⚛️ phenomenology

Charged lepton flavor violating decays and $(g-2)_{e_a}$ in an extended standard model with singlet and triplet leptoquarks

This paper investigates an extended Standard Model with singlet and triplet scalar leptoquarks, revealing that while the model predicts significant correlations between charged lepton anomalous magnetic moments and flavor-violating decays, it cannot simultaneously accommodate the observed discrepancies in both electron and muon magnetic moments while satisfying current experimental constraints.

Original authors: L. T. Hue, N. V. Hop, Vo Quoc Phong, N. H. T. Nha

Published 2026-09-21

📖 4 min read🧠 Deep dive

CC0 1.0

Original authors: L. T. Hue, N. V. Hop, Vo Quoc Phong, N. H. T. Nha

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe operates on a set of fundamental rules that govern how tiny particles interact, a framework physicists call the Standard Model. Within this model, particles known as leptons, which include the electron and its heavier cousins, the muon and the tau, are expected to behave in very specific ways. One of the most precise tests of these rules involves measuring how these particles respond to magnetic fields, a property known as their magnetic moment. For decades, scientists have compared the predicted values of these moments against experimental measurements. When the two do not match, it signals that something is missing from our understanding, perhaps a new type of particle or force that has not yet been discovered. At the same time, the Standard Model predicts that different types of leptons should not easily transform into one another. If a heavy tau particle were to spontaneously decay into a lighter muon or electron, it would be a clear sign of new physics, as such events are incredibly rare or forbidden in the current theory.

A team of researchers has investigated a specific proposal to explain these discrepancies by introducing two new types of particles called leptoquarks. These hypothetical particles act as bridges, connecting the world of quarks, which make up protons and neutrons, with the world of leptons. The researchers focused on a scenario where two distinct leptoquarks exist: one that is a singlet and another that is a triplet, referring to how they are organized under the rules of particle symmetry. By building a mathematical model that includes these two particles, the team explored how they would influence the magnetic moments of charged leptons and whether they would allow the forbidden transformations between different types of leptons. Their work involved calculating the complex interactions that would occur at the quantum level, specifically looking at how these new particles would circulate in loops during particle decays and magnetic interactions.

The study reveals a significant tension within this proposed model. The researchers found that the same interactions that could explain the observed differences in the magnetic moments of electrons and muons also drive the rates at which leptons change flavor. However, the model cannot accommodate large deviations for both the electron and the muon simultaneously. If the model is tuned to produce a large effect for the muon, which is currently a point of interest in experimental physics, the predicted rate for the electron to change its magnetic moment becomes far too small to match current experimental hints. Conversely, if the model is adjusted to fit the electron's magnetic moment, the effect on the muon becomes negligible. This suggests that a single framework containing just these two leptoquarks is likely insufficient to explain the anomalies seen in both particles at the same time.

Furthermore, the researchers examined the consequences of these interactions for the decay of heavy leptons into lighter ones, such as a tau particle turning into an electron or a muon. They discovered that if the model is set to explain the muon's magnetic moment anomaly, the rates for these flavor-changing decays are heavily suppressed. Specifically, the probability of a tau decaying into an electron via a photon would be extremely low, well below the sensitivity of current and near-future experiments. Similarly, the decay of the Higgs boson or the Z boson into pairs of different leptons would also be suppressed to levels that are difficult to detect. On the other hand, if the model is adjusted to fit the electron's magnetic moment, the decay rates involving the tau and muon are similarly suppressed, remaining far below what current detectors can observe.

The analysis indicates that while this extended model offers a rich structure for particle interactions, it faces strict limitations when compared to real-world data. The researchers concluded that the model cannot simultaneously satisfy the requirements for explaining the magnetic moment anomalies of both the electron and the muon while also respecting the stringent experimental limits on how often leptons change flavor. The study suggests that if new physics exists to explain the muon's behavior, it likely involves mechanisms more complex than just the addition of these two specific leptoquarks, or it must manifest in ways that do not produce the large effects seen in the electron sector. The work provides a clear boundary for future theories, showing that any successful explanation must navigate the delicate balance between magnetic moments and flavor-changing decays without violating the tight constraints set by existing experiments.

Technical Summary: Charged Lepton Flavor Violating Decays and (g − 2) in an Extended Standard Model with Singlet and Triplet Leptoquarks

Problem Statement
The paper addresses the phenomenological interplay between the anomalous magnetic moments (AMMs) of charged leptons ( $a_e, a_\mu$ ) and charged-lepton flavor-violating (cLFV) processes within a specific extension of the Standard Model (SM). While scalar leptoquarks (LQs) have been studied individually for their ability to explain anomalies such as the muon $(g-2)$ discrepancy or $R_{K^{(*)}}$ and $R_{D^{(*)}}$ anomalies, this work investigates a combined framework containing both an $SU(2)_L$ singlet ( $S$ ) and an $SU(2)_L$ triplet ( $T$ ) scalar leptoquark. The primary motivation is to determine whether this "LQST" model can simultaneously accommodate the observed deviations in electron and muon AMMs while satisfying stringent experimental constraints on cLFV decays (e.g., $\mu \to e\gamma$ , $\tau \to \mu\gamma$ ) and flavor-violating Higgs ( $h$ ) and $Z$ boson decays.

