A No-Lose Theorem for Discovering the New Physics of $(g-2{)}_{\mu }$ at Muon Colliders

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 $\mathcal{O}(100\mathrm{TeV})$, 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.

56 pages, 9 figures, 5 tables. Added references, fixed typos, no significant change to results/conclusions. Corrected NBSM dependence of naturalness bound for EW Scenarios, slightly strengthening theorem. Added discussion of EW Scenarios with fewer BSM states (Sec 4.8). Added discussion of avoiding Landau poles to the Planck scale (Sec 4.9). Added comment on higher loop scenarios (Sec 2)

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• Muonphilic Dark Matter explanation of gamma-ray galactic center excess: a comprehensive analysis
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• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Predictions for Muon Electric and Magnetic Dipole Moments from $h\to {\mu }^{+}{\mu }^{-}$ in Two-Higgs-Doublet Models with New Leptons
• Signals of a New Gauge Boson from IceCube and Muon $g-2$
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• Effective Field Theory of Chirally-Enhanced Muon Mass and Dipole Operators
• Probing Higgs-muon interactions at a multi-TeV muon collider
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• Direct production of SM-singlet scalars at the muon collider
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• Lepton Flavor Violation: From Muon Decays to Muon Colliders
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