Challenging Beyond-the-Standard-Model Solutions to the Fine-Structure Anomaly in Heavy Muonic Atoms

The leading-order contribution of a new boson to the muonic fine-structure anomaly, which refers to a discrepancy between the predicted transition energies and spectroscopic measurements of $\mu-^{90}$Zr, $\mu-^{120}$Sn, and $\mu-^{208}$Pb, is investigated. We consider bosons of scalar, vector, pseudoscalar, and pseudovector type. Spin-dependent couplings sourced by pseudoscalars or pseudovectors are disfavoured as solutions to the anomaly due to the nuclei in question having vanishing angular momentum. Spin-independent interactions resulting from scalar or vector exchange are also disfavoured because no parameter space exists to simultaneously fit different atomic states of the same nucleus. Therefore, we conclude that a `Beyond-the-Standard-Model' resolution of the muonic fine-structure anomaly is generally disfavoured, and the first-order solution by a single new boson is excluded.