Methodology
The authors construct a renormalizable model by adding the singlet $S$ and triplet $T$ leptoquarks to the SM particle content, subject to a discrete $Z_2$ symmetry to restrict flavor couplings and simplify the parameter space.

Model Structure: The leptoquarks are $SU(3)_C$ antitriplets. The triplet $T$ is represented as a $2\times2$ matrix. The Yukawa interaction Lagrangian couples these LQs to SM fermions, specifically retaining couplings to the top quark due to its potential for chirality-flipping enhancements.
Analytical Derivation: The authors derive general analytical expressions for one-loop contributions to:
- Charged lepton AMMs ( $a_e, a_\mu$ ).
- Radiative cLFV decays ( $e_b \to e_a \gamma$ ).
- Flavor-violating Higgs decays ( $h \to e_b e_a$ ).
- Flavor-violating $Z$ boson decays ( $Z \to e_b^\pm e_a^\mp$ ).
  These calculations involve identifying physical mass eigenstates, mixing parameters, and evaluating one-loop Feynman diagrams involving LQ exchanges and SM quarks (primarily up-type for the singlet/triplet mixing and down-type for the triplet). The results are expressed in terms of Passarino-Veltman functions.
Numerical Analysis: A comprehensive numerical scan is performed over the model's parameter space. The scan assumes leptoquark masses between 2 TeV and 8 TeV (satisfying current LHC lower bounds of $\sim 1.8$ TeV) and varies Yukawa couplings within perturbative limits. The analysis focuses on regions where at least one AMM deviation is significant ( $|\Delta a_e| > 10^{-16}$ or $|\Delta a_\mu| > 10^{-14}$ ) and checks consistency with current upper bounds on cLFV branching ratios.

Key Contributions and Results
The study reveals significant correlations between the AMMs and the rates of various LFV processes, driven largely by the shared Yukawa couplings and the chirality-flipping contributions involving the top quark.

Mutual Exclusivity of Large AMMs: A central finding is that the LQST model cannot simultaneously accommodate sizable values for both the electron and muon AMM deviations. Specifically, the model cannot satisfy $|\Delta a_e| \sim \mathcal{O}(10^{-13})$ and $|\Delta a_\mu| \sim \mathcal{O}(10^{-10})$ simultaneously without violating experimental limits on cLFV decays.
Scenario 1: Muon AMM Focus: For a scenario where $|\Delta a_\mu| \sim \mathcal{O}(10^{-10})$ $∣Δ a_{μ} ∣ \sim O (1 0^{- 10})$ and the branching ratio $Br(\mu \to e\gamma) > 10^{-15}$ $B r (μ \to e γ) > 1 0^{- 15}$ , the model predicts suppressed rates for other processes:
- $Br(\tau \to e\gamma) < \mathcal{O}(10^{-12})$
- $Br(h \to \tau e) < \mathcal{O}(10^{-6})$
- Other decays (e.g., $\tau \to \mu\gamma$ , $h \to \tau\mu$ ) may reach the sensitivity of forthcoming experiments.
Scenario 2: Electron AMM Focus: Conversely, if the model is tuned to explain a larger electron AMM deviation ( $|\Delta a_e| \sim \mathcal{O}(10^{-13})$ $∣Δ a_{e} ∣ \sim O (1 0^{- 13})$ ), the predicted rates for tau decays are suppressed:
- $Br(\tau \to \mu\gamma) < \mathcal{O}(10^{-11})$
- $Br(h \to \tau\mu) < \mathcal{O}(10^{-7})$
Correlations: The branching ratios for radiative decays ( $Br(e_b \to e_a \gamma)$ ) and Higgs decays ( $Br(h \to e_b e_a)$ ) exhibit strong correlations, allowing for cross-checks of the model's parameter space.

Significance
The paper claims that the simultaneous presence of a singlet and triplet leptoquark introduces new structures in one-loop amplitudes that lead to distinct correlations among observables, which are absent in models with a single LQ representation. The work demonstrates that while the LQST framework offers a mechanism to address specific anomalies (like the muon $(g-2)$ ), it imposes strict constraints on the electron sector and vice versa. The inability to simultaneously explain large deviations in both $a_e$ and $a_\mu$ serves as a critical phenomenological test for this specific two-LQ framework. The analysis provides a detailed mapping of the viable parameter space, highlighting which LFV processes are most likely to be observed in future experiments if the model is to explain the muon anomaly, while remaining consistent with current bounds.

More like this