arXiv subjects

Hoang Ngoc Long

Publications and source records attributed to Hoang Ngoc Long.

At least 19 recordsLinked to original sources

arXiv2023

Dual electroweak phase transition in the two-Higgs-doublet model with the $S_3$ discrete symmetry

In this work, dual electroweak phase transition (EWPT) consisting of two phases, is carefully studied in the two-Higgs-doublet model with the $S_3$ discrete symmetry. The role of $S_3$ here is to further separate the stages of the electroweak phase transition, compared to that of the original two-Higgs-doublet model (2HDM). The strength of the electroweak phase transition $(S)$ in the model under consideration is large enough for the first-order EWPT, specifically $1 < S < 2.8$. The ratio between the two vacuum expectation values (VEVs), $\tanβ= v_2/v_1$, is proven to have no effects on the strength of the phase transition. This ratio only affects the mass domain that causes the first-order phase transition. Furthermore, in this paper we will show clearly that when studying the EWPT in models of more than one scalar field that generates masses, one needs to analyze the problem of phase transition under multiple stages. In other words, the effect of the first stage of symmetry breaking to the second one, is to simplify by suggestion that vacuum expectation value of the Higgs boson responsible for the initial stage is proportional to that of the field for the next stage.

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arXiv2022

Baryogenesis and gravitational waves in the Zee-Babu Model

To explain the matter-antimatter asymmetry in the Zee-Babu (ZB) model, the sphaleron process in the baryogenesis scenario is calculated. It always satisfies the de-coupling condition and the strength of phase transition ($S$) is always greater than $1$ in the presence of triggers other than that in the Standard Model, which are singly ($h^{\pm}$) and doubly ($k^{\pm\pm}$) charged scalar bosons. Sphaleron energies are in the range of 5-10 TeV, in calculation with bubble profiles containing free parameters and assuming nuclear bubbles of $h^{\pm}$ and $k^{\pm\pm}$ are very small. We tested the scaling law of sphaleron again with an average error of $10\%$. When the temperature is close to the critical one ($T_c$), the density of nuclear bubble is produced very large and decreases as the temperature decreases. The key parameter is $α$ which results in the gravitational wave density parameter ($Ωh^2$) in the range of $10^{-14}$ to $10^{-12}$ when $β/H^*=22.5$, this is not enough to detect gravitational waves from electroweak phase transition (EWPT) according to the present LISA data but may be detected in the future. As the larger strength of phase transition is, the more $α$ increases (this increase is almost linear with $S$), the larger the gravitational wave density parameter is. Also in the context of considering the generation of gravitational waves, in the ZB model we calculated $α\sim \text{a few} \times 10^{-2}\ll 1$, so rigorously conclude that the EWPT is not strong even though $S>1$. We also suggest that, for a model with a lot of extra scalar particles and particles which play a role in mass generation, the stronger the EWPT process and the larger $Ωh^2$ can be.

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arXiv2020

Sphaleron in the first-order electroweak phase transition with the dimension-six Higgs operator

By adding the dimension-six operator for the Higgs potential (denoted $\mathcal{O}_6$) in Standard Model, we have a first-order electroweak phase transition (EWPT) whose strength is larger than unity. The cutoff parameter of the dimension-six Higgs operator ($Λ$) is found to be in the range 593-860 GeV with the Wilson parameter equals to unity; it is also shown that the greater the $Λ$, the lower the phase transition strength and the larger the Wilson parameter, the wider the domain of $Λ$. At zero temperature, the sphaleron energy is calculated with a smooth ansatz and an ansatz with scale-free parameters, thereby we find that smooth profiles are not more accurate than profiles with scale-free parameters. Then, using the one-loop effective Higgs potential with the inclusion of $\mathcal{O}_6$ instead of all possible dimension-six operators, we directly calculate the electroweak sphaleron energy at finite temperature with the scale-free parameters ansatz and show that the decoupling condition is satisfied during the phase transition. Moreover, we can reevaluate the upper bound of the cutoff scale inferred from the first-order phase transition. In addition, with the upper bound of the cutoff parameter (about 800-860 GeV), EWPT is a solution to the energy scale of the dimension-six operators. There is an extended conclusion that EWPT can only be solved at a large energy scale than that of SM.

