Muon Magnetic Moment and Lepton Flavor Violation in the Economical 3-3-1 Model
MMuon Magnetic Moment and Lepton Flavor Violation in the Economical 3-3-1 Model
D. Cogollo a ∗ a Departamento de F´ısica, Universidade Federal de Campina Grande,Caixa Postal 10071, 58109-970, Campina Grande, PB, Brazil
In this work we compute all relevant contributions stemming from the economical 3-3-1 model to the muonmagnetic moment and the lepton flavor violation decay µ → eγ . Using the current bounds on these phenomena,we derive lower limits on the scale of symmetry breaking of the model. Moreover, taking into account existinglimits from meson and collider studies we show that there is still room for a possible signal in µ → eγ in thenear future. I. INTRODUCTION
The Standard Model (SM) has passed all precision teststhus far and therefore it provides an accurate descriptions ofthe fundamental laws of nature. Although, we have observa-tional and experimental evidences for going beyond the stan-dard model such as the existence of neutrino masses [1, 2]and dark matter [3, 4]. From that perspective 3-3-1 mod-els are quite plausible extensions of the SM. 3-3-1 modelsstand for electroweak extensions of the SM, where left-handedfermions are arranged in the fundamental representation of SU (3) L . Such models can naturally explain the number ofgenerations [5, 6], might offer plausible dark matter candi-dates with gripping phenomenology [4, 7–32], explain neu-trino masses through the seesaw mechanism [33, 34], featureinteresting connections to cosmology [35–39] and prospectsto collider physics [40–44], among others [38, 45–58]. Inthis work we will focus our attention on the ecoomical 3-3-1 model, which has in its scalar sector two scalar triplets[59], and discuss the long standing discrepancy on the muonanomalous magnetic moment and the lepton flavor violatingdecay µ → eγ (see [60] for a recent review).The muon anomalous magnetic moment, g-2, is one of themost precisely measured quantities in particle physics, reach-ing a precision of 0.54 ppm. Ever since the first experimen-tal limits were reported, a discrepancy between the SM pre-diction and the experimental value on g-2 has been observed.Today this anomaly is in the ballpark of . σ , leading to sev-eral speculations in the context of 3-3-1 models [15, 61–65].In this work we will assess the possibility of explaining g-2 inthe context of the economical 3-3-1 model.A much more appealing phenomena is lepton flavor vio-lation. The existence of lepton flavor violation (LFV) hastremendous implications to particle physics, since any sig-nal of LFV would constitute an irrefutable proof the existenceof new physics not far from the TeV scale. Given the cur-rent limits on LFV, new physics effects should live at energiesabove the TeV scale. In this work we focus the attention onthe µ → eγ rate since it has a much larger rate than otherLFV observables [60]. Our goal as far as LFV is concernedis to derive limits on the scale of symmetry breaking of theeconomical 3-3-1 model and check whether a possible signal ∗ [email protected] in this decay mode can be originated in this model in the lightof current and future constraints from other sources.The paper is structured as follows: In section II we dis-cuss the model; in section III we address existing constraintsand discuss future experimental sensitivities. In section IVwe present our results for g-2; in section V we discuss LFV;finally in section VI we draw our conclusions. II. THE ECONOMICAL 3-3-1 MODEL
The Economical 3-3-1 model is a model that inherits thefermion content of the well-known 3-3-1 model with right-handed neutrinos but featuring a reduced scalar sector, thusanomaly free. In what follows we discuss separately the keyingredients that will allow the reader to follow our reasoning.
