arXiv subjects

H. N. Long

Publications and source records attributed to H. N. Long.

At least 19 recordsLinked to original sources

arXiv2026

Probing axion in the DFSZ model

We show that with the introduction of new right-handed neutrinos $N_R$, the Peccei--Quinn ($PQ$) transformation in the DFSZ (Dine--Fischler--Srednicki--Zhitnitsky) model depends only on the $PQ$ charge of the scalar singlet $\phi$, namely $PQ_\phi$, and is independent of the sine and cosine of $\arctan(v_u/v_d)$. The model consists of four new scalars: a charged Higgs boson $H^\pm$, a CP-odd scalar $A$, and two CP-even scalars with masses at the EW scale (of a few hundred GeV), and a superheavy inflaton $\Phi$. The scalar fields have been presented in the form of unitary matrices, in which there is no mixing between the axion and the Goldstone boson $G_Z$. As a result, there are two kinds of couplings between the axion and fermions, namely Yukawa-like interactions and anomaly-induced ones associated with derivative axion couplings. {The model belongs to the DFSZ I kind since the axion - photon coupling with $\fr E N = \fr 8 3$.} The trilinear Higgs self-coupling is investigated. We have shown that, in the parameter region where new scalar fields such as the singly charged Higgs boson $H^\pm$ and the CP-odd scalar $A$ have masses around 150 GeV and the vacuum expectation value of one Higgs doublet ($v_u$) is of the order of a few GeV, the coupling modifier $\kappa_\lambda$-a probe of new physics-is consistent with the current experimental constraints.

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arXiv2025

Heavy neutral bosons and dark matter in the 3-3-1 model with axionlike particle

We consider heavy neutral bosons in the 3-3-1 model with axionlike particles (331ALP), including the Higgs boson and the $Z^\prime$ boson which are outside the standard model (SM). Based on gluon-gluon fusion at the LHC, we investigate the signals of cross-sections in the parameter space region satisfying the current experimental limits of lepton flavor violating decay, including processes involving both charged leptons and Higgs boson, and provide predictions of $m_{h_2}\geq 630 ~\mathrm{GeV}$. A new gauge boson, labeled as $Z^{\prime}$, has its mass excluded in the smaller domain $5.1 ~\mathrm{TeV}$ based on investigating the cross-section of the processes that $Z^{\prime}$ mediates combined with experimental limits of the search for high-mass dilepton resonances at ATLAS and CMS. We consider the stability of odd-$Z_2$ particles, with $Z_2$ is assumed a residual symmetry after spontaneous symmetry breaking stages, to point out dark matter candidates in the model. Investigating the relic density of dark matter within experimentally permissible limits, we established a relationship between the mass of dark matter and the breaking scale of axion.

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arXiv2025

Form of axion in DFSZ models with $U(1)_{PQ}$ symmetry

Form of axion state in the DFSZ model is determined by exacted diagonalizing of the mass mixing matrix of $CP$-odd sector. After applying $PQ$ mechanism to determine $PQ$ charges of particles of the model, these $PQ$ charges are used to define the general form of axion. Both of these two methods give consistent and reasonable physical state of axion. The constraint of $PQ$ charge in $DFSZ - I$ model is also pointed out. Then, anomalous couplings of axion-photon-photon is re-examined. Triple-couplings of axion with two fermions are studied. The decay of and axion into a pair of photon is also considered via re-normalizable interactions arising from kinetic terms of scalar fields.

