Clockwork graviton contributions to muon $g-2$

The clockwork mechanism for gravity introduces a tower of massive graviton modes, "clockwork gravitons," with a very compressed mass spectrum, whose interaction strengths are much stronger than that of massless gravitons. In this work, we compute the lowest order contributions of the clockwork gravitons to the anomalous magnetic moment, $g-2$, of muon in the context of extra dimensional model with a five dimensional Planck mass, $M_5$. We find that the total contributions are rather insensitive to the detailed model parameters, and determined mostly by the value of $M_5$. In order to account for the current muon $g-2$ anomaly, $M_5$ should be around $0.2~{\rm TeV}$, and the size of the extra dimension has to be quite large, $l_5 \gtrsim 10^{-7}\,$m. For $M_5\gtrsim1~{\rm TeV}$, the clockwork graviton contributions are too small to explain the current muon $g-2$ anomaly. We also compare the clockwork graviton contributions with other extra dimension models such as Randall-Sundrum models or large extra dimension models. We find that the leading contributions in the small curvature limit are universal, but the cutoff-independent subleading contributions vary for different background geometries and the clockwork geometry gives the smallest subleading contributions.