Tiny Neutrino Masses Research Articles

Probing dirac neutrino properties with dilepton signature

The neutrinophilic two Higgs doublet model is one of the simplest models to explain the origin of tiny Dirac neutrino masses. This model introduces a new Higgs doublet with eV scale VEV to naturally generate the tiny neutrino masses. Depending on the same Yukawa coupling, the neutrino oscillation patterns can be probed with the dilepton signature from the decay of charged scalar H±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^\\pm $$\\end{document}. For example, the normal hierarchy predicts BR(H+→e+ν)≪\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow e^+\ u )\\ll $$\\end{document} BR(H+→μ+ν)≈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow \\mu ^+\ u )\\approx $$\\end{document} BR(H+→τ+ν)≃0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow \ au ^+\ u )\\simeq 0.5$$\\end{document} when the lightest neutrino mass is below 0.01 eV, while the inverted hierarchy predicts BR(H+→e+ν)/2≃\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow e^+\ u )/2\\simeq $$\\end{document} BR(H+→μ+ν)≃\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow \\mu ^+\ u )\\simeq $$\\end{document} BR(H+→τ+ν)≃0.25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow \ au ^+\ u )\\simeq 0.25$$\\end{document}. By precise measurement of BR(H+→ℓ+ν)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(H^+\\rightarrow \\ell ^+\ u )$$\\end{document}, we are hopefully to probe the lightest neutrino mass and the atmospheric mixing angle θ23\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{23}$$\\end{document}. Through the detailed simulation of the dilepton signature and corresponding backgrounds, we find that the 3 TeV CLIC could discover MH+≲1220\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{H^+}\\lesssim 1220$$\\end{document} GeV for NH and MH+≲1280\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{H^+}\\lesssim 1280$$\\end{document} GeV for IH. Meanwhile, the future 100 TeV FCC-hh collider could probe MH+≲1810\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{H^+}\\lesssim 1810$$\\end{document} GeV for NH and MH+≲2060\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{H^+}\\lesssim 2060$$\\end{document} GeV for IH.

Phenomenological aspects of the fermion and scalar sectors of a S4 flavored 3-3-1 model

We proposed a viable and predictive model based on the SU(3)C×SU(3)L×U(1)X gauge symmetry, supplemented by the global U(1)Lg symmetry, the S4 family symmetry and several auxiliary cyclic symmetries, which successfully reproduces the experimentally observed SM fermion mass and mixing pattern. The tiny active neutrino masses are generated through an inverse seesaw mechanism mediated by right-handed Majorana neutrinos. The model is consistent with the SM fermion masses and mixings and successfully accommodates the current Higgs diphoton decay rate constraints as well as the constraints arising from oblique S, T and U parameters and we studied the meson mixing due to flavor changing neutral currents mediated by heavy scalars, finding parameter space consistent with experimental constraints.

Heavy neutral leptons in gauged U(1) L µ −L τ at muon collider* *Supported by the National Natural Science Foundation of China (12375074, 11805081) and the Natural Science Foundation of Shandong Province, China (ZR2019QA021)

Heavy neutral leptons N are the most appealing candidates to generate tiny neutrino masses. We studied the signature of heavy neutral leptons in gauged at a muon collider. Charged under the symmetry, the heavy neutral leptons can be pair produced via the new gauge boson at the muon collider as and . We then performed a detailed analysis on the lepton number violation signature and at the 3 TeV muon collider, where the hadronic decays of W boson are treated as fat-jets J. These lepton number violation signatures have quite clean backgrounds at the muon collider. Our simulation shows that a wide range of viable parameter space is within the reach of the 3 TeV muon collider. For instance, with new gauge coupling and an integrated luminosity of 1000 fb , the signal could probe TeV. Meanwhile, if the gauge boson mass satisfies , the signature would be more promising than the signature.

