# New Physics in the 3-3-1 models

^{}

## Author affiliations

## DOI:

https://doi.org/10.15625/0868-3166/21033## Keywords:

physics beyond the SM## Abstract

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, new main versions of the 3-3-1 models and their consequences are presented.

### Downloads

### Metrics

## References

Particle Data Group Collaboration, *Review of particle physics*, Phys. Rev. D **110** (2024) 030001.

A Crivellin and B. Mellado, *Anomalies in particle physics and their implications for physics beyond the standard model*, Nat. Rev. Phys. **6** (2024) 294.

F. Pisano and V. Pleitez, *SU(3)⊗ U(1) model for electroweak interactions*, Phys. Rev. D **46** (1992) 410.

P. H. Frampton, *Chiral dilepton model and the flavor question*, Phys. Rev. Lett. **69** (1992) 2889.

R. Foot, O. F. Hernandez, F. Pisano, and V. Pleitez, *Lepton masses in an SU(3)_{L} ⊗ U(1)_{N} gauge model*, Phys. Rev. D

**47**(1993) 4158.

D. Ng, *Electroweak theory of SU(3) × U(1)*, Phys. Rev. D

**49**(1994) 4805

M. Singer, J. W. F. Valle and J. Schechter, *Canonical neutral-current predictions from the weak-electromagnetic gauge group SU(3) × U(1)*, Phys. Rev. D

**22**(1980) 738.

R. Foot, H. N. Long and Tuan A. Tran, * SU(3)_{L} ⊗ U(1)_{N} and SU(4)_{L} ⊗ U(1)_{N} gauge models with right-handed neutrinos*, Phys. Rev. D

**50**(1994) 34(R). J. C. Montero, F. Pisano and V. Pleitez,

*Neutral currents and Glashow-Iliopoulos-Maiani mechanism in*, Phys. Rev. D

*S**U*(3)_{L}⊗*U*(1)_{N}models for electroweak interactions**47**(1993) 2918.

H. N. Long, * SU(3)_{L} ⊗ U(1)_{N} model for right-handed neutrino neutral currents*, Phys. Rev. D

**54**(1996) 4691.

H. N. Long, * SU(3)_{C} ⊗ SU(3)_{L} ⊗ U(1)_{N} model with right-handed neutrinos*, Phys. Rev. D

**53**(1996) 437.

M. Ozer, * SU(3)_{L} ⊗ U(1)_{X} model of electroweak interactions without exotic quarks*,

Phys. Rev. D **54** (1996) 1143. P. B. Pal, *Strong-CP question in SU(3)_{c} × SU(3)_{L} × U(1)_{N} models*, Phys. Rev. D

**52**(1995) 1659.

A. G. Dias, R. Martinez and V. Pleitez, *Concerning the Landau pole in 3-3-1 models*, Eur. Phys. J. C **39** (2005) 101. A. Doff and C. A. de S. Pires, *Evading the Landau pole in the minimal 3-3-1 model with leptoquarks*, Nucl. Phys. B **992** (2023) 116254. L. T. Hue and L. D. Ninh, *The simplest 3-3-1 model*, Mod. Phys. Lett. A **31** (2016) 1650062 A. J. Buras, F. De Fazio, *331 models facing the tensions in ΔF = 2 processes with the impact on ε^{′}/ε, Bs → μ^{+}μ^{−} and B → K^{*}μ^{+}μ^{−}*, JHEP

**2016**(2016) 115. A. E. Carcamo Hernandez, R. Martinez and F. Ochoa,

*, Phys. Rev. D 73 (2006) 035007.*

*Z*and*Z*^{′}decays with and without FCNC in 331 models

W. A. Ponce, Y. Giraldo and L. A. Sanchez, *Minimal scalar sector of 3-3-1 models without exotic electric charges*, Phys. Rev. D **67** (2003) 075001. P. V. Dong, H. N. Long, D. T. Nhung and D. V. Soa, *SU(3) _{C} ⊗ SU(3)_{L} ⊗ U(1)_{X} model with two Higgs triplets*, Phys. Rev. D

**73**(2006) 035004. P. V. Dong and H. N. Long,

*The economical*, Adv. High Energy Phys.

