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The low-energy effective field theory (LEFT) provides the appropriateframework to describe particle interactions below the scale of electroweaksymmetry breaking, $\mu_w\sim v$. By matching the Standard Model onto the LEFT,non-zero Wilson coefficients of higher-dimensional operators are generated,suppressed by the corresponding power of $1/v$. An axion or axion-like particle(ALP) with mass $m_a\ll\mu_w$ that interacts with the Standard Model viaclassically shift-invariant dimension-five operators would also contribute tothe LEFT Wilson coefficients, since it can appear as a virtual particle indivergent Green's functions and thus has an impact on the renormalization ofthe LEFT operators. We present the full set of one-loop ALP-induced sourceterms modifying the renormalization-group evolution equations of the LEFTWilson coefficients up to dimension-six order. Our framework allows formodel-independent ALP searches at low energies from current bounds on LEFTWilson coefficients. As a concrete application, we present an improvedprediction for ALP effects on the anomalous magnetic moment of the muon.

ALP-LEFT Interference and the Muon $(g-2)$