Low scale leptogenesis in singlet-triplet scotogenic model

The scotogenic model presents an elegant and succinct framework for elucidating the origin of tiny neutrino masses within the framework of the Standard Model, employing radiative corrections within the domain of the dark sector. We investigate the possibility of achieving low-scale leptogenesis in the singlet-triplet scotogenic model (STSM), where dark matter mediates neutrino mass generation. We initially considered a scenario involving two moderately hierarchical heavy fermions, N and Σ, wherein the lepton asymmetry is generated by the out-of-equilibrium decay of both particles. Our analysis indicates that the scale of leptogenesis in this scenario is similar to that of standard thermal leptogenesis and is approximately M N,Σ ∼ 109 GeV, which is comparable to the Type-I seesaw case. Further, we consider the case with three heavy fermions (N 2, N 2, and Σ) with the hierarchy M N 1 < M Σ ≪ MM N 2 , which yields the lower bound on heavy fermions up to 3.1 TeV, therefore significantly reduce the scale of the leptogenesis up to TeV scale. The only prerequisite is suppression in the N 1 and Σ Yukawa couplings, which causes suppressed washout effects and a small active neutrino mass of about 10-5 eV. This brings about the fascinating insight that experiments aiming to measure the absolute neutrino mass scale can test low-scale leptogenesis in the scotogenic model. Further, the hyperchargeless scalar triplet Ω provides an additional contribution to mass of the W-boson explaining CDF-II result.

Disentangle neutrino electromagnetic properties with atomic radiative pair emission

We elaborate the possibility of using the atomic radiative emission of neutrino pair (RENP) to probe the neutrino electromagnetic properties, including magnetic and electric dipole moments, charge radius, and anapole. With the typical O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(eV) momentum transfer, the atomic RENP is sensitive to not just the tiny neutrino masses but also very light mediators to which the massless photon belongs. The neutrino EM properties introduce extra contribution besides the SM one induced by the heavy W/Z gauge bosons. Since the associated photon spectrum is divided into several sections whose boundaries are determined by the final-state neutrino masses, it is possible to identify the individual neutrino EM form factor elements. Most importantly, scanning the photon spectrum inside the particular section with deviation from the SM prediction once observed allows identification of the neutrino EM form factor type. The RENP provides an ultimate way of disentangling the neutrino EM properties to go beyond the current experimental searches or observations.

A minimal inverse seesaw model with S4 flavour symmetry

We construct an S4 flavour symmetric minimal inverse seesaw model where the standard model is extended by adding two right-handed and two standard model gauge singlet neutrinos to explain the origin of tiny neutrino masses. The resulting model describes the lepton mass spectra and flavour mixing quite well for the case of the normal hierarchy of neutrino masses. The prediction of the model on the Dirac CP-violating phase is centered around 370.087°. Furthermore, using the allowed region for the model parameters, we have calculated the value of the effective Majorana neutrino mass, |〈mee〉|, which characterizes neutrinoless double beta decay.

Interplay among gravitational waves, dark matter and collider signals in the singlet scalar extended type-II seesaw model

We study the prospect of simultaneous explanation of tiny neutrino masses, dark matter (DM), and the observed baryon asymmetry of the Universe in a Z3-symmetric complex singlet scalar extended type-II seesaw model. The complex singlet scalar plays the role of DM. Analyzing the thermal history of the model, we identify the region of the parameter space that can generate a first-order electroweak phase transition (FOEWPT) in the early Universe, and the resulting stochastic gravitational waves (GW) can be detected at future space/ground-based GW experiments. First, we find that light triplet scalars do favor an FOEWPT. In our study, we choose the type-II seesaw part of the parameter space in such a way that light triplet scalars, especially the doubly charged ones, evade the strong bounds from their canonical searches at the Large Hadron Collider (LHC). However, the relevant part of the parameter space, where FOEWPT can happen only due to strong SM doublet-triplet interactions, is in tension with the SM-like Higgs decay to a pair of photons, which has already excluded the bulk of this parameter space. On the other hand, the latest spin-independent DM direct detection constraints from XENON-1T and PANDA-4T eliminate a significant amount of parameter space relevant for the dark sector assisted FOEWPT scenarios, and it is only possible when the complex scalar DM is significantly underabundant. In short, we conclude from our analysis that the absence of new physics at the HL-LHC and/or various DM experiments in the near future will severely limit the prospects of detecting a stochastic GW at future GW experiments and will exclude the possibility of electroweak baryogenesis within this model.