A. Fermion Fields
The model has the following particle content, ψ iL = ν i e i ν ci L ∼ (cid:18) , − (cid:19) , e iR ∼ (1 , − ,Q L = u d U L ∼ (cid:18) , (cid:19) , Q αL = d α − u α D α L ∼ (3 ∗ , ,u iR ∼ (cid:18) , (cid:19) , d iR ∼ (cid:18) , − (cid:19) U R ∼ (cid:18) , (cid:19) , D αR ∼ (cid:18) , − (cid:19) . (1)where i = 1 , , , and α = 2 , . . The values in the parenthesesrepresent the quantum numbers under the ( SU (3) L , U (1) X ) symmetry. In this model the electric charge operator takes aform, Q = T − √ T + X, (2)where T a ( a = 1 , , ..., are the generators of SU (3) and X the charged under U (1) X . The exotic quarks U and D α have the same electric charge as usual up and down quarks,i.e. with q U = 2 / and q D α = − / . a r X i v : . [ h e p - ph ] J u n B. Scalar Sector
The scalar sector of the model is comprised of two scalartriplets. The pattern of spontaneous symmetry breaking is viatwo steps. Firstly, the scalar triplet χ = χ χ − χ ∼ (cid:18) , − (cid:19) (3)developing the non-trivial vevs (cid:104) χ (cid:105) = 1 √ u ω , (4)and in a second step the scalar triplet φ = φ +1 φ φ +3 ∼ (cid:18) , (cid:19) (5)develops a vev as follows, (cid:104) φ (cid:105) = 1 √ v . (6)These scalars form the scalar potential, V ( χ, φ ) = µ χ † χ + µ φ † φ + λ ( χ † χ ) + λ ( φ † φ ) + λ ( χ † χ )( φ † φ ) + λ ( χ † φ )( φ † χ ) . (7)Notice that just two scalar triplets simplifies greatly thescalar potential. For this reason the economical model is atruly attractive 3-3-1 model. C. Fermion Masses
With the scalar sector above the fermion gain massesthrough the Yukawa lagrangian below, L Y = h (cid:48) Q L χU R + h (cid:48) αβ Q αL χ ∗ D βR + h eij ψ iL φe jR + h (cid:15)ij (cid:15) pmn ( ψ ciL ) p ( ψ jL ) m ( φ ) n + h d i Q L φd iR + h dαi Q αL φ ∗ u iR , + h u i Q L χu iR + h uαi Q αL χ ∗ d iR + h (cid:48)(cid:48) α Q L φD αR + h (cid:48)(cid:48) α Q αL φ ∗ U R + h.c. (8)Notice that the exotic quarks U and D α have masses pro-portional to the vev ω , whereas the SM fermions to u, v .Therefore, ω (cid:29) u, v . One may realize that the Yukawa la-grangian features a global symmetry ( L (cid:48) ) which is related tothe lepton number (L) through, L (cid:48) = L − √ T . (9) Using Eq.9 one finds, L (cid:48) ( ψ iL , Q L , Q αL , φ, χ, e iR , u iR , d iR , U R , D αR ) =13 , − , , − , , , , , − , . (10)The field χ carries two units of lepton number, thus abilepton. Since this global symmetry is broken by the vev u ,then u is a sort of lepton-number violating parameter, whichshould be very small. In our procedure we take v = 246 GeV.Anyways, it has been shown that this Yukawa lagrangiansucessfully explain the fermion masses according to data [66,67]
D. Gauge Bosons
The covariant derivative of the scalar triplets is given by D µ = ∂ µ − igT a W aµ − ig X T XB µ (11)here the gauge fields W a and B transform as the adjointrepresentations of SU(3) L and U(1) X , with the correspond-ing gauge coupling constants g , g X . Having in mind that T = √ diag(1 , , , expanding this covariant derivative weget, g A √ W + µ √ X (cid:48) µ √ W − µ B √ W (cid:48)− µ √ X (cid:48) ∗ µ √ W (cid:48) + µ C , (12)where t ≡ g X /g , A ≡ W µ + √ W µ + t (cid:113) XB µ , B ≡− W µ + √ W µ + t (cid:113) XB µ , C ≡ − √ W µ + t (cid:113) XB µ ,and W ± µ ≡ W µ ∓ iW µ √ ,W (cid:48)∓ µ ≡ W µ ∓ iW µ √ ,X (cid:48) µ ≡ W µ − iW µ √ . (13)Since we are investigating an SU (3) ⊗ U (1) X gauge groupthere are in total nine gauge bosons with four of them belong-ing to the SM spectrum ( W ± , Z, A ). The new gauge bosonsare the heavy charged gauge boson W (cid:48)± , the electrically neu-tral X that carries two units of lepton number, and a heavy Z (cid:48) boson.In the limit ω (cid:29) u, v the masses of the gauge bosons areeasily obtained and read, M W = g v , (14) M W (cid:48) = g u + v + ω ) , (15) M X = g ω + u ) , (16) M Z (cid:48) = g c w w − s w . (17)This is the gauge boson spectrum of the model and thesegauge bosons are the main characters of our phenomenology.Before discussing g-2 and LFV we need to present the neutraland charged currents. E. Neutral and Charged Currents
The neutral and charged currents arise from the kinect termsof the fermions, ¯ ψ L D µ γ µ ψ L + ¯ ψ r D µ γ µ ψ R , yielding, L NC ⊃ ¯ f γ µ [ g V f + g Af γ ] f Z (cid:48) µ . (18)with, g V f = g c W (1 − s W ) (cid:112) − s W , g Af = − g c W (cid:112) − s W , (19)and L CCl ⊃ − g √ (cid:2) ¯ ν c γ µ (1 − γ ) l W (cid:48)− µ + h.c. (cid:3) , (20)Obvisouly Eq.18 and Eq.20 are not the complete current ofthe model. There are more terms involving quarks, and neu-trinos but these will not be relevant for our discussion whichis concentrated on the charged leptonic sector.We have gather all important ingridient for our g-2 and LFVcomputation. Thus we now move these phenomena. III. EXISTING BOUNDSA. Meson Decays
With the enormous improvement over the experimental pre-cision on meson decays, new physics contributions to rare me-son decays can now be tested. In particular, data on the me-son B decays B s,d → µ + µ − and B d → K (cid:63) ( K ) µ + µ − turnedout to be great laboratories to test the existence of new vectorgauge bosons [68]. In light of no significant deviation overthe SM predictions, bounds were derived on the Z (cid:48) mass, ex-cluding Z (cid:48) below ∼ − TeV. The uncertainty in the boundstems from the depedence on the parametrization in the quarkmixing matrices [68].
