Abstract
We present here two concrete examples of models where a sub-TeV scale breaking of their respective $\mathcal{T}_{13}$ and $A_5$ flavor symmetries is able to account for the recently observed discrepancy in the muon anomalous magnetic moment, $(g-2)_\mu$. Similarities in the flavor structures of the charged-lepton Yukawa matrix and dipole matrix yielding $(g-2)_\mu$ give rise to strong constraints on low-scale flavor models when bounds from lepton flavor violation (LFV) are imposed. These constraints place stringent limits on the off-diagonal Yukawa structure, suggesting a mostly (quasi-)diagonal texture for models with a low flavor breaking scale $\Lambda_f$. We argue that many of the popular flavor models in the literature designed to explain the fermion masses and mixings are not suitable for reproducing the observed discrepancy in $(g-2)_\mu$, which requires a delicate balance of maintaining a low flavor scale while simultaneously satisfying strong LFV constraints.
Highlights
At the dawn of the LHC era, the physics community awaited with bated breath for new electroweak physics whose discovery many were convinced was just around the corner
We show that the required absence of lepton flavor violation (LFV) transitions while maintaining a sizable contribution to the muon anomalous magnetic moment restricts the structure of the flavor symmetry or, alternatively, the scale of flavor symmetry breaking
II, we review the salient features of the framework proposed in Refs. [1,2] for constraining low-scale flavor models using the anomalous magnetic moment of the muon and LFV observables in the language of effective field theories
Summary
At the dawn of the LHC era, the physics community awaited with bated breath for new electroweak physics whose discovery many were convinced was just around the corner. Since we are only concerned with mass ratios, the flavor symmetry breaking scale Λf remains unresolved at this stage This scale can be determined if the physics responsible for new contributions to the dipole operator, which mitigates the observed discrepancy in the muon anomalous magnetic moment, is the very same flavor symmetry which determines the Yukawa couplings; in this case, the dipole operator LσμνPRlFμν will inherit the same basic flavor structure as the Yukawa interactions. Using the observed discrepancy in the measured muon anomalous magnetic moment to fix the scale Λf, we can employ the limits on various entries of the dipole operators to obtain the following constraints on the flavor structure of the leptonic Yukawa matrix:. As a proof of concept that it can be done, in principle, in the following two sections we build two explicit models based on the flavor groups T 13 and A5, respectively
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