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arXiv2019

Inverted neutrino mass hierarchy and mixing in the Zee-Babu model

We show that the neutrino mass matrix of the Zee-Babu model is able to fit the recent data on neutrino masses and mixing with non-zero $θ_{13}$ in the inverted neutrino mass hierarchy. The results show that the Majorana phases are equal to zero and the Dirac phase ($\de$) is predicted to either $0$ or $π$, i. e, there is no CP violation in the Zee-Babu model at the two loop level. The effective mass governing neutrinoless double beta decay and the sum of neutrino masses are consistent with the recent analysis.

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arXiv2018

Baryogenesis in the Zee-Babu model with arbitrary $ξ$ gauge

We consider the baryogenesis picture in the Zee-Babu model. Our analysis shows that electroweak phase transition (EWPT) in the model is a first-order phase transition at the $100$ GeV scale, its strength ranges from 1 to 4.15 and the masses of charged Higgs boson are smaller than $300$ GeV. The EWPT is strengthened by only the new bosons and this strength is enhanced by arbitrary $ξ$ gauge. However, the $ξ$ gauge does not break the first-order EWPT or, in other words, the $ξ$ gauge is not the cause of the EWPT. This leads to the fact that the calculation of EWPT in Landau gauge is enough; and the latter may provide baryon-number violation (B-violation) necessary for baryogenesis in the relationship with nonequilibrium physics in the early universe.

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arXiv2015

Electroweak phase transition in the economical 3-3-1 model

We consider the EWPT in the economical 3-3-1 (E331) model. Our analysis shows that the EWPT in the model is a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2) \rightarrow U(1)$ at the $100$ GeV scale. The EWPT $SU(3) \rightarrow SU(2)$ is triggered by the new bosons and the exotic quarks; its strength is about $1 - 13$ if the mass ranges of these new particles are $10^2 \,\mathrm{GeV} - 10^3 \,\mathrm{GeV}$. The EWPT $SU(2) \rightarrow U(1)$ is strengthened by only the new bosons; its strength is about $1 - 1.15$ if the mass parts of $H^0_1$, $H^\pm_2$ and $Y^\pm$ are in the ranges $10 \,\mathrm{GeV} - 10^2 \,\mathrm{GeV}$. The contributions of $H^0_1$ and $H^{\pm}_2$ to the strengths of both EWPTs may make them sufficiently strong to provide large deviations from thermal equilibrium and B violation necessary for baryogenesis.

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arXiv2015

Neutrino Mixing with Non-Zero $θ_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry

The 3-3-1 model proposed in 2011 based on discrete symmetry $S_4$ responsible for the neutrino and quark masses is updated, in which the non-zero $θ_{13}$ is focused. Neutrino masses and mixings are consistent with the most recent data on neutrino oscillations without perturbation. The new feature is adding a new $SU(3)_L$ anti-sextet lying in doublet under $S_4$ which can result the non-zero $θ_{13}$ without perturbation, and consequently, the number of Higgs multiplets required is less than those of other models based on non-Abelian discrete symmetries and the 3-3-1 models. The exact tribimaximal form obtained with the breaking $S_4 \rightarrow Z_3$ in charged lepton sector and $S_4 \rightarrow \mathcal{K}$ in neutrino sector. If both breakings $S_4\rightarrow \mathcal{K}$ and $\mathcal{K} \rightarrow Z_2$ are taken place in neutrino sector, the realistic neutrino spectrum is obtained without perturbation. The upper bound on neutrino mass and the effective mass governing neutrinoless double beta decay at the tree level are presented. The model predicts the Dirac CP violation phase $δ=292.45^\circ$ in the normal spectrum (with $θ_{23}\neq \fracπ{4}$) and $δ=303.14^\circ$ in the inverted spectrum.

