The answer, worked out by a team of theorists based in Brazil and Chile, is a striking demonstration of how low-energy precision experiments can outmuscle the world’s most powerful particle accelerator. In the scenarios where both seesaw contributions matter, the forbidden decay of a muon into three electrons can push the lower mass limit on a doubly charged scalar particle to roughly 3 TeV, a figure that surpasses the current direct collider constraint of about 856 GeV derived from same-sign dilepton searches at the LHC. The result underscores a recurring theme in beyond-the-Standard-Model physics: processes that never occur in the Standard Model, and are suppressed even when neutrino masses are added by hand, act as extraordinarily sensitive probes of new physics.

To understand the significance of the finding, it helps to unpack the machinery of the seesaw mechanism itself. Neutrino masses can be generated at tree level through the dimension-five Weinberg operator, which admits three canonical realizations. The type I seesaw introduces heavy right-handed neutrinos that are singlets under the Standard Model gauge groups. The type II seesaw instead adds a scalar triplet that acquires a vacuum expectation value, generating neutrino masses directly and bringing with it a zoo of new charged scalars, including particles carrying two units of electric charge. The type III seesaw replaces the scalars with a triplet of heavy fermions. Each option produces characteristic experimental signatures, and combining type I with type II enriches the phenomenology considerably, because the two contributions to the neutrino mass matrix can interfere constructively or destructively.

Rather than studying the combined seesaw in a generic effective framework, the authors embedded it in a complete gauge theory built on the symmetry group SU(3) in color, SU(3) in lepton flavor, and U(1) in a new hypercharge-like interaction, a construction known in the literature as the 3-3-1 model. This framework has an attractive bonus feature: gauge anomalies cancel only if the model contains a multiple of three fermion generations, and considerations of asymptotic freedom forbid more than three, so the theory actually explains why nature has exactly three copies of matter. In this model, each left-handed lepton family is promoted to an SU(3) triplet containing the neutrino, the charged lepton, and a right-handed neutrino, which immediately sets up the type I seesaw. Adding a scalar sextet representation then does double duty: after spontaneous symmetry breaking it decomposes into a scalar triplet, a scalar doublet, and a scalar singlet, and together with the right-handed neutrinos it naturally yields the combined type I plus type II seesaw structure.

The details of symmetry breaking matter enormously for what experiments can see. When a neutral component of one of the scalar triplets acquires a vacuum expectation value, the 3-3-1 symmetry breaks down to the usual electroweak symmetry, which subsequently breaks to electromagnetism through the familiar Higgs-like doublets. The scalar sextet contributes vacuum expectation values that feed into both the Dirac and Majorana mass terms for neutrinos. A single parameter, denoted kappa, controls the relative weight of the two seesaw contributions: when kappa is very large the type I mechanism dominates, when it is near unity the type II mechanism takes over, and when it approaches zero both mechanisms contribute comparably. Electroweak precision measurements constrain the triplet-scale vacuum expectation value to be below about 2 GeV, and the analysis adopts a benchmark of roughly 1 eV, which keeps the new contributions to the W and Z boson masses safely small.

On the experimental side, the model’s most conspicuous collider signature is the doubly charged scalar, which can be pair-produced at the LHC through Drell-Yan processes and decays into pairs of same-sign charged leptons, a background-free channel that ATLAS has searched for using 13 TeV proton-proton collisions with 36.1 inverse femtobarns of integrated luminosity. The team adopted the published limit of 856 GeV for a doubly charged scalar decaying predominantly into muon pairs with only a small electron fraction, matching the branching pattern in their model. Searches for the model’s new neutral and charged gauge bosons, the Z-prime and W-prime, impose limits in the 4 to 5 TeV range, but the authors note that the 3-3-1 symmetry breaking scale can be raised high enough to evade them, and crucially the doubly charged scalar mass is controlled by an independent parameter in the scalar potential rather than by that breaking scale.

The heart of the analysis lies in lepton flavor violation. Because neutrinos have mass and mix, processes such as a muon decaying into an electron and a photon, or into three electrons, are allowed in principle, but they are so suppressed in the minimal extension of the Standard Model that any observation would be an unambiguous signal of new physics. The current experimental bounds are formidable: the MEG II collaboration limits the branching ratio of muon to electron plus photon to below 1.5 times ten to the minus thirteen, while the SINDRUM experiment limits muon to three electrons to below ten to the minus twelve. Future experiments are expected to sharpen these limits to 6 times ten to the minus fourteen and ten to the minus sixteen respectively, making the coming decade a golden era for charged lepton flavor violation searches.

The theoretical predictions connect directly to measured neutrino observables. The Yukawa couplings that drive the rare decays are fixed, up to the kappa parameter and the sextet vacuum expectation value, by the PMNS mixing matrix and the neutrino masses. The authors used two benchmark sets of oscillation parameters drawn from recent global fits, corresponding to the two possible octants of the atmospheric mixing angle theta-23, which remains undetermined. They also confronted the cosmological constraint on the sum of neutrino masses, adopting a value of 0.07 eV consistent with the DESI baryon acoustic oscillation measurements and Planck data, and checked whether a more relaxed limit of 0.1 eV would change their conclusions. Remarkably, neither the choice of oscillation benchmark nor the precise value of the neutrino mass sum significantly alters the predicted branching ratios, which makes the model’s constraints unusually robust against ongoing refinements in neutrino and cosmological data.

The resulting hierarchy of constraints is the paper’s most interesting twist. For the muon to electron plus photon channel, both the singly and doubly charged scalars contribute, and in the dominant type II and mixed type I plus II scenarios this decay already constrains the model more strongly than the LHC same-sign dilepton searches. But the muon to three electrons decay, mediated solely by the doubly charged scalar, is the true powerhouse: it yields a lower mass limit of about 3 TeV for kappa equal to zero or one, comfortably exceeding the collider bound. In stark contrast, when the type I seesaw dominates, lepton flavor violation processes fall far below experimental sensitivity, and only the direct collider limit on the charged scalar masses applies. This asymmetry carries a clear experimental message: continuing and intensifying the search for lepton flavor violating signals, both in dedicated muon experiments and at colliders, is essential, because the reach of each probe depends sensitively on which seesaw mechanism nature has chosen.

Looking ahead, the interplay between precision muon physics and collider searches will only deepen. Next-generation experiments targeting muon to three electron decays, together with proposed future facilities such as high-luminosity collider upgrades and muon colliders, will probe exactly the parameter space this model occupies. If a doubly charged scalar or a forbidden muon decay ever turns up, the pattern of rates across channels will reveal whether neutrino masses arise from heavy singlets, scalar triplets, or, as this work suggests is entirely possible, an intricate conspiracy of both.

Subject of Research: Lepton flavor violation and collider constraints in a type I + II seesaw model of neutrino masses

Article Title: Type I + II seesaw model in light of the new neutrino oscillation measurements

Article References: Aguilar, M., Helo, J. C., Ota, T., Queiroz, F. S., Suarez, D., & Rodríguez, A. (2026). Type I + II seesaw model in light of the new neutrino oscillation measurements. The European Physical Journal C, 86(9), Article 1122. https://doi.org/10.1140/epjc/s10052-026-16328-1

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16328-1

Keywords: neutrino masses, seesaw mechanism, lepton flavor violation, doubly charged scalar, muon decay, LHC, 3-3-1 model, neutrino oscillations, DESI, cosmology, particle physics, beyond the Standard Model