331 Economical Δ a μ −10 −9 −8 Scale of Symmetry Breaking (GeV)
1σ bounds
Z' x (-1) W'Δa μ CurrentΔa μ Proj
FIG. 1. Individual contributions from the 331 Economical modelas a function of the scale of symmetry breaking. The Z (cid:48) and W (cid:48) contributions are negative and positive, respectively. Since the W (cid:48) correction to g-2 is larger, the overall correction to g − is positive. B. Dilepton
In addition to meson physics, the advent of the LargeHadron Collider (LHC) has set a new era in the search fornew physics [69]. In particular, both ATLAS and CMS col-laborations have searched for neutral vector gauge bosons inthe dilepton channel ( ee and µµ ) finding no evidence, set-ting stringent lower mass bounds on the Z (cid:48) mass [70–72] ofvarious models. A speficic study for the economical 3-3-1model was peformed in [43, 73, 74]. There the authors found M Z (cid:48) > . TeV for f b − of integrated luminosity, possiblyreaching M Z (cid:48) > . TeV and M Z (cid:48) > . TeV for − and f b − integrated luminosity, respectively. C. Charged Lepton + MET
The economical 3-3-1 model predicts the existence of acharged gauge boson that interacts with charged leptons asshown in Eq.20. Such a W (cid:48) when produced at the reso-nance decays into a charged lepton plus a neutrino. There-fore, searches for charged lepton + MET are suitable for thesecharged gauge bosons [75, 76]. Since no excess has beenobserved, a lower mass bound of . TeV was found with . f b − of luminosity at TeV of center of mass energy[73]. Moreover, future limits were projected for and f b − of data, which would lead the exclusion of W (cid:48) masses below . TeV and TeV [73].Now we outlined the most stringent limits on the mass ofthe gauge bosons we will discuss the g-2 and µ → eγ decay. IV. MUON ANOMALOUS MAGNETIC MOMENT
Fundamental charged particles feature a magnetic dipolemoment ( g ) which according to classical quantum mechan-ics should be equal two. However, in the framework of rel-ativistic quantum mechanism there are quantum correctionsbeyond the tree-level which deviates g from two. This devia-tion is parametrized in terms of a = ( g − / , known as theanomalous magnetic moment, for short g − .Interestingly the SM prediction for g-2 ( a µSM ) does notagree with the experimental measurement ( a µexp ) at the . σ level [77] pointing to, ∆ a µ = a µexp − a µSM = (287 ± × − . (21)This long standing discrepancy has trigged several modelbuilding efforts. Fortunately, the ongoing g − experiment atFERMILAB will shed light into this problem in the upcomingyears. If the central value remains intact, a σ evidence fornew physics would result, with ∆ a µ = (287 ± × − .Thus it is worthwhile to assess which models this discrep-ancy can address this anomaly in agreement with current andplanned experimental limits.In our model, the main particles contributing to g-2 are theneutral and electrically charged gauge bosons. The scalar par-ticles in the model lead to very suppressed contributions to g-2 because their couplings to the muon are proportional to themuon mass. That said, the gauge boson corrections to g − are found to be [60], ∆ a µ ( Z (cid:48) ) = m µ π M (cid:48) Z (cid:18) g V µ − g Aµ (cid:19) . (22) ∆ a µ ( W (cid:48) ) = 14 π m µ M W (cid:48) (cid:20) g V (cid:18) − m ν m µ (cid:19) + g A (cid:18)