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arXiv2025

Fermion masses and mixings and charged lepton flavor violation in a 3-3-1 model with inverse seesaw

We present a extension of the 3-3-1 gauge model supplemented by an $A_4$ flavor symmetry and cyclic discrete symmetries, including $Z_2$, $Z_2'$, $Z_3$, $Z_4$, $Z_7$ and $Z_{10}$. The model successfully reproduces the observed SM fermion mass hierarchies and mixing patterns in quark and lepton sectors. The smallness of the active neutrino masses is explained through an inverse seesaw mechanism, enabled by the introduction of right-handed and sterile Majorana neutrinos. In the quark sector, flavor-changing neutral currents (FCNCs) arise at tree level exclusively for up-type quarks via the new heavy neutral gauge boson exchange, leading to strong constraints from $D^0$ - $\bar{D}^0$ mixing. The charged lepton sector exhibits sizeable flavor-violating effects, especially in the $μ\rightarrow e γ$ decay, mediated by loops involving heavy neutrinos, new charged gauge bosons as well as charged scalars. We perform a detailed numerical fit of fermion masses and mixing parameters and identify viable regions of parameter space consistent with experimental data on CKM and PMNS mixing matrices. The model predicts branching ratios for charged lepton flavor violating decays and $μ$-$e$ conversion rates within the sensitivity of future experiments.

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arXiv2024

New Physics in the 3-3-1 models

Two main ingredients of current particle physics such as local gauge symmetry and mass generation via the Higgs mechanism being basic ground of the Standard Model are widely confirmed by experimental data. However, some problems such as neutrino masses, dark matter, baryon asymmetry of Universe have clearly indicated that the Standard Model cannot be the ultimate theory of nature. To surpass the mentioned puzzles, many extensions of the Standard Model (called beyond Standard Model) have been proposed. Among beyond Standard Models, the 3-3-1 models have some intriguing features and they get wide attention. The pioneer models develop in some directions. In this paper, %some new main versions of the 3-3-1 models and their consequences are presented.

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arXiv2024

On axion properties in the 3-3-1 model with $U(1)_{B-L}$ and Peccei-Quinn symmetries

The Peccei-Quinn ($PQ$) mechanism is applied to the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model with $U(1)_{B-L}$ symmetry. The structures in the $PQ$ charges of all fermions and scalar fields in the model are investigated by applying the invariant condition under the symmetry group transformations on all Yukawa interaction terms. All defined $PQ$ charges depend just on the $PQ$ charge of the complex singlet scalar field which causes the $U(1)_{PQ}$ spontaneous symmetry breaking in the model. The mixing and mass hierarchy in the scalar sector of the model are studied in detail. The constraints on the $PQ$ charges and imaginary parts of scalars are derived. It is shown that only neutral scalar fields carry $PQ$ charges while charged ones do not. As the result, the physical state of axion which obeys the invariance under $\mathrm{SU(3)_L \otimes U(1)_X}$ and $PQ$ transformations, is a linear combination of all imaginary parts associated with the $X$ charges of scalar triplets. The anomaly axion-fermion interactions are presented. Explicit expressions for axion and light Standard Model (SM) like Higgs boson are shown. Mass of the axion and its coupling to photon are derived. The decays of the SM-like Higgs boson into a pair of either charged leptons or bottom quarks are presented and constrained. The triple-coupling axion-photon-photon arisen from kinetic terms of scalar fields is derived. Hence, the decay of axion into a pair of photons consists of two parts: the first is related to the anomaly coupling and the second is come from kinetic terms of scalar fields. The result shows that the new contribution can be helpful for searching axion with mass at hundred keV.

