Abstract
We perform a model-exhaustive analysis of all possible beyond Standard Model (BSM) solutions to the $(g-2)_\mu$ anomaly to study production of the associated new states at future muon colliders, and formulate a no-lose theorem for the discovery of new physics if the anomaly is confirmed and weakly coupled solutions below the GeV scale are excluded. Our goal is to find the highest possible mass scale of new physics subject only to perturbative unitarity, and optionally the requirements of minimum flavour violation (MFV) and/or naturalness. We prove that a 3 TeV muon collider is guaranteed to discover all BSM scenarios in which $\Delta a_\mu$ is generated by SM singlets with masses above $\sim $ GeV; lighter singlets will be discovered by upcoming low-energy experiments. If new states with electroweak quantum numbers contribute to $(g-2)_\mu$, the minimal requirements of perturbative unitarity guarantee new charged states below $\mathcal{O}(100 {\rm TeV})$, but this is strongly disfavoured by stringent constraints on charged lepton flavour violating (CLFV) decays. Reasonable BSM theories that satisfy CLFV bounds by obeying Minimal Flavour Violation (MFV) and avoid generating two new hierarchy problems require the existence of at least one new charged state below $\sim 10$ TeV. This strongly motivates the construction of high-energy muon colliders, which are guaranteed to discover new physics: either by producing these new charged states directly, or by setting a strong lower bound on their mass, which would empirically prove that the universe is fine-tuned and violates the assumptions of MFV while somehow not generating large CLFVs. The former case is obviously the desired outcome, but the latter scenario would perhaps teach us even more about the universe by profoundly revising our understanding of naturalness, cosmological vacuum selection, and the SM flavour puzzle.
Highlights
AND EXECUTIVE SUMMARYThe magnetic moments of leptons have spurred the development of quantum field theory and provided the most precise comparison between theory and experiment in the history of science
We prove that a 3 TeV muon collider is guaranteed to discover all beyond Standard Model (BSM) scenarios in which Δaμ is generated by Standard Model (SM) singlets with masses above ∼GeV; lighter singlets will be discovered by upcoming low-energy experiments
Since the muon mass is much closer to the QCD scale than the electron mass, hadronic contributions to ðg − 2Þμ are an important part of the calculation, and a recent tour-de-force effort [8] combining lattice calculations with quantities extracted from experimental data [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] has recently confirmed the discrepancy to be Δaoμbs 1⁄4 aeμxp − atμheory 1⁄4 ð2.79 Æ 0.76Þ × 10−9; ð1Þ
Summary
The magnetic moments of leptons have spurred the development of quantum field theory and provided the most precise comparison between theory and experiment in the history of science. A series of colliders with energies from the test bed scale Oð100 GeVÞ to the far more ambitious but still imaginable Oð10 TeVÞ scale and beyond has excellent prospects to discover the new particles necessary to explain this mystery Regardless of what these direct searches find, each will make invaluable contributions to allow us to understand the precise nature of the new physics that must be present.
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