*S**U*(3)_{C}⊗*S**U*(3)_{L}⊗*U*(1)_{X}model**2008**(2008) 739492. P. V. Dong, Tr. T. Huong, D. T. Huong and H. N. Long,

*Fermion masses in the economical 3-3-1 model*, Phys. Rev. D

**74**(2006) 053003. J. C. Montero and B. L. Sánchez-Vega,

*Natural PQ symmetry in the 3-3-1 model with a minimal scalar sector*, Phys. Rev. D

**84**(2011) 055019. P. V. Dong, H. N. Long and H. T. Hung,

*Question of Peccei-Quinn symmetry and quark masses in the economical 3-3-1 model*, Phys. Rev. D

**86**(2012) 033002. P. V. Dong, D. Q. Phong, D. V. Soa, N. C. Thao,

*The economical 3-3-1 model revisited*, Eur. Phys. J. C

**78**(2018) 653. P. V. Dong, N. T. K. Ngan and D. V. Soa,

*Simple 3-3-1 model and implication for dark matter*, Phys. Rev. D

**90**(2014) 075019. J. G. Ferreira Jr, P. R. D. Pinheiro, C. A. de S. Pires and P. S. Rodrigues da Silva,

*Minimal 3-3-1 model with only two Higgs triplets*Phys. Rev. D

**84**(2011) 095019. R. M. Fonseca and M. Hirsch,

*A flipped 331 model*, J. High Energy Phys.

**2016**(2016) 3. T. T. Hong, H. T. Hung, H. H. Phuong, L. T. T. Phuong and L. T. Hue,

*Lepton flavor violating decays of the SM-like Higgs boson*, Prog. Theor. Exp. Phys.

*h*→*e*_{i}*e*_{j}, and*e*_{i}→*e*_{j}*γ*in a flipped 3-3-1 model**2020**(2020) 043B03 . A. G. Dias, C. A. de S. Pires, P. S. Rodrigues da Silva and A. Sampieri,

*Simple realization of the inverse seesaw mechanism*, Phys. Rev. D

**86**(2012) 035007. M. E. Catano, R. Martinez and F. Ochoa,

*Neutrino masses in a 331 model with right-handed neutrinos without doubly charged Higgs bosons via inverse and double seesaw mechanisms*, Phys. Rev. D

**86**(2012) 073015 S. M. Boucenna, J. W. F. Valle and A. Vicente,

*Predicting charged lepton flavor violation from 3-3-1 gauge symmetry*, Phys. Rev. D

**92**(2015) 053001. T. P. Nguyen, T. T. Le, T. T. Hong and L. T. Hue,

*Decay of standard model-like Higgs boson*, Phys. Rev. D

*h*→*μ**τ*in a 3-3-1 model with inverse seesaw neutrino masses**97**(2018) 073003. L. T. Hue, H. T. Hung, N. T. Tham, H. N. Long, T.Phong Nguyen,

*Large (*, Phys. Rev. D

*g*− 2_{μ}and signals of decays*e*_{a}→*e*_{b}*γ*in a 3-3-1 model with inverse seesaw neutrinos**104**(2021) 033007.

D. Chang and H. N. Long, *Interesting radiative patterns of neutrino mass in an SU(3) _{C} ⊗ SU(3)_{L} ⊗ U(1)_{X} model with right-handed neutrinos*, Phys. Rev. D

**73**, (2006) 053006.

A. E. Cárcamo Hernández, Sergey Kovalenko, H. N. Long, and Ivan Schmidt, *A variant of 3-3-1 model for the generation of the SM fermion mass and mixing pattern*, J. High Energy Phys. **07** (2018) 144.

J. A. Casas and A. Ibarra, *Oscillating neutrinos and μ → e, γ*, Nucl. Phys. B

**618**(2001) 171.

T. T. Hong, N. H. T. Nha, T. P. Nguyen, L. T. T. Phuong and L. T. Hue, *Decays h → e_{a}e_{b}, e_{b} → e_{a}γ, and (g − 2)_{e, μ} in a 3-3-1 model with inverse seesaw neutrinos*, PTEP

**2022**(2022) 093B05. F. Yin,

*Neutrino mixing matrix in the 3-3-1 model with heavy leptons and*Phys. Rev. D

*A*_{4}symmetry**75**(2007) 073010.