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arXiv2015

Michel parameter in 3-3-1 model with three lepton singlets

We show that the mass matrix of electrically neutral gauge bosons in the recently proposed model based on SU(3)_C X SU(3)_L X U(1)_X group with three lepton singlets [1] has two exact eigenvalues: a zero corresponding the photon mass and the second one equaling the mass of the imaginary component A_5μ}. Hence the neutral non-Hermitian gauge boson X^0_μ( defined as \sqrt{2} X^0_μ= A'_ 4μ- i A_5μ) is properly determined. With extra vacuum expectation value of the Higgs field n_2, there are mixings among the Standard Model W boson and the extra charged gauge boson Y carrying lepton number 2 (bilepton) as well as among neutral gauge bosons Z, Z' and X^0. These mixings lead to very rich phenomenology of the model. The leading order of the Michel parameter ($ρ$) has quite special form requiring an equality of the vacuum expectation values in the second step of spontaneous symmetry breaking, namely, k_1=k_2.

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arXiv2014

Electroweak sphalerons in the reduced minimal 3-3-1 model

We calculate the electroweak sphaleron rates in the reduced minimal 3-3-1 (RM331) model. In the context of the early Universe, this model undergoes a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2)\rightarrow U(1)$ at the $10^2$ GeV scale, as the Universe cools down from the hot big bang. By a thin-wall approximation, we show that for each phase transition in this sequence, the sphaleron rate is larger than the cosmological expansion rate at temperatures higher than the critical temperature, and after the phase transition, the sphaleron process is decoupled. This may provide baryon-number violation (B violation) necessary for baryogenesis in the relationship with nonequilibrium physics in the early Universe.

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arXiv2013

Electroweak phase transition in the reduced minimal 3-3-1 model

The electroweak phase transition is considered in framework of the reduced minimal 3-3-1 model (RM331). Structure of phase transition in this model is divided into two periods. The first period is the phase transition SU(3) ---> SU(2) at TeV scale and the second one is SU(2)--> U(1), which is the like-Standard Model electroweak phase transition. When mass of the neutral Higgs boson (h_1) is taken to be equal to the LHC value: m_{h_1}=125 GeV, then these phase transitions are the first order phase transitions, the mass of Z_2 is about 4.8 TeV; and we find the region of parameter space with the first order phase transition at v_{ρ_0}=246 GeV scale, leading to an effective potential, where mass of the charged Higgs boson is in range of 4.154 TeV < m_{h_{++}} < 5.946 TeV. Therefore, with this approach, new bosons are the triggers of the first order electroweak phase transition with significant implications for the viability of electroweak baryogenesis scenarios.

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arXiv2008

Bilepton contributions to the neutrinoless double beta decay in the economical 3-3-1 model

Possible contributions of the bilepton to the neutrinoless double beta $(ββ)_{0ν}$ decay in the economical 3-3-1 model are discussed. We show that the $(ββ)_{0ν}$ decay in this model is due to both sources--Majorana $ _{L}$ and Dirac $ _{D}$ neutrino masses. If the mixing angle between charged gauge bosons, the standard model $W$ and bilepton $Y$, is in range of the ratio of neutrino masses $ _{L}/< M_ν>_{D}$, both the Majorana and Dirac masses simultaneously give contributions dominant to the decay. As results, constraints on the bilepton mass are also given.

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arXiv2006

Photon - Axion Conversion Cross Sections in a Resonant Cavity

Photon - axion conversions in the resonant cavity with the lowest mode are considered in detail by the Feynman diagram method. The differential cross sections are presented and numerical evaluations are given. It is shown that there is a resonant conversion for the considered process, in which the conversion cross sections are much larger than those of the wave guide in the same conditions. Some estimates for experimental conditions are given from our results.

