Extra Dimensions and the Muon Anomalous Magnetic Moment

TL;DR

The paper investigates how extra-dimensional scenarios with bulk gravity and bulk fields modify the muon anomalous magnetic moment. Using an effective field theory framework, it computes one-loop corrections from bulk gravitons, bulk vector bosons, and bulk right-handed neutrinos, summing over Kaluza-Klein towers with a cutoff at the strong gravity scale $M_*$. It finds that per-mode KK graviton and radion contributions are finite and that the total MMM correction scales as $\Delta a_\mu \sim\mathcal{O}\left(\frac{m_\mu^2}{M_*^2}\right)$ with a phase-space enhancement, largely independent of the total number of extra dimensions; current and near-future experiments thus place meaningful bounds on $M_*$ that are complementary to collider and short-distance tests. The work also shows that bulk vector bosons can be severely constrained and that bulk RH neutrinos can yield corrections near the experimental sensitivity, illustrating how MMM measurements probe bulk physics and constrain the scale and structure of extra dimensions. Overall, the MMM serves as a robust, model-independent window into higher-dimensional gravity and bulk field dynamics, providing complementary limits alongside atomic parity violation and short-distance force measurements.

Abstract

It has been proposed recently that the scale of strong gravity can be very close to the weak scale. Dimensions of sizes anywhere from $\sim $mm to $\sim $TeV$^{-1}$ can be populated by bulk gravitons, vector bosons and fermions. In this paper the one-loop correction of these bulk particles to the muon magnetic moment (MMM) are investigated. In all the scenarios considered here it is found that the natural value for the MMM is $O(10^{-8}-10^{-9})$. One main result is that the contribution of each Kaluza$-$Klein graviton to the MMM is remarkably finite. The bulk graviton loop implies a limit of $\sim 400$ GeV on the scale of strong gravity. This could be pushed up to $\sim 1-2$ TeV, even in the case of six extra dimensions, if the BNL E821 experiment reaches an expected sensitivity of $\sim 10^{-9}$. Limits on a bulk $B-L$ gauge boson are interesting, but still allow for forces $10^6-10^7$ times stronger than gravity at mm$^{-1}$ distances. The correction of a bulk right-handed neutrino to the MMM in one recent proposal for generating small Dirac neutrino masses is considered in the context of a two Higgs doublet model, and is found to be close to $10^{-9}$. The contributions of all these bulk particles to the MMM are (roughly) independent of both the total number of extra dimensions and the dimension of the subspace occupied by the bulk states. Finally, limits on the size of ``small'' compact dimensions gotten from the MMM and atomic parity violation are determined and compared.

Figures (2)

• Figure 1: Bulk gravity contribution at the one-loop level to the anomalous magnetic moment. Dashed lines denote either bulk spin-2 graviton or bulk spin-0 radion. Wavy and solid lines denote on-the-wall photons and fermions, respectively.
• Figure 2: One-loop correction to the anomalous magnetic moment from: a) abelian bulk vector bosons (dashed wavy line), b) charged Higgs (dotted line) and bulk RH neutrinos. Wavy and solid lines denote on-the-wall photons and fermions, respectively.