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arXiv2024

Fermion masses and mixings and $g-2$ muon anomaly in a $Q_6$ flavored 2HDM

We propose an extended 2HDM with $Q_6\times Z_4\times Z_2$ symmetry that can successfully accommodate the SM fermion mass and mixing hierarchy. The tiny masses of the active neutrinos are generated from a type-I seesaw mechanism mediated by very heavy right-handed Majorana neutrinos. The model gives a natural explanation of the charged lepton mass hierarchy. Besides that, the experimental values of the physical observables of the neutrino sector: the neutrino mass squared splittings, the leptonic mixing angles and the leptonic Dirac CP violating phase, are also successfully reproduced for both normal and inverted neutrino mass hierarchies. We find a feasible range of values for the leptonic Dirac CP phase to be in the ranges $δ_{CP}\in (305.90, 348.70)^\circ$ for normal ordering and $δ_{CP}\in (308.00, 348.00)^\circ$ for inverted ordering, which is consistent with the 3$σ$ experimentally allowed limits. The sum of neutrino masses is obtained as $\sum m_i \in (58.03, 60.51)$ meV for normal ordering and $\sum m_i\in (98.07, 101.40)$ meV for inverted ordering which are well consistent with all the recent limits. In addition, the obtained ranges for the effective neutrino masses are $\langle m_{ee}\rangle \in (3.80, 4.38)$\, meV, $m_β \in (8.53, 9.34)\, \mbox{meV}$ for normal ordering and $\langle m_{ee}\rangle \in (47.85, 49.58) $ meV, $m_β \in (48.39, 50.09)\, \mbox{meV}$ for inverted ordering which are in agreement with the recent experimental bounds. For the quark sector, the derived results are also in agreement with the recent data on the quark masses and mixing angles. The model under consideration can also accommodate the muon anomalous magnetic moment.

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arXiv2024

Phenomenology of 3-3-1 models with radiative inverse seesaw mechanism

We propose two models based on the $SU(3)_C \times SU(3)_L \times U(1)_X$ gauge symmetry, each incorporating distinct inverse seesaw mechanisms for generating neutrino masses at the radiative level. Therefore, neutrino masses are suppressed by the radiative nature of the mass generation mechanism, which occurs after the spontaneous breaking of the global lepton number symmetry. Both scenarios discussed here are characterized by the presence of vector-like charged leptons, which are involved in generating the masses of the Standard Model charged leptons. These additional vector-like fermions contribute to the anomalous magnetic moments of the electron and the muon. We perform a detailed analysis of the scalar sectors, show that these models can successfully accommodate the observed baryon asymmetry through resonant leptogenesis, and compute charged lepton flavor-violating decays, such as $μ\rightarrow e γ$. We discuss the constraints of the model arising from these processes and those associated the non-unitarity of the lepton mixing matrix.

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arXiv2023

Peccei-Quinn mechanism and axion interactions in the 3-3-1 model with Cosmological Inflation

Based on the Peccei-Quinn (PQ) assignment, the PQ charge operator in the 3-3-1 model with Cosmological Inflation is constructed in terms of diagonal generators $T_3$ and $T_8$ of the $SU(3)_L$ subgroup. The formula shows that difference of PQ charges of up and down quarks is 2, i.e., $\De Q_A =2$, while for electric charge, are assumed to be equal, while the ($Q_A$) are opposite. PQ charge of neutral scalars equal $\pm 2$, while for charged scalars, it vanishes. The couplings of axion with fermions are presented. To have correct kinetic term for the axion, the PQ scale $f_{a}$ is to be VEV of the singlet scalar boson, namely, $f_{a}= v_ϕ$. The photon couples to charged particles only, while in this model, the axion does not couple to charged scalar/gauge bosons. The point is worth emphasizing that the axion has doubly derivative coupling with scalar playing the role of inflaton. The new effects mainly happen in the energy region from $10^7 \, \gev$ to $10^{11} \, GeV$. The chiral effective Lagrangian as usually provides axion mass consistent with model-independent prediction.

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arXiv2023

One-loop contributions to decays $e_b\to e_a γ$ and $(g-2)_{e_a}$ anomalies, and Ward identity

In this paper, we will present analytic formulas to express one-loop contributions to lepton flavor violating decays $e_b\to e_a γ$, which are also relevant to the anomalous dipole magnetic moments of charged leptons $e_a$. These formulas were computed in the unitary gauge, using the well-known Passarino-Veltman notations. We also show that our results are consistent with those calculated previously in the 't Hooft-Veltman gauge, or in the limit of zero lepton masses. At the one-loop level, we show that the appearance of fermion-scalar-vector type diagrams in the unitary gauge will violate the Ward Identity relating to an external photon. As a result, the validation of the Ward Identity guarantees that the photon always couples with two identical particles in an arbitrary triple coupling vertex containing a photon.