Baryogenesis

The standard model of particle physics describes matter and antimatter as coming from the same fields and this fact has been confirmed experimentally. It is then curious that the observable universe is made of matter and not antimatter. We will first discuss the evidence that we live in a matter-dominated (or matter-antimatter asymmetric) Universe and then proceed to discuss if this can be explained according to our current understanding of the cosmology and particle physics. We will argue that an important process known as baryogenesis to generate a cosmic matter-antimatter asymmetry had to occur before the Universe was a few second old. Then, we will discuss the necessary ingredients for a successful baryogenesis and point out that the current model contains all the ingredients but not in a sufficient amount. Finally, we will discuss possible extensions to the current model which allow successful baryogenesis and how they can be tested experimentally. Interestingly, they might also be connected to other open puzzles in the fundamental physics, like the tiny neutrino mass.

Linear seesaw mechanism from dark sector

We propose a minimal model where a dark sector seeds neutrino mass generation radiatively within the linear seesaw mechanism. Neutrino masses are calculable, since tree-level contributions are forbidden by symmetry. They arise from spontaneous lepton number violation by a small Higgs triplet vacuum expectation value. Lepton flavour violating processes e.g. μ → eγ can be sizeable, despite the tiny neutrino masses. We comment also on dark-matter and collider implications.

On the Higgs spectra of the 3-3-1 model with the sextet of scalars engendering the type II seesaw mechanism

In the 3-3-1 model with right-handed neutrinos (331RHNs), three triplets of scalars engender the correct sequence of symmetry breaking, SU(3)C×SU(3)L×U(1)X→SU(3)C×SU(2)L×U(1)Y→SU(3)C×U(1)EM, generating mass for all fermions, except neutrinos. Tiny neutrino masses may be achieved by implementing the type II seesaw mechanism into the model, requiring the addition of one sextet of scalars to the original scalar content. As consequence, it emerges a very complex scalar sector, involving terms that violate lepton number explicitly, too. The main obstacle to the development of the phenomenology of such scenario is the knowledge of its spectrum of scalars since, now, there are 15 massive scalar particles on it. The proposal of this work is to do an exhaustive analysis of such scalar sector with lepton number being explicitly violated at low, electroweak and high energy scales by means of trilinear terms in the potential. The first case can be addressed analytically and, as a nice result, we have observed that the scalar content of such case is split into two categories: One belonging to the 331 energy scale and the other belonging to the EWSB energy scale, with the last recovering the well know 2THDM + triplet. For the other cases, the scalar sector can be addressed only numerically. Hence, we proposed a very general approach for the numerical study of the potential, avoiding simplifications that can make us reach conclusions without foundation. We show that, in the case of lepton number being explicitly violated at electroweak scale, it is possible to recover the same physics of the 2HDM + triplet, as the previous case. Among all the possibilities, we call the attention to one special case which generates the 3HDM+triplet scenario. For the last case, when lepton number is violated at high energy scale, the sextet becomes very massive and decouples from the original scalar content of the 3-3-1 model. We also discuss, when possible, the phenomenological aspects of each case.

Can we really detect relic neutrinos?

Detecting relic neutrinos is a longstanding goal in fundamental physics. Experimentally, this goal is extremely challenging as the required energy resolution is defined by the tiny neutrino masses (\sim∼ 10 meV). The current consensus is that sufficient statistics together with a clean spectrum could only be achieved if beta decayers are attached to a solid state substrate. However, this inevitably imposes irreducible intrinsic limitations on the energy resolution coming from Heisenberg’s uncertainty principle. This limitation appears to be critical for the currently accepted decayer - Tritium. Here, we analyze the state of the art approaches to mitigate this limitation and conclude that the most promising solution is to change Tritium for a heavier emitter. We find that the two suitable candidates are ^{171}171Tm, ^{63}63Ni.

