⚛️ phenomenology

$(g-2)_{\ell}$ and LFV decays in a $U(1)_{L_{\mu} -L_{\tau}}$ left-right model with inverse seesaw neutrinos

This paper demonstrates that a $U(1)_{L_{\mu} -L_{\tau}}$ left-right model with inverse seesaw neutrinos can simultaneously explain the observed discrepancies in the anomalous magnetic moments of electrons and muons via heavy singly charged Higgs boson contributions while naturally suppressing lepton-flavor violating decays due to the underlying gauge symmetry.

Original authors: L. T. Hue, Vo Quoc Phong, T. D. Tham, N. H. T. Nha

Published 2026-09-01

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: L. T. Hue, Vo Quoc Phong, T. D. Tham, 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

In the vast landscape of modern physics, there is a persistent puzzle regarding the behavior of subatomic particles known as leptons. These include the electron, which orbits the nucleus of every atom, and its heavier cousins, the muon and the tau. For decades, scientists have measured a specific property of these particles called their magnetic moment, which essentially describes how they spin and interact with magnetic fields. The Standard Model, our best current theory of how the universe works at the smallest scales, predicts a very precise value for this spin. However, recent experiments have revealed a small but significant gap between the theoretical prediction and the actual measurement, particularly for the muon. This discrepancy suggests that there might be unseen particles or forces influencing these leptons, acting like a hidden hand that nudges their spin just slightly off the expected path. To solve this mystery, physicists often look for new theories that extend the Standard Model, proposing the existence of heavier, undiscovered particles that could bridge the gap between what we calculate and what we observe.

A team of researchers has recently explored one such theoretical framework to see if it can explain these anomalies without breaking other established rules of physics. They focused on a specific model that introduces a new symmetry between the muon and the tau, while also proposing a mechanism to explain why neutrinos have mass. This model includes a new type of particle called a singly charged Higgs boson, which is heavier than the familiar Higgs boson discovered a decade ago. The researchers performed detailed calculations to see if the interactions involving this heavy particle could generate the extra "push" needed to match the experimental data for the muon and the electron. Their work involved mapping out every possible way these new particles could influence the magnetic moments of charged leptons through quantum loops, a process where particles briefly pop in and out of existence to affect the behavior of their neighbors.

The study found that this specific model can indeed accommodate the observed discrepancies. The calculations showed that the exchange of the heavy singly charged Higgs boson can produce a contribution large enough to explain the difference seen in the muon's magnetic moment, which is on the order of one part in a billion. Similarly, it can account for the smaller but still significant difference observed in the electron's magnetic moment. Crucially, the researchers demonstrated that this explanation works without violating other strict experimental limits. In many theories, a mechanism that fixes the magnetic moment problem often leads to unwanted side effects, such as particles decaying into other particles in ways that have never been seen. For instance, a muon might spontaneously turn into an electron and a photon, or a heavy tau particle might decay into a muon and an electron.

However, in this specific model, the new symmetry between the muon and the tau acts as a protective shield. The researchers found that the rates for these forbidden decays are suppressed to such a tiny degree that they are effectively invisible to current detectors. This means the model can solve the magnetic moment puzzle while remaining consistent with the fact that we do not see these rare decays happening in nature. The study also looked at the behavior of the Higgs boson and the Z boson, which are carriers of fundamental forces, checking if they would decay into different types of leptons in violation of conservation laws. The results were consistent: the model predicts that these decays are so rare that they are far below the threshold of what current experiments can detect.

The researchers also examined how the properties of the new particles, such as their masses and the strength of their interactions, relate to the size of the magnetic moment effect. They discovered that to get the right amount of correction for the muon and tau, the interactions must be relatively strong, but this is balanced by the masses of the new particles being quite heavy. For the electron, the effect can be achieved even with weaker interactions, provided the mass of the new particle is within a certain range. The study confirms that there is a viable region of parameters where the model works for all three types of leptons simultaneously. This suggests that the universe could indeed contain these heavy particles and the new symmetry they rely on, offering a plausible explanation for the long-standing anomalies in lepton physics without contradicting the wealth of data we already have from particle accelerators.