56 + m ν m µ (cid:19)(cid:21) , (23)where g V and g A are the vector and vector-axial couplings inEq. (19) and Eq. (20).With these equations at hand we compute the contributionsof these gauge bosons to ∆ a µ . These contributions are shownin Fig.1 as function of the scale of symmetry breaking of themodel. Moreover, we overlay the current (projected) σ errorband, that reads × − (34 × − ) , to derive boundson the scale of symmetry based upon the assumption that theanomaly is otherwise resolved by any other means.From Fig.1 we see that Z (cid:48) ( W (cid:48) ) give rise to a negative (pos-itive) correction to g-2. However, since the contribution from W (cid:48)
331 Economical model is larger, it generates an overallpositive contribution to g-2. The scale of symmetry below1TeV needed to accommodate the anomaly is too small and ithass been excluded by other data sets. Therefore, the 331 Eco-nomical model cannot trully accommodate g − . To clearlynote this statement lets take a closer look into Eq.17. Fromthis equation we get that M (cid:48) Z ≈ . w . Hence the limit of3.8TeV on the Z (cid:48) implies w ≥ TeV, making it impossibleto accommodate g-2 in the economical 331 model, since weneeded w < TeV to do so. Moreover, the bound we get on w by imposing the σ error bar aforementioned lead to a lowerlimit of w > . TeV which is less competetive than collidersearches. V. µ → eγ DECAY
In the SM the lepton flavor is a conserved quantity and neu-trinos are massless. Although, neutrinos experience flavor os-cillations [78–80] constituting an experimental confirmationthat lepton flavor is violated. The mechanism responsible forlepton flavor violation is completely unknown but there aresome proposal in the literature [76, 81, 82]. Anyways, an ob-servation of charged LFV would necessarily imply into newphysics with huge implications to model building endeavours.The charged current mediated by the W (cid:48) gauge bosonmight induce the non-observed decay µ → eγ . The non-observation of this decay yields tight bounds on new physicseffects. Indeeed, current (projected) bound from MEG collab-oration reads [83], Br( µ → e γ ) < . × − (4 × − ) .Adapting the results from [60] to our model we get, Br( µ → e γ ) = 6 . × − (cid:18) M W (cid:48) (cid:19) (cid:88) f ( g fe ∗ g fµ ) , (24)with g fe = g U Ne ∗ / (2 √ and g fµ = g U Nµ ∗ / (2 √ .Hence, one can use the experimental bound on this branch-ing ratio to place a restrictive limit on the product U Ne ∗ U Nµ as function of the W (cid:48) mass as shown in Fig.2. There, we over-laid the current collider limits on the W (cid:48) mass for . f b − and the projected for f b − as described before, as wellas the possible signal region for the µ → eγ decay whichis delimited by the current and future sensitivity values for Br ( µ → eγ ) .From Fig.2 we can conclude that:(i) Depending on value of the product U Ne ∗ U Nµ of inter-est, the µ → eγ observable can outperform collider probes inthe search for W (cid:48) gauge bosons.(ii) The observation of possible signal in µ → eγ decaymight be accommodate within the economical 3-3-1 model inagreement with current and foreseen limits. VI. CONCLUSIONS