Charged Higgs induced 5 and 6 lepton signatures from heavy neutrinos at the LHC

We propose an anomaly free gauged U(1) extension of the SM where three right handed heavy neutrinos, being charged under the general U(1) gauge group, are introduced to explain the origin of the tiny neutrino mass through the seesaw mechanism after the general U(1) symmetry is broken. Due to the breaking of the general U(1) symmetry a neutral beyond the standard model gauge boson Z^prime acquires mass. There are two Higgs doublets in this model where one interacts with the SM fermions and the other one interacts with the right handed heavy neutrinos and charged leptons. The charged multiplet of the second Higgs can completely decay into the heavy neutrinos and charged lepton in the neutrinophilic limit of the model parameters. The charged Higgs pair production can be influenced due to presence of the Z^prime boson at the High Luminosity LHC (HL-LHC) in addition to the neutral SM gauge bosons. The pair produced charged Higgs bosons decay into SM charged leptons and heavy neutrinos. Following the leading decay modes of the heavy neutrinos into charged leptons and W boson we study the 5 and 6 lepton final states after the leptonic and hadronic decay of the W bosons considering solely muons and electrons in the final state. Combining the electron and muon final states we estimate the significance of the 5 and 6 charged lepton processes in the m_{H^pm }-m_N plane for different benchmark points of m_{Z^prime }. It is found that the 5 (6) charged lepton processes could be probed at the High Luminosity LHC (HL-LHC) with at least 5 (3) sigma significance and there are parameter regions where the significance could be larger.

Sterile neutrino portal dark matter in nu THDM

In this paper, we propose the sterile neutrino portal dark matter in nu THDM. This model can naturally generate tiny neutrino mass with the neutrinophilic scalar doublet Phi _{nu } and sterile neutrinos N around TeV scale. Charged under a Z_2 symmetry, one Dirac fermion singlet chi and one scalar singlet phi are further introduced in the dark sector. The sterile neutrinos N are the mediators between the DM and SM. Depending on the coupling strength, the DM can be either WIMP or FIMP. For the WIMP scenario, pair annihilation of DM into NN is the key channel to satisfy various bounds, which could be tested at indirect detection experiments. For the FIMP scenario, besides the direct production of DM from freeze-in mechanism, contributions from late decay of NLOP is also important. When sterile neutrinos are heavier than the dark sector, NLOP is long-lived due to tiny mixing angle between sterile and light neutrinos. Constrains from free-streaming length, CMB, BBN and neutrino experiments are considered.

Leptogenesis in an anomaly-free U(1) extension with higher-dimensional operators

We explore an anomaly-free U(1) gauge extended beyond the Standard model (BSM) framework, to account for the baryon asymmetry of the Universe, along with arranging for tiny neutrino mass. Neutrino masses are generated via higher-dimensional operators (HDOs) involving three right-handed neutrinos (RHNs) with gauge charges (4, 4 and −5 respectively) and two BSM scalars. This is an attractive framework as it can accommodate a keV scale dark matter, with the lightest RHN being the candidate. The remaining two RHNs are quasi-degenerate at the TeV-scale, actively participating in the process of resonant leptogenesis through their decay governed by the same set of HDOs. The RHNs being at the TeV scale, make this framework relevant for studying flavored resonant leptogenesis. This TeV-scale resonant leptogenesis, after satisfying the neutrino oscillation data, leads to interesting predictions on the Yukawa sector of the model. The thermal evolution of the baryon asymmetry has followed the experimental results rather accurately in that corner of parameter space. As a matter of fact, this TeV-scale framework which in principle relies on the low scale resonant leptogenesis typically leads to predictions that potentially can be tested at the colliders. In particular, we consider the same-sign dilepton signature that arises from the RHN pair production through the decay of heavy gauge boson of the extra U(1).

Twin cogenesis

We investigate a cogenesis mechanism within the twin Higgs setup that can naturally explain the nature of dark matter, the cosmic coincidence puzzle, little hierarchy problem, leptogenesis, and the tiny neutrino masses. Three heavy Majorana neutrinos are introduced to the standard model sector and the twin sector respectively, which explain the tiny neutrino masses and generate the lepton asymmetry and the twin lepton asymmetry at the same time. The twin cogenesis mechanism applies to any viable twin Higgs model without an explicit breaking in the leptonic sector and evading the ΔN eff constraint. We illustrate the twin cogenesis mechanism using the neutrino-philic twin two Higgs doublet model, a newly proposed model to lift the twin neutrino masses with spontaneous breaking. The dark photon with a Stueckelberg mass MeV ensures the energy in the twin sector as well as the symmetric component of twin sector particles can be depleted. The lightest twin baryons are the dark matter candidates with masses of approximately 5.5 GeV, which explains naturally the amount of dark matter and visible matter in the Universe are of the same order. We also demonstrate twin cogenesis in the fraternal twin Higgs setup, in which the dark matter candidate is the twin bottom bound state .

