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Unitarity Bounds on the Massive Spin-2 Particle Explanation of Muon $g-2$ Anomaly

Motivated by the long-standing discrepancy between the Standard Model prediction and the experimental measurement of the muon magnetic dipole moment, we have recently proposed to interpret this muon $g-2$ anomaly in terms of the loop effect induced by a new massive spin-2 field $G$. In the present paper, we investigate the unitarity bounds on this scenario. We calculate the $s$-wave projected amplitudes for two-body elastic scatterings of charged leptons and photons mediated by $G$ at high energies for all possible initial and final helicity states. By imposing the condition of the perturbative unitarity, we obtain the analytic constraints on the charged-lepton-$G$ and photon-$G$ couplings. We then apply our results to constrain the parameter space relevant to the explanation of the muon $g-2$ anomaly.