The economical 3-3-1 model is an attractive model wherethe number of generations is addressed while featuring a re-duced scalar spectrum in comparison with other incarnationsof 3-3-1 models. In this work we computed the relevant con-tributions to the muon anomalous magnetic moment to showthat the Economical 3-3-1 model, while generating a positivecontribution to g-2, it cannot accommodate the anomaly sincethe scale of symmetry breaking needed to explain g-2 has beenexcluded by LHC probes for new physics.Moreover, we have investigated the µ → eγ decay toconclude that µ → eγ observable provides an interestingprobe for new physics, particularly complementary to collidersearches. Lastly, we found that in case of a positive signatureof µ → eγ in the foreseeable future, the Economical 3-3-1model offers a plausible new physics interpretation in agree-ment with current and future experimental limits. | U e n * U μ n | −8 −7 −6 −5 −4 −3 −2 −1 M W' [GeV]
100 1,000 10,000222 l + M E T . f b - l + M E T f b - S i g n a l R e g i o n f o r μ → e γ FIG. 2. Region of parameter space with . × − < Br( µ → e γ ) < × − in green. The current (projected) boundfrom l+MET searches at the LHC is shown as shaded region (dashedline). ACKNOWLEDGEMENT
The author would like to thank Farinaldo Queiroz for usefuldiscussions. [1] Y. Fukuda et al. , “Evidence for oscillation of atmospheric neu-trinos,”
Phys. Rev. Lett. , vol. 81, pp. 1562–1567, 1998.[2] Q. R. Ahmad et al. , “Direct evidence for neutrino flavor trans-formation from neutral-current interactions in the Sudbury Neu-trino Observatory,”
Phys. Rev. Lett. , vol. 89, p. 011301, 2002.[3] Y. Sofue and V. Rubin, “Rotation curves of spiral galaxies,”
Ann. Rev. Astron. Astrophys. , vol. 39, pp. 137–174, 2001.[4] F. S. Queiroz, W. Rodejohann, and C. E. Yaguna, “Is the darkmatter particle its own antiparticle?,” 2016.[5] F. Pisano and V. Pleitez, “An SU(3) x U(1) model for elec-troweak interactions,”
Phys. Rev. , vol. D46, pp. 410–417, 1992.[6] R. Foot, O. F. Hernandez, F. Pisano, and V. Pleitez, “Lep-ton masses in an SU(3)-L x U(1)-N gauge model,”
Phys. Rev. ,vol. D47, pp. 4158–4161, 1993.[7] J. K. Mizukoshi, C. A. de S. Pires, F. S. Queiroz, and P. S. Ro-drigues da Silva, “WIMPs in a 3-3-1 model with heavy Sterileneutrinos,”
Phys. Rev. , vol. D83, p. 065024, 2011.[8] D. T. Huong, C. S. Kim, H. N. Long, and N. T. Thuy, “ProbingDark Matter in the Economical 3-3-1 Model,” 2011.[9] J. D. Ruiz-Alvarez, C. A. de S. Pires, F. S. Queiroz, D. Restrepo,and P. S. Rodrigues da Silva, “On the Connection of Gamma-Rays, Dark Matter and Higgs Searches at LHC,”
Phys. Rev. ,vol. D86, p. 075011, 2012.[10] D. Hooper, C. Kelso, and F. S. Queiroz, “Stringent and Ro-bust Constraints on the Dark Matter Annihilation Cross Sec-tion From the Region of the Galactic Center,”
Astropart. Phys. ,vol. 46, pp. 55–70, 2013.[11] S. Profumo and F. S. Queiroz, “Constraining the Z (cid:48) mass in331 models using direct dark matter detection,” Eur. Phys. J. ,vol. C74, no. 7, p. 2960, 2014.[12] F. Queiroz,
Direct and Indirect Dark Matter Detection in GaugeTheories . PhD thesis, Paraiba U., 2013.[13] F. S. Queiroz, “Non-thermal WIMPs as Dark Radiation,”
AIPConf. Proc. , vol. 1604, pp. 83–90, 2014.[14] A. Alves, S. Profumo, and F. S. Queiroz, “The dark Z (cid:48) portal:direct, indirect and collider searches,” JHEP , vol. 04, p. 063,2014. [15] P. V. Dong, D. T. Huong, F. S. Queiroz, and N. T. Thuy, “Phe-nomenology of the 3-3-1-1 model,”
Phys. Rev. , vol. D90, no. 7,p. 075021, 2014.[16] A. X. Gonzalez-Morales, S. Profumo, and F. S. Queiroz, “Ef-fect of Black Holes in Local Dwarf Spheroidal Galaxies onGamma-Ray Constraints on Dark Matter Annihilation,”
Phys.Rev. , vol. D90, no. 10, p. 103508, 2014.[17] F. S. Queiroz, K. Sinha, and A. Strumia, “Leptoquarks, DarkMatter, and Anomalous LHC Events,”