Complete one-loop structure of the type-(I+II) seesaw effective field theory

Besides the three canonical seesaw mechanisms, the hybrid scenario, i.e., the so-called type-(I+II) seesaw mechanism containing both the right-handed neutrinos NR and the triplet Higgs Φ is also an appealing extension of the Standard Model (SM) to account for tiny neutrino masses. Recently, the seesaw effective field theories (SEFTs) of the three canonical seesaw mechanisms have already been completely constructed up to one-loop level. In this work, we carry out the one-loop matching of the type-(I+II) seesaw mechanism onto the corresponding type-(I+II) SEFT, which is by no means the trivial combination of the type-I and type-II SEFTs and contains additional contributions even though the right-handed neutrinos and the triplet Higgs have no direct interactions. Employing the Feynman diagrammatic approach, we calculate all those additional contributions from the entangled effects of NR and Φ, and finally achieve the complete one-loop structure of the type-(I+II) SEFT. In the type-(I+II) SEFT, the number and content of dim-6 operators are exactly the same as those in the type-II SEFT, but the Wilson coefficients of the unique dim-5 and nine dim-6 operators as well as the quartic coupling constant of the SM Higgs gain some additional contributions, which are absent in the type-I and type-II SEFTs.

The decomposition of neutron-antineutron oscillation operators

We study the systematic decomposition of the dimension nine neutron-antineutron oscillation operators at tree and one-loop levels. We discuss the topologies’ generation and the assignment of the chiral quarks. The completed lists of the decompositions are provided. We furthermore show an example that the neutron-antineutron oscillation occurs at one-loop level, with the tiny neutrino mass being generated via the scotogenic model and proton decay being evaded.

Leptonic flavor changing processes ℓi → ℓjγ and ℓi → ℓjℓkℓl in the Twin Higgs models

Heavy neutrinos are usually introduced to accommodate tiny neutrino masses via seesaw mechanism, or to alleviate the cosmology problem, and there may exist charged Higgs which couple to the leptons with different flavors. These two features can appear in the Twin Higgs models. What interests us is that such new particles and interactions may lead to new contributions to the lepton flavor violating processes [Formula: see text] and [Formula: see text]. We find that current experimental data can constrain the parameter spaces and certain lepton flavor violating processes can possibly be tested by the next generation experiments.

Unraveling the Scotogenic model at muon collider

The Scotogenic model extends the standard model with three singlet fermion Ni and one inert doublet scalar η to address the common origin of tiny neutrino mass and dark matter. For fermion dark matter N1, a hierarchical Yukawa structure mid {y}_{1e}mid ll mid {y}_{1mu}mid sim mid {y}_{1tau}mid sim mathcal{O}(1) is usually favored to satisfy constraints from lepton flavor violation and relic density. Such large μ-related Yukawa coupling would greatly enhance the pair production of charged scalar η± at the muon collider. In this paper, we investigate the dilepton and mono-photon signature of the Scotogenic model at a 14 TeV muon collider. For the dimuon signature , we find that most viable samples can be probed with 200 fb−1 data. The ditau signature is usually less promising, but it is important to probe the small |y1μ| region. The mono-photon signature could also probe the compressed mass region M1 ≲ {M}_{eta^{pm }} . Masses of charged scalar η± and dark matter N1 can be further extracted by a binned likelihood fit of the dilepton energy.

One-loop matching of scotogenic model onto standard model effective field theory up to dimension 7

The scotogenic neutrino seesaw model is a minimal extension of the standard model with three ℤ2-odd right-handed singlet fermions N and one ℤ2-odd Higgs doublet η that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional matching formalism to the one-loop matching of the model onto the standard model effective field theory up to dimension seven for the case when all new states N and η are heavy to be integrated out. This is a realistic example which has no tree-level matching due to the ℤ2 symmetry. Using the matching results, we analyze their phenomenological implications for several physical processes, including the lepton number violating effect, the CDF W mass excess, and the lepton flavor violating decays like μ → eγ and μ → 3e.