Custodial symmetry for muon

We discuss the recent results on the muon anomalous magnetic moment in the context of new physics models with light scalars. We propose a model of one-loop contributions to of a scalar and a pseudoscalar which naturally cancel in the massless limit by symmetry. This model allows us to interpolate between two possible interpretations while keeping new physics light. In the first interpretation, the results provide a strong evidence of the existence of new physics, dominated by the (positive) contribution of a -even scalar. In the second one, supported by the recent lattice result, the data provides a strong upper bound on new physics, specifically in the case of (negative) pseudoscalar contributions. We emphasize that tree-level signatures of the new scalars are enhanced relative to conventional explanations of the discrepancy. As a result, this model can be tested in the near future with accelerator-based experiments and possibly also at the precision frontier.