Ultimately, this work provides a concrete example of how a specific extension of our current theories can resolve experimental tensions. By carefully balancing the contributions of new heavy particles against the constraints of known physics, the researchers showed that the observed deviations in the magnetic moments of the electron and muon do not necessarily require a complete overhaul of our understanding. Instead, they could be the subtle fingerprints of a heavier, hidden sector of particles that respects the delicate symmetries of the muon and tau. While this remains a theoretical proposal that awaits experimental confirmation, it narrows the search for new physics by identifying a specific set of conditions and particle behaviors that future experiments could look for. The findings serve as a guide, telling physicists exactly what kind of signals to expect if nature has indeed chosen this particular path to explain the quirks of the subatomic world.

Technical Summary: $(g-2)_{\ell}$ and LFV Decays in a $U(1)_{L_\mu-L_\tau}$ Left-Right Model with Inverse Seesaw Neutrinos

Problem Statement
The paper investigates the tension between experimental anomalies in the anomalous magnetic moments of charged leptons, specifically $(g-2)_\mu$ and $(g-2)_e$ , and the stringent experimental constraints on Lepton Flavor Violating (LFV) decays. While various Beyond Standard Model (BSM) scenarios attempt to explain the muon $(g-2)$ discrepancy ( $\Delta a_\mu \sim 10^{-9}$ ) and the electron discrepancy ( $|\Delta a_e| \sim 10^{-13}$ ), they often struggle to simultaneously satisfy limits on processes like $\mu \to e\gamma$ , $\tau \to \ell\gamma$ , and LFV decays of the Higgs ( $h$ ) and $Z$ bosons. The authors aim to determine whether a viable parameter space exists within a specific BSM framework—the $U(1)_{L_\mu-L_\tau}$ Left-Right model with Inverse Seesaw (LRiss) neutrinos—that can accommodate these magnetic moment discrepancies while naturally suppressing LFV rates.

Methodology
The authors perform a detailed one-loop analysis within the LRiss framework, which extends the Standard Model gauge group to $SU(2)_L \otimes SU(2)_R \otimes U(1)_{B-L} \otimes U(1)_{L_\mu-L_\tau}$ . The model incorporates:

Particle Content: Singly charged Higgs bosons ( $h^\pm$ ), heavy singly charged gauge bosons ( $W'^\pm$ ), a new neutral gauge boson ( $Z'_{\mu\tau}$ ), and inverse seesaw (ISS) neutrinos (including active neutrinos and heavy sterile singlets $S_L$ ).
Theoretical Derivation: The authors derive the relevant Feynman rules and couplings for the interaction of leptons with Higgs and gauge bosons. They explicitly calculate the one-loop contributions to the anomalous magnetic moments ( $\Delta a_\ell$ ) and the branching ratios for LFV decays ( $e_b \to e_a \gamma$ , $h \to e_b e_a$ , $Z \to e_b e_a$ ).
Symmetry Analysis: A critical component of the methodology is the analysis of the $U(1)_{L_\mu-L_\tau}$ charge assignments for the sterile neutrino singlets ( $S_L$ ). The authors explore six possible charge permutations to determine how the structure of the heavy neutrino mass matrix ( $M_R$ ) affects flavor mixing.
Numerical Scan: A numerical analysis is conducted scanning the parameter space, including the $SU(2)_R$ $S U (2)_{R}$ breaking scale ( $v_R$ $v_{R}$ ), the ratio of Higgs vacuum expectation values ( $\tan \beta$ $tan β$ ), the masses of heavy neutrinos ( $M_{1,2,3}$ $M_{1, 2, 3}$ ) and the charged Higgs ( $m_{h^+}$ $m_{h^{+}}$ ), and the Yukawa couplings ( $\tilde{Y}^\ell$ $\tilde{Y}^{ℓ}$ ). The scan is constrained by:
- Neutrino oscillation data (normal ordering).
- Perturbativity limits on Yukawa couplings.
- Experimental upper bounds on LFV branching ratios (e.g., $Br(\mu \to e\gamma) < 1.5 \times 10^{-13}$ ).
- Constraints on the non-unitarity of the active neutrino mixing matrix ( $\eta$ ).