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arXiv2023

Higgs sector phenomenology in the 3-3-1 model with an axionlike particle

The scalar sector of the 3-3-1 model with axion like particle is studied in detail. In the model under consideration, there are two kinds of scalar fields: the bilepton scalars carrying lepton number two and the ordinary ones without lepton number. We show that there is no mixing among these two kinds of scalar fields. We analyze in detail the CP-odd scalar sector of the model to find the physical fields of the axion like particle and a pseudoscalar with mass in the range 100 GeV to 1 TeV. The results are different from others which have been published before. The CP-even scalar sector of the model is analyzed as well. The results of our analysis of the scalar sector allow us to accommodate scalar masses in the $100$ GeV-$1$ TeV region. Furthermore we analyze the implications of the model in several flavor changing neutral decays of the top quark as well as in rare top quark decays. Besides that, the leptonic decays of the SM like Higgs boson as well as the meson oscillations are also analyzed. Our numerical analysis show that the model under consideration is consistent with the experimental constraints imposed by these processes.

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arXiv2023

$A_4$-based model with linear seesaw scheme for lepton mass and mixing

We suggest a low-scale model based on $A_4\times Z_4 \times Z_2$ symmetry and a global lepton number $U(1)_L$ symmetry capable of generating the current neutrino data. The neutrino mass smallness is reproduced by the linear seesaw mechanism. The model can explain the current observed pattern of lepton mixing in which the reactor and atmospheric angles get the best-fit values, and the solar angle and Dirac phase lie within $3σ$ limits. The obtained values of the sum of neutrino mass and the effective neutrino mass are below the present experimental limits.

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arXiv2022

Heavy singly charged Higgs bosons and inverse seesaw neutrinos as origins of large $(g-2)_{e,μ}$ in two higgs doublet models

We show that simple extensions of two Higgs doublet models consisting of new heavy neutrinos and a singly charged Higgs boson singlet can successfully explain the experimental data on muon and electron anomalous magnetic moments thanks to large chirally-enhanced one-loop level contributions. These contributions arise from the large couplings of inverse seesaw neutrinos with singly charged Higgs bosons and right-handed charged leptons. The regions of parameter space satisfying the experimental data on $(g-2)_{e,μ}$ anomalies allow heavy singly charged Higgs boson masses above the TeV scale, provided that heavy neutrino masses are above few hundred GeV, the non-unitary part of the active neutrino mixing matrix must be large enough, two singly charged Higgs bosons are non degenerate, and the mixing between singly charged Higgs bosons must be non-zero.

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arXiv2022

Lepton masses and mixings, and muon anomalous magnetic moment in an extended $B-L$ model with type I seesaw mechanism

We propose a $B-L$ model combined with the $S_4\times Z_3\times Z_4$ discrete symmetry which successfully explains the recent $3+1$ sterile - active neutrino data. The smallness of neutrino mass is obtained through the type-I seesaw mechanism. The active-active and sterile-active neutrino mixing angles are predicted to be consistent with the recent constraints in which $0.3401\, (0.3402) \leq \sin^2θ_{12}\leq 0.3415\, (0.3416), \, 0.456\, (0.433) \leq \sin^2θ_{23}\leq 0.544\, (0.545), \, 2.00\, (2.018) \leq 10^2\times \sin^2θ_{13}\leq 2.405\, (2.424),\,\, 156 \, (140.8) \leq δ^{(\circ)}_{CP}\leq 172\, (167.2)$ for normal (inverted) ordering of the three neutrino scenario, and $0.015 \,(0.022) \leq s^2_{14}\leq 0.045 \,(0.029), \, 0.005 (0.0095)\leq s^2_{24}\leq 0.012\, (0.012), \, 0.003 \,(0.009)\leq s^2_{34} \leq 0.011$ for normal (inverted) ordering of the $3+1$ neutrino scenario. Our model predicts flavour conserving leptonic neutral scalar interactions and successfully explains the muon $g-2$ anomaly.