P. V. Dong, L. T. Hue, H. N. Long, D. V. Soa, *The 3-3-1 model with A_{4} flavor symmetry*, Phys. Rev. D

**81**(2010) 053004.

P. V. Dong, H. N. Long, C. H. Nam and V. V. Vien, *The S_{3} flavor symmetry in 3-3-1 models*, Phys. Rev. D

**85**(2012) 053001.

P. V. Dong, H. N. Long, D. V. Soa and V. V. Vien, *The 3-3-1 model with S_{4} flavor symmetry*, Eur. Phys. J. C

**71**(2011) 1544.

V. V. Vien and H. N. Long, The *D*_{4} flavor symmery in 3-3-1 model with neutral leptons, Int. J. Mod. Phys. A **28** (2013) 1350159.

V. V. Vien and H. N. Long, *The T_{7} flavor symmetry in 3-3-1 model with neutral leptons*, J. High Energy Phys.

**04**(2014) 133. C. D. Froggatt and H. B. Nielsen,

*Hierarchy of quark masses, cabibbo angles and CP violation*, Nucl. Phys. B

**147**(1979) 277. M. Leurer, Y. Nir and N. Seiberg,

*Mass matrix models*, Nucl. Phys. B

**398**(1993) 319. V. V. Vien,

*Particles and Fields; Gravitation; Cosmology; Astrophysics; Nuclear Physics; Accelerator Physics; Quantum Information*, Mod. Phys. Lett. A

**37**(2022) 2250094.

H. N. Long, N. V. Hop, L. T. Hue, N. H. Thao, A. E. Cárcamo Hernández, *Some phenomenological aspects of the 3-3-1 model with the Cárcamo-Kovalenko-Schmidt mechanism*, Phys. Rev. D **100** (2019) 015004 . J. C. Montero, Ana R. Romero Castellanos and B. L. Sanchez-Vega, *Axion dark matter in a 3-3-1 model*, Phys. Rev. D **97** (2018) 063015 . Duong Van Loi, Cao H. Nam, Phung Van Dong, *Dark matter in the fully flipped 3-3-1-1 model*, Eur. Phys. J. C **81** (2021) 591 . R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. Müller, *Measurement of the fine-structure constant as a test of the Standard Model*, Science **360** (2018) 191. M. I. Ali, M. Chakraborti, U. Chattopadhyay and S. Mukherjee, *Muon and electron anomalies with non-holomorphic interactions in MSSM*, Eur. Phys. J. C **83** (2023) 60. L. Morel, Z. Yao, P. Cladé and S. Guellati-Khélifa, *Determination of the fine-structure constant with an accuracy of 81 parts per trillion*, Nature **588** (2020) 61. A. E. Cárcamo Hernández, Yocelyne Hidalgo Velásquez, Sergey Kovalenko, H. N. Long, Nicolás A. Pérez-Julve and V. V. Vien, *Fermion spectrum and g–2 anomalies in a low scale 3-3-1 model*, Eur. Phys. J. C

**81**(2021) 191. A. E. Cárcamo Hernández, H. N. Long, M. L. Mora-Urrutia, N. H. Thao and V. V. Vien,

*Fermion masses and mixings and muon anomaly in a 3-3-1 model with family symmetry*, Eur. Phys. J. C

**82**(2022) 769. R. D. Peccei and H. Quinn,

*CP conservation in the presence of instantons*, Phys. Rev. Lett.

**38**(1977) 1440.

R. D. Peccei and H. Quinn, *Constraints imposed by CP conservation in the presence of pseudoparticles*, Phys. Rev. D **16** (1977) 1791.

A. G. Dias, V. Pleitez and M. D. Tonasse, *Naturally light invisible axion in models with large local discrete symmetries*, Phys. Rev. D **67** (2003) 095008.

A. G. Dias, C. A. de S. Pires and P. S. Rodrigues da Silva, *Discrete symmetries, invisible axion, and lepton number symmetry in an economic 3-3-1 model*, Phys. Rev. D **68** (2003) 115009. A. G. Dias and V. Pleitez, *Stabilizing the invisible axion in 3-3-1 models*, Phys. Rev. D **69** (2004) 077702. A. G. Dias, J. Leite, D. D. Lopes and C. C. Nishi, *Fermion mass hierarchy and double seesaw mechanism in a 3-3-1 model with an axion*, Phys. Rev. D **98** (2018) 115017. A. G. Dias, J. Leite, José W. F. Valle and C. A. Vaquera-Araujo, *Reloading the axion in a 3-3-1 setup*, Phys. Let. B **810** (2020) 135829. J. G. Ferreira, C. A. de S. Pires, J. G. Rodrigues and P.S. Rodrigues da Silva, *Embedding cosmological inflation, axion dark matter and seesaw mechanism in a 3-3-1 gauge model*, Phys. Lett. B **771** (2017) 199. V. H. Binh, D. T. Binh, A. E. Cárcamo Hernández, D. T. Huong, D. V. Soa, and H. N. Long, *Higgs sector phenomenology in the 3-3-1 model with an axionlike particle*, Phys. Rev. D **107** (2023) 095030.

