mixing through gravity alone, requires at least six loops and could be as large as $\sim 10^{-13}$. In the top-down approach we consider embedding the Standard Model and a $U(1)_X$ in a single grand-unified gauge group as well as the mixing between Abelian and non-Abelian gauge sectors.