Phys. Rev. , vol. D91,no. 3, p. 035006, 2015.[18] D. Cogollo, A. X. Gonzalez-Morales, F. S. Queiroz, and P. R.Teles, “Excluding the Light Dark Matter Window of a 331Model Using LHC and Direct Dark Matter Detection Data,”
JCAP , vol. 1411, no. 11, p. 002, 2014.[19] A. Alves, A. Berlin, S. Profumo, and F. S. Queiroz, “Dark Mat-ter Complementarity and the Z (cid:48)
Portal,”
Phys. Rev. , vol. D92,no. 8, p. 083004, 2015.[20] M. G. Baring, T. Ghosh, F. S. Queiroz, and K. Sinha, “NewLimits on the Dark Matter Lifetime from Dwarf SpheroidalGalaxies using Fermi-LAT,” 2015.[21] Y. Mambrini, S. Profumo, and F. S. Queiroz, “Dark Matter andGlobal Symmetries,”
Phys. Lett. , vol. B760, pp. 807–815, 2016.[22] A. Alves, A. Berlin, S. Profumo, and F. S. Queiroz, “Dirac-fermionic dark matter in U(1) X models,” JHEP , vol. 10, p. 076,2015.[23] B. Allanach, F. S. Queiroz, A. Strumia, and S. Sun, “ Z modelsfor the LHCb and g − muon anomalies,” Phys. Rev. , vol. D93,no. 5, p. 055045, 2016.[24] M. Klasen, F. Lyonnet, and F. S. Queiroz, “NLO+NLL Col-lider Bounds, Dirac Fermion and Scalar Dark Matter in the B-LModel,” 2016.[25] W. Altmannshofer, S. Gori, S. Profumo, and F. S. Queiroz, “Ex-plaining dark matter and B decay anomalies with an L µ − L τ model,” JHEP , vol. 12, p. 106, 2016.[26] F. S. Queiroz, “Dark Matter Overview: Collider, Direct and In-direct Detection Searches,” 2016. [27] S. Profumo, F. S. Queiroz, and C. E. Yaguna, “Extend-ing Fermi-LAT and H.E.S.S. Limits on Gamma-ray Linesfrom Dark Matter Annihilation,”
Mon. Not. Roy. Astron. Soc. ,vol. 461, no. 4, pp. 3976–3981, 2016.[28] F. S. Queiroz, C. E. Yaguna, and C. Weniger, “Gamma-ray Lim-its on Neutrino Lines,”
JCAP , vol. 1605, no. 05, p. 050, 2016.[29] A. Alves, G. Arcadi, Y. Mambrini, S. Profumo, and F. S.Queiroz, “Augury of darkness: the low-mass dark Z portal,”
JHEP , vol. 04, p. 164, 2017.[30] G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini,M. Pierre, S. Profumo, and F. S. Queiroz, “The Waning of theWIMP? A Review of Models, Searches, and Constraints,” 2017.[31] M. D. Campos, F. S. Queiroz, C. E. Yaguna, and C. Weniger,“Search for right-handed neutrinos from dark matter annihila-tion with gamma-rays,” 2017.[32] G. Arcadi, M. Lindner, Y. Mambrini, M. Pierre, and F. S.Queiroz, “GUT Models at Current and Future Hadron Collidersand Implications to Dark Matter Searches,” 2017.[33] J. Schechter and J. W. F. Valle, “Neutrino Masses in SU(2) xU(1) Theories,”
Phys. Rev. , vol. D22, p. 2227, 1980.[34] F. Queiroz, C. A. de S. Pires, and P. S. R. da Silva, “A mini-mal 3-3-1 model with naturally sub-eV neutrinos,”
Phys. Rev. ,vol. D82, p. 065018, 2010.[35] D. Hooper, F. S. Queiroz, and N. Y. Gnedin, “Non-ThermalDark Matter Mimicking An Additional Neutrino Species In TheEarly Universe,”
Phys. Rev. , vol. D85, p. 063513, 2012.[36] C. Kelso, C. A. de S. Pires, S. Profumo, F. S. Queiroz, and P. S.Rodrigues da Silva, “A 331 WIMPy Dark Radiation Model,”
Eur. Phys. J. , vol. C74, no. 3, p. 2797, 2014.[37] C. Kelso, S. Profumo, and F. S. Queiroz, “Non-thermal WIMPsas ”Dark Radiation” in Light of ATACAMA, SPT, WMAP9 andPlanck,”
Phys. Rev. , vol. D88, no. 2, p. 023511, 2013.[38] F. S. Queiroz, K. Sinha, and W. Wester, “Rich tapestry: Super-symmetric axions, dark radiation, and inflationary reheating,”
Phys. Rev. , vol. D90, no. 11, p. 115009, 2014.[39] R. Allahverdi, B. Dutta, F. S. Queiroz, L. E. Strigari, and M.-Y.Wang, “Dark Matter from Late Invisible Decays to/of Graviti-nos,”