H. N. Long and L. T. Hue, Peccei-Quinn mechanism and axion interactions in the 3-3-1 model with Cosmological Inflation, arXiv:2310.02820.

H. Georgi, D. B. Kaplan and L. Randall, *Manifesting the invisible axion at low energies*, Phys. Lett. **B 169** (1986) 73. J. E. Kim and G. Carosi, *Axions and the strong CP problem*, Rev. Mod. Phys. 82 (2010) 557.

J. E. Kim and G. Carosi, *Erratum: Axions and the strong CP problem [Rev. Mod. Phys. 82 (2010) 557]*, Rev. Mod. Phys. **91** (2019) 049902.

L. Di Luzio, M. Giannotti, E. Nardi and L. Visinelli, *The landscape of QCD axion models*, Phys. Rept. 870 (2020) 1. P.-H. Gu, *Peccei-Quinn symmetry for Dirac seesaw and leptogenesis*, JCAP07 (2016) 004.

K. Choi, S. H. Im, H. J. Kim and H. Seong, *Precision axion physics with running axion couplings*, J. High Energ. Phys. **2021** (2021) 58.

S. Scherer, Introduction to chiral perturbation theory, In: J. W. Negele, E. W. Vogt (eds) Advances in Nuclear Physics, Volume 27, Springer, Boston, MA, (2003).

L. Di Luzio, G. Martinelli and G. Piazza, *Breakdown of Chiral perturbation theory for the axion hot dark matter bound*, Phys. Rev. Lett. **126** (2021) 241801.

M. Srednicki, *Axion couplings to matter: (I). CP-conserving parts*, Nucl. Phys. B **260** (1985) 689.

F. Cuypers and S. Davidson, Bileptons: present limits and future prospects, Eur. Phys. J. C 2 (1998) 503.

J. E. C. Montalvo and M. D. Tonasse, Neutral Higgs bosons in the SU(3)_{L} ⊕ U(1)_{L} model, Phys. Rev. D 71 (2005) 095015.

Le Duc Ninh and H. N. Long, *Standard-model-like Higgs boson production at the CERN LHC in 3-3-1 model with right-handed neutrinos*, Phys. Rev. D **72** (2005) 075004.

V. Oliveira and C. A. de S. Pires, *PandaX-4T limits on Z′ mass in 3-3-1LHN model*, Phys. Rev. D **106** (2022) 1 015031.

Qing-Hong Cao, Dong-Ming Zhang. *Collider Phenomenology of the 3-3-1 Model*, arXiv:1611.09337 [hep-ph].

P. H. Frampton, J. T. Liu, B. C. Rasco and D. Ng, *Phenomenology of an SU(3)_{C} × SU(3)_{L} × U(1)_{x} model of flavor*, Mod. Phys. Lett. A

**9**(1994) 1975.

A. Alves, E. Ramirez Barreto, A. G. Dias, *Production of Charged Higgs Bosons in a 3-3-1 Model at the CERN LHC*, Phys. Rev. D 84 (2011) 075013.

E. Ramirez Barreto, Y. A. Coutinho, J. Sá Borges, *Vector- and scalar-bilepton pair production in hadron colliders* Phys. Rev. D **83** (2011) 075001.

H. N. Long and D. V. Soa, *Trilinear gauge boson couplings and bilepton production in the SU(3) _{C} ⊗ SU(3)_{L} ⊗ U(1)_{N} models*, Nucl. Phys. B

**601**(2001) 361.

D. T. Binh, D. T. Huong, Tr. T. Huong, H. N. Long, and D. V. Soa, *Quartic gauge boson couplings and tree unitarity in the SU(3) _{C} ⊗ SU(3)_{L} ⊗ U(1)_{N} models.*, J. Phys. G: Nucl. Part. Phys.

