No-lose theorem for discovering the new physics of (g-2)μ at muon colliders

Article
Report number	arXiv:2101.10334 ; FERMILAB-PUB-21-012-T
Title	No-lose theorem for discovering the new physics of (g-2)μ at muon colliders
Related title	A No-Lose Theorem for Discovering the New Physics of $(g-2)_\mu$ at Muon Colliders
Author(s)	Capdevilla, Rodolfo (Toronto U. ; Perimeter Inst. Theor. Phys.) ; Curtin, David (Toronto U.) ; Kahn, Yonatan (Illinois U., Urbana, Astron. Dept.) ; Krnjaic, Gordan (Fermilab ; Chicago U., KICP)
Publication	2022
Imprint	2021-01-25
Number of pages	35
In:	Phys. Rev. D 105 (2022) 015028
DOI	10.1103/PhysRevD.105.015028 (publication)
Subject category	hep-ph ; hep-ex ; Particle Physics - Phenomenology ; Particle Physics - Experiment ; Particle Physics - Phenomenology ; Particle Physics - Experiment
Study	IMCC
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.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2022-2024 authors (License: CC BY 4.0)

$The philosophy of our ``model-exhaustive'' analysis. Traditional model-independent analyses express the new physics contribution to $\g$ as a non-renormalizable operator, either in the low-energy theory after EW symmetry breaking (left) or in the full SM gauge invariant formulation (middle). This makes no assumptions about the new physics but is limited to indirect signatures of the new physics produced by the same operator. Since we want to probe direct signatures of the BSM physics which solves the $\g$ anomaly, we add the single assumption of perturbativity to the traditional model-independent analysis, which resolves the new $\deltaa$ contributions into explicit loop diagrams of new states $\{\psi_i \}$ carrying specific SM quantum numbers (right). If the Higgs insertion lies on the external muon, $\Delta a_\mu$ is suppressed by $y_\mu$, while $\deltaa$ can be significantly enhanced if the Higgs couples to new particles in the loop. By exhaustively analyzing all possible choices of new states, we can derive predictions for direct signatures that are as universal as the traditional model-independent predictions for indirect signatures.$ $Schematic representation of the model-exhaustive space of BSM theories that can solve the $\g$ anomaly, and our mutually exclusive and collectively exhaustive categorization into Singlet Scenarios and Electroweak Scenarios. For these two classes of theories, the phenomenological questions are distinct. To understand how to discover Singlet Scenarios, we have to not only find the heaviest possible mass of the singlet(s), but also how to discover this singlet for all possible masses, since its phenomenology depends on its stability and decay mode, and lighter singlets have weaker coupling. Electroweak Scenarios predict new charged states, and since those have to produce visible final states in a collider and are efficiently produced at lepton colliders for $m \lesssim \sqrt{s}/2$, we only have to find the maximum mass the lightest new charged state in the BSM theory can have. (We limit ourselves to scenarios that generate $\deltaaexp$ at one-loop, since higher-loop solutions have lower BSM mass scales.)$ $Representative 1-loop contributions to $\g$ in the simplified models we consider. Top row: Singlet Scenarios with a SM neutral vector $V$ or scalar $S$ that couple to the muon. Note that the Higgs VEV on the muon line gives both the chirality flip and the EW breaking insertions in these models. Bottom left: EW Scenario of SSF type, with one BSM fermion and two BSM scalars that mix via a Higgs insertion. Bottom right: EW Scenario of FFS type, with one BSM scalar and two BSM fermions that mix via a Higgs insertion.$ Show more plots

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