Phys. Rev. , vol. D91, no. 5, p. 055033, 2015.[40] A. Alves, E. Ramirez Barreto, A. G. Dias, C. A. de S. Pires,F. S. Queiroz, and P. S. Rodrigues da Silva, “Probing 3-3-1Models in Diphoton Higgs Boson Decay,”
Phys. Rev. , vol. D84,p. 115004, 2011.[41] D. Cogollo, A. V. de Andrade, F. S. Queiroz, and P. Re-bello Teles, “Novel sources of Flavor Changed Neutral Currentsin the
RHN model,”
Eur. Phys. J. , vol. C72, p. 2029, 2012.[42] A. Alves, E. Ramirez Barreto, A. G. Dias, C. A. de S. Pires, F. S.Queiroz, and P. S. Rodrigues da Silva, “Explaining the HiggsDecays at the LHC with an Extended Electroweak Model,”
Eur.Phys. J. , vol. C73, no. 2, p. 2288, 2013.[43] F. S. Queiroz, C. Siqueira, and J. W. F. Valle, “Constraining Fla-vor Changing Interactions from LHC Run-2 Dilepton Boundswith Vector Mediators,”
Phys. Lett. , vol. B763, pp. 269–274,2016.[44] W. Caetano, C. A. de S. Pires, P. S. Rodrigues da Silva, D. Co-gollo, and F. S. Queiroz, “Explaining ATLAS and CMS Re-sults Within the Reduced Minimal 3-3-1 model,”
Eur. Phys. J. ,vol. C73, no. 10, p. 2607, 2013.[45] P. V. Dong, D. T. Huong, M. C. Rodriguez, and H. N.Long, “Supersymmetric economical 3-3-1 model,”
Nucl. Phys. ,vol. B772, pp. 150–174, 2007.[46] P. V. Dong, T. T. Huong, N. T. Thuy, and H. N. Long, “Sfermionmasses in the supersymmetric economical 3-3-1 model,”
JHEP ,vol. 11, p. 073, 2007. [47] D. Van Soa, P. V. Dong, T. T. Huong, and H. N. Long, “Bileptoncontributions to the neutrinoless double beta decay in the eco-nomical 3-3-1 model,”
J. Exp. Theor. Phys. , vol. 108, pp. 757–763, 2009.[48] P. V. Dong, D. T. Huong, M. C. Rodriguez, and H. N.Long, “Neutrino Masses in Supersymmetric Economical SU (3) C XSU (3) L XU (1) X Model,”
J. Mod. Phys. , vol. 2,pp. 792–802, 2011.[49] P. V. Dong, H. T. Hung, and T. D. Tham, “3-3-1-1 model fordark matter,”
Phys. Rev. , vol. D87, no. 11, p. 115003, 2013.[50] D. Cogollo, F. S. Queiroz, and P. Vasconcelos, “Flavor Chang-ing Neutral Current Processes in a Reduced Minimal ScalarSector,”
Mod. Phys. Lett. , vol. A29, no. 32, p. 1450173, 2014.[51] F. S. Queiroz and K. Sinha, “The Poker Face of the MajoronDark Matter Model: LUX to keV Line,”
Phys. Lett. , vol. B735,pp. 69–74, 2014.[52] P. V. Dong, N. T. K. Ngan, and D. V. Soa, “Simple 3-3-1 modeland implication for dark matter,”
Phys. Rev. , vol. D90, no. 7,p. 075019, 2014.[53] V. Q. Phong, H. N. Long, V. T. Van, and L. H. Minh, “Elec-troweak phase transition in the economical 3-3-1 model,”
Eur.Phys. J. , vol. C75, no. 7, p. 342, 2015.[54] J. C. Montero and B. L. SnchezVega, “Accidental symmetriesand massless quarks in the economical 3-3-1 model,”
Phys.Rev. , vol. D91, no. 3, p. 037302, 2015.[55] A. Alves, S. Profumo, F. S. Queiroz, and W. Shepherd, “Ef-fective field theory approach to the Galactic Center gamma-rayexcess,”
Phys. Rev. , vol. D90, no. 11, p. 115003, 2014.[56] H. N. Long, “Early Universe in the SU (3) L XU (1) X elec-troweak models,” 2015.[57] P. V. Dong and D. T. Si, “Kinetic mixing effect in the 3-3-1-1model,” Phys. Rev. , vol. D93, no. 11, p. 115003, 2016.[58] A. E. Crcamo Hernndez, H. N. Long, and V. V. Vien, “A 3-3-1model with right-handed neutrinos based on the ∆ (27) familysymmetry,” Eur. Phys. J. , vol. C76, no. 5, p. 242, 2016.[59] P. V. Dong, H. N. Long, and H. T. Hung, “Question of Peccei-Quinn symmetry and quark masses in the economical 3-3-1model,”
Phys. Rev. , vol. D86, p. 033002, 2012.[60] M. Lindner, M. Platscher, and F. S. Queiroz, “A Call for NewPhysics : The Muon Anomalous Magnetic Moment and LeptonFlavor Violation,” 2016.[61] N. A. Ky, H. N. Long, and D. Van Soa, “Anomalous mag-netic moment of muon in 3 3 1 models,”
