A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation (1610.06587v2)

Abstract: We review how the muon anomalous magnetic moment ($g-2$) and the quest for lepton flavor violation are intimately correlated. Indeed the decay $\mu \to e \gamma$ is induced by the same amplitude for different choices of in- and outgoing leptons. In this work, we try to address some intriguing questions such as: Which hierarchy in the charged lepton sector one should have in order to reconcile possible signals coming simultaneously from $g-2$ and lepton flavor violation? What can we learn if the $g-2$ anomaly is confirmed by the upcoming flagship experiments at FERMILAB and J-PARC, and no signal is seen in the decay $\mu \rightarrow e\gamma$ in the foreseeable future? On the other hand, if the $\mu \rightarrow e\gamma$ decay is seen in the upcoming years, do we need to necessarily observe a signal also in $g-2$?. In this attempt, we generally study the correlation between these observables in a detailed analysis of simplified models. We derive master integrals and fully analytical and exact expressions for both phenomena, and adress other flavor violating signals. We investigate under which conditions the observations can be made compatible and discuss their implications. Lastly, we discuss in this context several extensions of the SM, such as the Minimal Supersymmetric Standard Model, Left-Right symmetric model, $B-L$ model, scotogenic model, two Higgs doublet model, Zee-Babu model, 331 model, and $L_{\mu}-L_{\tau}$, dark photon, seesaw models type~I, II and III, and also address the interplay with $\mu \to eee$ decay and $\mu-e$ conversion.

• The paper demonstrates that discrepancies in the muon g‑2 measurement can signal new physics when analyzed alongside lepton flavor violation constraints.
• It employs simplified and extended Standard Model frameworks to derive predictions for both g‑2 deviations and LFV decay rates.
• Numerical analyses highlight how mass scales, coupling hierarchies, and mixing angles inform the compatibility between theoretical predictions and experimental limits.

An Essay on "A Call for New Physics: The Muon Anomalous Magnetic Moment and Lepton Flavor Violation"

In the pursuit of identifying signals for new physics beyond the Standard Model (SM), the paper "A Call for New Physics: The Muon Anomalous Magnetic Moment and Lepton Flavor Violation" stands as a substantial contribution to the field, elucidating the intricate link between two compelling phenomena: the muon anomalous magnetic moment (muon $g-2$) and lepton flavor violation (LFV). The authors of this paper investigate the theoretical underpinnings and implications of discrepant experimental measurements of the muon $g-2$ compared to SM predictions and the non-observation of LFV decays among charged leptons, in light of upcoming experimental results.

The motivation for this paper arises from the persistent discrepancy between the measured and expected values of the muon $g-2$. This discrepancy, potentially indicative of physics beyond the SM, necessitates a robust theoretical framework to accommodate potential new physics phenomena while remaining consistent with current LFV constraints imposed by strong experimental bounds on processes such as $\mu \to e \gamma$.

The authors approach this complex topic by providing a comprehensive review of theoretical models that attempt to reconcile these observations, with particular attention given to simplified extensions to the SM, respecting $SU(2)_L$ symmetry. In this context, numerous models, including the Minimal Supersymmetric Standard Model (MSSM), Left-Right symmetric model, various seesaw models, and others like the 331 model and $L_{\mu}-L_{\tau}$ models, are explored to account for both muon $g-2$ and LFV within their theoretical confines.

The paper investigates theoretical frameworks both in general terms and through model-specific pathways to provide detailed predictions for the expected muon $g-2$ and LFV signals as functions of model parameters. For instance, in scenarios with additional scalar particles, interactions between neutral or charged scalar fields and leptons are explored, providing expressions for deviations in $g-2$ and lepton flavor-violating decays. Similarly, contributions from vector particles and their interactions with fermions are analyzed, demonstrating the effects of such extensions on the muon $g-2$ anomaly and LFV processes.

Numerical analyses in the paper emphasize the significance of mass scales, coupling hierarchies, and mixing angles in determining the observability of deviations and potential signals in LFV. The interplay between muon $g-2$ and LFV indicates that resolving one anomaly without affecting the other often necessitates specific model configurations or parameter fine-tuning. This is exemplified in the evaluations of simplified models wherein the authors demonstrated the difficulty in achieving compatibility with both experimental and future sensitivity limits across various contexts.

The authors stress the relevance of discerning LFV as a definitive probe for new physics, particularly if future measurements establish that the muon $g-2$ anomaly is an artifact of systematic misestimations. Thus, upcoming particle physics experiments at high-intensity facilities such as Mu3e, MEG II, and Mu2e hold considerable promise in scrutinizing LFV with unprecedented precision, with projected sensitivity improvements positioning $\mu \to e \gamma$ and $\mu \to e$ conversion as crucial observables.

In conclusion, the paper offers an extensive overview of the diverse approaches taken to theoretically capture the correlations between muon $g-2$ and LFV. It highlights the potential for combining results from precision measurements to constrain new physics models and speculates on the compelling immediacy for experiments to either confirm or refute these predicted phenomena. As research in this domain progresses, the detailed theoretical landscape delineated in this paper will remain pivotal for elucidating the symbiotic relationship between existing models, potential future extensions, and experimental findings in particle physics.