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arXiv2022

An explanation of experimental data of $(g-2)_{e,μ}$ in 3-3-1 models with inverse seesaw neutrinos

We show that the anomalous magnetic moment experimental data of muon and electron $(g-2)_{μ,e}$ can be explained simultaneously in simple extensions of the 3-3-1 models consisting of new heavy neutrinos and a singly charged Higgs boson. The heavy neutrinos generate active neutrino masses and mixing through the general seesaw mechanism. They also have non-zero Yukawa couplings with singly charged Higgs bosons and right-handed charged leptons, which result in large one-loop contributions known as \emph{chirally-enhanced} ones. Numerical investigation confirms a conclusion indicated previously that these contributions are the key point to explain the large $(g-2)_{μ,e}$ data, provided that the inverse seesaw mechanism is necessary to allow both conditions that heavy neutrino masses are above few hundred GeV and non-unitary part of the active neutrino mixing matrix must be large enough.

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arXiv2022

Fermion masses and mixings and $g-2$ muon anomaly in a 3-3-1 model with $D_4$ family symmetry

We propose a predictive model based on the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge symmetry, which is supplemented by the $D_4$ family symmetry and several auxiliary cyclic symmetries whose spontaneous breaking produces the observed SM fermion mass and mixing pattern. The masses of the light active neutrinos are produced by an inverse seesaw mechanism mediated by three right handed Majorana neutrinos. To the best of our knowledge the model corresponds to the first implementation of the $D_4$ family symmetry in a $SU(3)_C\times SU(3)_L\times U(1)_X$ theory with three right handed Majorana neutrinos and inverse seesaw mechanism. Our proposed model successfully accommodates the experimental values of the SM fermion mass and mixing parameters, the muon anomalous magnetic moment as well as the Higgs diphoton decay rate and meson oscillations constraints. The consistency of our model with the muon anomalous magnetic moment requires charged exotic vector like leptons at the TeV scale.

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arXiv2021

An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism

Low energy linear seesaw mechanism responsible for the generation of the tiny active neutrino masses, is implemented in the extended 3-3-1 model with two scalar triplets and right handed Majorana neutrinos where the gauge symmetry is supplemented by the $A_4$ flavor discrete group and other auxiliary cyclic symmetries, whose spontaneous breaking produces the observed pattern of SM charged fermion masses and fermionic mixing parameters. Our model is consistent with the low energy SM fermion flavor data as well as with the constraints arising from meson oscillations. Some phenomenological aspects such as the $Z^\prime$ production at proton proton collider and the lepton flavor violating decay of the SM-like Higgs boson are discussed. The scalar potential of the model is analyzed in detail and the SM-like Higgs boson is identified.

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arXiv2021

COHERENT constraints on $Z'$ in 331$β$ model

We investigate coherent-elastic neutrino-nucleus scattering ($CEνNS$) in 3-3-1 models for different values of $β$ in which $β$ is a parameter used to define the charge operator of the 331 models. We show that the number of events predicted by 331$β$ model is in agreement with the data given by COHERENT experiment. We evaluate the sensitivity of the mass of Z' boson with 90% confidence level (CL) and find that $m_{Z'}\geq 1.4 $TeV for $β=-\sqrt{3}$ with 90% CL. We perform $χ^2$ fit for liquid Argon, Germanium and NaI detector subsystems, we obtain $m_{Z'} \geq [2,3.1 ]$ TeV with 90\% CL. Our results indicate low-energy high-intensity measurements can provide a valuable probe, complementary to high energy collider searches at LHC and electroweak precision measurements.

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