Phys. Lett. , vol. B486,pp. 140–146, 2000.[62] C. Kelso, P. R. D. Pinheiro, F. S. Queiroz, and W. Shepherd,“The Muon Anomalous Magnetic Moment in the Reduced Min-imal 3-3-1 Model,”
Eur. Phys. J. , vol. C74, p. 2808, 2014.[63] C. Kelso, H. N. Long, R. Martinez, and F. S. Queiroz, “Connec-tion of g − µ , electroweak, dark matter, and collider constraintson 331 models,” Phys. Rev. , vol. D90, no. 11, p. 113011, 2014.[64] F. S. Queiroz and W. Shepherd, “New Physics Contributions tothe Muon Anomalous Magnetic Moment: A Numerical Code,”
Phys. Rev. , vol. D89, no. 9, p. 095024, 2014.[65] G. De Conto and V. Pleitez, “Electron and muon anomalousmagnetic dipole moment in a 3-3-1 model,” 2016.[66] P. V. Dong, D. T. Huong, T. T. Huong, and H. N. Long,“Fermion masses in the economical 3-3-1 model,”
Phys. Rev. ,vol. D74, p. 053003, 2006.[67] P. V. Dong, H. N. Long, and D. V. Soa, “Neutrino masses inthe economical 3-3-1 model,”
Phys. Rev. , vol. D75, p. 073006,2007.[68] A. J. Buras, F. De Fazio, and J. Girrbach-Noe, “ Z - Z (cid:48) mixingand Z -mediated FCNCs in SU (3) C × SU (3) L × U (1) X mod-els,” JHEP , vol. 08, p. 039, 2014. [69] M. Lindner, F. S. Queiroz, and W. Rodejohann, “Dileptonbounds on leftright symmetry at the LHC run II and neutrino-less double beta decay,”
Phys. Lett. , vol. B762, pp. 190–195,2016.[70] S. Patra, F. S. Queiroz, and W. Rodejohann, “Stringent DileptonBounds on Left-Right Models using LHC data,”
Phys. Lett. ,vol. B752, pp. 186–190, 2016.[71] V. Khachatryan et al. , “Search for narrow resonances in dilep-ton mass spectra in proton-proton collisions at √ s = 13 TeV andcombination with 8 TeV data,” Phys. Lett. , vol. B768, pp. 57–80, 2017.[72] T. A. collaboration, “Search for new high-mass phenomena inthe dilepton final state using 36.1 fb − of proton-proton colli-sion data at √ s =
13 TeV with the ATLAS detector,” 2017.[73] A. Alves, G. Arcadi, P. V. Dong, L. Duarte, F. S. Queiroz, andJ. W. F. Valle, “R-parity as a residual gauge symmetry : probinga theory of cosmological dark matter,” 2016.[74] Q.-H. Cao and D.-M. Zhang, “Collider Phenomenology of the3-3-1 Model,” 2016.[75] F. S. Queiroz, “Comment on Polarized window for left-rightsymmetry and a right-handed neutrino at the Large Hadron-Electron Collider,”
Phys. Rev. , vol. D93, no. 11, p. 118701,2016.[76] M. Lindner, F. S. Queiroz, W. Rodejohann, and C. E. Yaguna,“Left-Right Symmetry and Lepton Number Violation at the Large Hadron Electron Collider,”
JHEP , vol. 06, p. 140, 2016.[77] T. Blum, A. Denig, I. Logashenko, E. de Rafael, B. Lee Roberts,T. Teubner, and G. Venanzoni, “The Muon (g-2) Theory Value:Present and Future,” 2013.[78] D. Forero, M. Tortola, and J. Valle, “Neutrino oscillations refit-ted,”
Phys.Rev. , vol. D90, no. 9, p. 093006, 2014.[79] T. Kajita, “Nobel Lecture: Discovery of atmospheric neutrinooscillations,”
Rev. Mod. Phys. , vol. 88, no. 3, p. 030501, 2016.[80] A. B. McDonald, “Nobel Lecture: The Sudbury Neutrino Ob-servatory: Observation of flavor change for solar neutrinos,”
Rev. Mod. Phys. , vol. 88, no. 3, p. 030502, 2016.[81] S. Pascoli, S. T. Petcov, and W. Rodejohann, “On the connec-tion of leptogenesis with low-energy CP violation and LFVcharged lepton decays,”
Phys. Rev. , vol. D68, p. 093007, 2003.[82] S. T. Petcov, W. Rodejohann, T. Shindou, and Y. Takanishi,“The See-saw mechanism, neutrino Yukawa couplings, LFVdecays l(i) —¿ l(j) + gamma and leptogenesis,”