**29**(2003) 1213.

E. Ramirez Barreto, Y. A. Coutinho, J. Sá Borges, *Extra neutral gauge boson from two versions of the 3-3-1 model in future linear colliders*, Eur. Phys. J. C **50** (2007) 909.

F. Queiroz, C. A. de S. Pires, P. S. Rodrigues da Silva, *Minimal SU(3) _{C} × SU(3)_{L} × U(1)_{N} model with natural sub-eV neutrinos*, Phys. Rev. D

**82**(2010) 065018.

W. Caetano, D. Cogollo, C. A. de S. Pires, P. S. Rodrigues da Silva, *Combining type I and type II seesaw mechanisms in the minimal 3-3-1 model*, Phys. Rev. D 86 (2012) 055021. N. A. Ky, N. T. H. Van, *Scalar sextet in the 331 model with right-handed neutrinos*, Phys. Rev. D **72** (2005) 115017.

A. G. Dias, C.A. de S.Pires, P.S. Rodrigues da Silva, *Naturally light right-handed neutrinos in a 3–3–1 model*, Phys. Lett. B **628** (2005) 85. A. G. Dias, C. A. de S. Pires, P . S. Rodrigues da Silva, *Left-right SU(3) _{L} × SU(3)_{R} × U(1)_{X} model with light, keV, and heavy neutrinos*, Phys. Rev. D

**82**(2010) 035013. D. Cogollo, H. Diniz and C. A. de S. Pires,

*keV right-handed neutrinos from type II seesaw mechanism in a 3-3-1 model*, Phys. Lett. B

**677**(2009) 338.

A. Palcu, *Implementing canonical seesaw mechanism in the exact solution of a 3-3-1 gauge model without exotic electric charges*, Mod. Phys. Lett. A **21** (2006) 2591.

P. V. Dong and H. N. Long, *Neutrino masses and lepton flavor violation in the 3-3-1 model with right-handed neutrinos*, Phys. Rev. D **77** (2008) 057302.

D. Cogollo, H. Diniz, C. A. de S.Pires, P.S. Rodrigues da Silva, *The seesaw mechanism at TeV scale in the 3-3-1 model with right-handed neutrinos*, Eur. Phys. J. C **58** (2008) 455.

C. A. de S. Pires, *Neutrino mass mechanisms in 3-3-1 models: A short review*, Phys. Inter. **6** (2015) 33

M. E. Catao, R. Martinez, F. Ochoa, *Neutrino masses in a 331 model with right-handed neutrinos without doubly charged Higgs bosons via inverse and double seesaw mechanisms*, Phys. Rev. D **86** (2012) 073015.

T. Kitabayashi, M. Yasue, *Radiatively induced neutrino masses and oscillations in an SU(3)_{L} × U(1)_{N} Gauge model*, Phys.Rev. D

**63**(2001) 095002. T. Kitabayashi and M. Yasue,

*Neutrino oscillations induced by two-loop radiative mechanism*, Phys. Lett. B

**490**(2000) 236.

T. Kitabayashi, M. Yasue, *Large mixing angle MSW solution in an SU(3) _{L} × U(1)_{N} gauge model with two-loop radiative mechanism*, Phys.Lett. B

**508**(2001) 85.

L. Lavoura, *General formulae for f_{1} → f_{2}γ*, Eur. Phys. J. C 29 (2003) 191.

L. T. Hue, L. D. Ninh, T. T. Thuc, N. T. T. Dat, *Exact one-loop results for l_{→}l_{j}ν in 3-3-1 models*, Eur. Phys. J. C

**78**(2018) 128.

L. T. Hue, H. T. Hung, N. T. Tham, H. N. Long, T. Phong Nguyen, *Large ( g − 2)_{μ} and signals of decays e_{b} → e_{a}γ in a 3-3-1 model with inverse seesaw neutrinos*, Phys. Rev. D

**104**(2021) 033007.

N. A. Ky, H. N. Long, and D. V. Soa, *Anomalous magnetic moment of muon in 3-3-1 models*, Phys. Lett. **B 486**, (2000) 140.

Muon *g* − 2 Collaboration, *Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm*, Phys. Rev. Lett. 131 (2023) 161802.

