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We compute the renormalization group equations (RGEs) of the Standard Modeleffective field theory (EFT) extended with a real scalar singlet, up todimension-five and one-loop accuracy. We compare our renormalization resultswith those found in the shift-symmetry preserving limit, which characterizesaxion-like particles (ALPs). The matching and running equations below theelectroweak scale are also obtained, including the mixing effects in the scalarsector. Such mixing leads to interesting phenomenological consequences that areabsent in the EFT at the renormalizable level, namely new correlations amongthe triplet and quartic Higgs couplings are predicted. All RGEs obtained inthis work are implemented in a new Mathematica package - ALPRunner, togetherwith functions to solve the running numerically for an arbitrary set of UVparameters. As an application, we obtain the improved electric dipole momentconstraints on particular regions of the singlet parameter space, and quantifythe level of shift-breaking in these regions.

Running beyond ALPs: shift-breaking and CP-violating effects