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arXiv2006

Higgs-gauge boson interactions in the economical 3-3-1 model

Interactions among the standard model gauge bosons and scalar fields in the framework of SU(3)_C X SU(3)_L X U(1)_X gauge model with minimal (economical) Higgs content are presented. From these couplings, all scalar fields including the neutral scalar $h$ and the Goldstone bosons can be identified and their couplings with the usual gauge bosons such as the photon, the charged $W^\pm$ and the neutral $Z$, without any additional condition, are recovered. In the effective approximation, full content of scalar sector can be recognized. The CP-odd part of Goldstone associated with the neutral non-Hermitian bilepton gauge boson $G_{X^0}$ is decouple, while its CP-even counterpart has the mixing by the same way in the gauge boson sector. Masses of the new neutral Higgs boson $H^0_1$ and the neutral non-Hermitian bilepton $X^0$ are dependent on a coefficient of Higgs self-coupling ($λ_1$). Similarly, masses of the singly-charged Higgs boson $H_2^\pm$ and of the charged bilepton $Y^\pm$ are proportional through a coefficient of Higgs self-interaction ($λ_4$). The hadronic cross section for production of this Higgs boson at the LHC in the effective vector boson approximation is calculated. Numerical evaluation shows that the cross section can exceed 260 $fb$.

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arXiv2006

Interesting radiative patterns of neutrino mass in an SU(3)_C X SU(3)_L X U(1)_X model with right-handed neutrinos

We investigate a simple model of neutrino mass based on SU(3)_C X SU(3)_L X U(1)_X gauge unification. The Yukawa coupling of the model has automatic lepton-number symmetry which is broken only by the self-couplings of the Higgs boson. At tree level, neutrino spectrum contains three Dirac fermions, one massless and two degenerate in mass. At the two loop-level, neutrinos obtain Majorana masses and correct the tree-level result which naturally gives rise to an inverted hierarchy mass pattern and interesting mixing which can fit the current data with minor fine-tuning. In another scenarios, one can pick the scales such that the loop-induced Majorana mass matrix is bigger than the Dirac one and thus reproduces the usual seesaw mechanism.

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arXiv2005

Standard-model-like Higgs boson production at the CERN LHC in 3-3-1 model with right-handed neutrinos

The models based on ${SU}(3)_C\otimes {SU}(3)_L \otimes {U}(1)_X$ gauge group (3-3-1) contain new Higgs bosons and one of them is the SM-like Higgs boson $h$. Production of this Higgs boson at $p p$ colliders in the framework of 3-3-1 model with right-handed neutrinos is calculated. We found that the contribution of the real $Z^\prime$ to the process $pp\to hZ$ is nearly 60 fb if $M_{Z^\prime}$ is about 1 TeV. The decay width and the branching ratios of the $Z'$ extra neutral gauge boson are systematically discussed.

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arXiv2005

Surface Integral of Babu Diagram

We point out that the surface integral of the Babu diagram gives non-trivial main contribution independent of the charged lepton masses and the scale of new physics. It can fit the experimental data on both solar and atmospheric neutrino oscillations. However, then the coupling constants of the new Higgs singlets with the leptons gain values smaller than that in the usual two-loop radiative analyses. This yields distinction between our consideration on ultraviolet-behaviors and the former based on the infrared radiative corrections.

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arXiv2005

Electric Charge Quantization in SU(3)_C X SU(3)_L X U(1)_X Models

Basing on the general photon eigenstate and the anomaly cancelation, we have naturally explained the electric charge quantization in two models based on the SU(3)_C X SU(3)_L X U(1)_X gauge group, namely in the minimal model and in the model with right-handed neutrinos. In addition, we have shown that the electric charges of the proton and of the electron are opposite; and the same happens with the neutron and the neutrino. We argue that the electric charge quantization is not dependent on the classical constraints on generating mass to the fermions, but it is related closely with the generation number problem. In fact, both problems are properly solved as the direct consequences of the fermion content under the anomaly free conditions.

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arXiv2005

U(1)_Q invariance and SU(3)_C X SU(3)_L X U(1)_X models with beta arbitrary

Using the U(1)_Q invariance, the photon eigenstate and matching gauge coupling constants in SU(3)_C X SU(3)_L X U(1)_X models with beta arbitrary are given. The mass matrix of neutral gauge bosons is exactly diagonalized, and the photon eigenstate is independent on the symmetry breaking parameters - VEV's of Higgs scalars. By obtaining the electromagnetic vertex, the model is embedded naturally into the standard model.

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