T. Aoyama, T. Kinoshita and M. Nio, *Theory of the AMM of the electron*, Atoms **7** (2019) 28

T. T. Hong, L. T. T. Phuong, T.Phong Nguyen, N. H. T. Nha and L. T. Hue, *( g − 2)_{e, μ} anomalies and decays h, Z → e_{b}e_{a} in 3-3-1 models with inverse seesaw neutrinos*, arXiv:2404.05524 [hep-ph].

C. Kelso, H. N. Long, R. Martinez, Farinaldo S. Queiroz, *Connection of g − 2_{μ}, electroweak, dark matter, and collider constraints on 331 models*, Phys. Rev. D

**90**(2014) 113011.

A. E. Cárcamo Hernández, D. T. Huong, H. N. Long, *Minimal model for the fermion flavor structure, mass hierarchy, dark matter, leptogenesis, and the electron and muon anomalous magnetic moments*, Phys. Rev. D **102** (2020) 055002.

A. E. Cárcamo Hernández, Yocelyne Hidalgo Velásquez, Sergey Kovalenko, H. N. Long, Nicolás A. Pérez-Julve, V. V. Vien, *Fermion spectrum and ( g − 2) anomalies in a low scale 3-3-1 model*, Eur. Phys. J. C

**81**(2021) 191.

D. Fregolente and M. D. Tonasse, *Self-interacting dark matter from a SU(3)_{L} ⊕ U(1)_{N} electroweak model*, Phys. Lett. B 555 (2003) 7.

H. N. Long and N. Q. Lan, *Self-interacting dark matter and Higgs bosons in the SU(3) _{C} ⊗ SU(3)_{L} ⊗ U(1)_{N} model with right-handed neutrinos*, Europhys. Lett.

**64**(2003) 571.

P. V. Dong, N. T. K. Ngan, D. V. Soa, *Simple 3-3-1 model and implication for dark matter*, Phys. Rev. D **90** (2014) 075019.

P. V. Dong, D. T. Huong, D. A. Camargo, Farinaldo S. Queiroz and José W. F. Valle, Asymmetric Dark Matter, Inflation and Leptogenesis from B-L Symmetry Breaking, Phys. Rev. D **99** (2019) 055040.

D. T. Huong, P. V. Dong, C. S. Kim and N. T. Thuy, *Inflation and leptogenesis in the 3-3-1-1 model*, Phys. Rev. D **91** (2015) 055023.

V. Q. Phong, V. T. Van and H. N. Long, *Electroweak phase transition in the reduced minimal 3-3-1 model*, Phys. Rev. D **88** (2013) 096009.

V. Q. Phong, H. N. Long, V. T. Van and L. H. Minh, Electroweak phase transition in the economical 3-3-1 model, Eur. Phys. J. C **75** (2015) 342.

V. Q. Phong, N. T. Tuong, N. C. Thao, H. N. Long, Multi-period structure of electro-weak phase transition in the 3-3-1-1 model, Phys. Rev. D **99** (2019) 015035.

D. T. Huong, H. N. Long, *Non-thermal leptogenesis in supersymmetric 3-3-1 model with inflationary scenario*, J. Phys. G: Nucl. Part. Phys. **38** (2011) 015202.

A. E. Cárcamo Hernández, D. T. Huong and H. N. Long, *Minimal model for the fermion flavor structure, mass hierarchy, dark matter, leptogenesis, and the electron and muon anomalous magnetic moments*, Phys. Rev. D 102 (2020) 055002.

V. Q. Phong, H. N. Long, V. T. Van and N. C. Thanh, *Electroweak sphalerons in the reduced minimal 3-3-1 model*, Phys. Rev. D **90** (2014) 085019.

## Downloads

## Published

## How to Cite

*Comm. Phys.*, vol. 34, no. 3, p. 203, Aug. 2024.

## Issue

## Section

## License

Authors who publish with CIP agree with the following terms:- The manuscript is not under consideration for publication elsewhere. When a manuscript is accepted for publication, the author agrees to automatic transfer of the copyright to the editorial office.
- The manuscript should not be published elsewhere in any language without the consent of the copyright holders. Authors have the right to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of their work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are encouraged to post their work online (e.g., in institutional repositories or on their websites) prior to or during the submission process, as it can lead to productive exchanges or/and greater number of citation to the to-be-published work (See The Effect of Open Access).

Accepted 05-08-2024

Published 30-08-2024