Key Contributions and Results

Accommodation of $(g-2)$ Anomalies: The study demonstrates that the LRiss model can successfully accommodate the observed discrepancies in both the muon and electron anomalous magnetic moments.
- For the muon, the model can generate $\Delta a_\mu \sim 10^{-9}$ .
- For the electron, it can accommodate $|\Delta a_e| \sim O(10^{-13})$ .
- The dominant contribution to these discrepancies arises from the "chirally-enhanced" one-loop diagrams involving the exchange of singly charged Higgs bosons ( $h^\pm$ ) and heavy neutrinos. This contribution is proportional to the Yukawa couplings $\tilde{Y}^\ell$ and $\tan \beta$ .
Suppression of LFV Decays: A central finding is that the gauged $U(1)_{L_\mu-L_\tau}$ symmetry leads to a highly suppressed LFV decay rate, effectively decoupling the $(g-2)$ anomalies from LFV constraints.
- Mechanism: The authors show that for specific charge assignments of the sterile neutrinos, the "chirally-enhanced" terms (proportional to $g^{LR}$ ) that drive the large $(g-2)$ contributions are diagonal in flavor space ( $\propto \delta_{ab}$ ). Consequently, these terms do not contribute to flavor-changing processes ( $a \neq b$ ).
- Quantitative Results: The predicted branching ratios for LFV decays are found to be negligible:
  - $Br(e_b \to e_a \gamma) < 10^{-50}$ (dominated by active neutrino contributions which are tiny).
  - $Br(h \to e_b e_a) < O(10^{-28})$ .
  - $Br(Z \to e_b e_a) < O(10^{-34})$ .
- These values are far below current experimental sensitivities, meaning the model is naturally consistent with all existing LFV limits.
Role of Charge Assignments: The paper details how different permutations of the $U(1)_{L_\mu-L_\tau}$ charges for the singlets $S_L$ affect the mass matrix $M_R$ . While the specific permutation changes the structure of the mixing matrices, the qualitative result remains robust: the dominant contributions to $\Delta a_\ell$ are flavor-diagonal, while flavor-off-diagonal contributions are either zero or heavily suppressed by the small active neutrino masses.
Parameter Space Constraints: The numerical analysis reveals that achieving large values of $|\Delta a_\mu|$ and $|\Delta a_\tau|$ requires sizable Yukawa couplings ( $|\tilde{Y}_{2,3}|$ ) and specific ranges of $\tan \beta$ . However, the non-unitarity constraints on the active neutrino mixing matrix ( $\eta_{ii} \leq 10^{-3}$ ) impose limits on the product $\tilde{Y} \tan \beta$ , restricting the viable parameter space.

Significance and Claims
The paper claims that the $U(1)_{L_\mu-L_\tau}$ Left-Right model with inverse seesaw neutrinos provides a theoretically consistent framework where the one-loop contributions from heavy singly charged Higgs bosons can explain the current $(g-2)_\mu$ and $(g-2)_e$ anomalies without violating the extremely tight experimental bounds on lepton flavor violation.

The authors emphasize that the suppression of LFV rates is a direct consequence of the gauged $U(1)_{L_\mu-L_\tau}$ symmetry and the specific structure of the inverse seesaw mechanism, rather than a fine-tuning of parameters. This allows the model to generate sizable contributions to the magnetic moments (via flavor-diagonal loops) while keeping flavor-changing loops (which drive LFV decays) vanishingly small. The work highlights that in this specific BSM scenario, the strong correlations often found between $(g-2)$ and LFV in other models are broken, allowing for a viable explanation of the magnetic moment discrepancies that remains compatible with all current experimental data.

More like this