One-loop electroweak radiative and ISR O(α 2 ) corrections to µ − µ + → ZZ → hh at future multi-TeV muon colliders

In this work, we present the first resultsfor the full one-loop electroweak radiative corrections(EW) and initial-state photon radiation (ISR)$\\mathcal{O}(\\alpha^2)$ corrections to the process$\\mu^- \\mu^+ \\to ZZ \\to hh$at future multi-TeV muon colliderswithin the Standard Model framework.The results are validated by several consistency checks, including the independence of the non-linear gauge parameters,as well as ultraviolet and infrared finiteness.We find that the results exhibit good numerical stability,thereby confirming the reliability of the calculated results.In our phenomenological analysis, we study the impactsof both the EW corrections and ISR $\\mathcal{O}(\\alpha^2)$ corrections on the considered process at future multi-TeV muon colliderswith center-of-mass energies $\\sqrt{s}=3$ TeV to $30$ TeV. We find that the corrections contributeat the level of $\\mathcal{O}(10\\%)$.Such sizable contributions are crucial for high-precision programsat future multi-TeV muon colliders.