HEFT approach to investigate the muon g-2 anomaly at a muon collider

In a previous work {Buttazzo:2020ibd}, it has been pointed out that heavy new physics (NP) contributions to lepton dipole moments and high-energy cross-sections of lepton pairs into Higgs and γ/Z bosons are connected, if the electroweak symmetry breaking is realized linearly. As a consequence, a multi-TeV muon collider would provide a unique test of NP in the muon g-2 through the study of high-energy processes such as μ⁺ μ⁻→ h +γ /Z. Since the analysis involved a SMEFT approach to Higgs-processes, it could also be studied by the more general HEFT formulation. We compute the modification of the high-energy cross-section μ⁺ μ⁻→ h +γ/Z and h→ μ⁺ μ⁻ +γ /Z decay using the dimension six HEFT Lagrangian and compare them with the SMEFT analysis. We find that, in some reasonable cases, the HEFT approach could lead to a higher sensitivity to test the NP contributions in the muon g-2, requiring thus a less energetic muon collider for such a purpose.