The extensions of the Standard Model based on the $SU(3)_{C} \otimes SU(3)_{L} \otimes U(1)_{X}$ gauge group are known as 331 Models. Different properties such as the fermion assignment and the electric charges of the exotic spectrum, that defines a particular 331 model, are fixed by a $β$ parameter. In this article we study the electric charge quantization in two versions of the 331 models, set by the conditions $β=1/\left( 3\sqrt{3}\right)$ and $β=0$. In these frameworks, arise exotic particles, for instance, new leptons and gauge bosons with a fractional electric charge. Additionally, depending on the version, quarks with non-standard fractional electric charges or even neutral appear. Considering the definition of electric charge operator as a linear combination of the group generators that annihilates the vacuum, classical constraints from the invariance of the lagrangian, and gauge and mixed gauge-gravitational anomalies cancellation, the quantization of the electric charge can be verified in both versions.
The distinction between the rigid rotor and Callan-Klebanov approaches to the quantization of SU(3) solitons is considered in the context of exotic baryons. A numerically tractable quantum mechanical analog system is introduced to test the reliability of the two quantization schemes. We find that in the equivalent of the large N_c limit of QCD, the Callan-Klebanov approach agrees with a numerical solution of the quantum mechanical analog. Rigid rotor quantization generally does not. The implications for exotic baryons are briefly discussed.
We classify the meson and baryon long lived resonances considering quarks with electric charge 5/3 and $-4/3$ (in units of $\vert e\vert$) predicted by some 3-3-1 models. Some of these exotic resonances have the usual electric charges $0,\pm1$, others have $\pm(3,4,5)$, and the lightest ones decaying only into leptons plus known resonances. We propose another heavy $SU(3)_H$ global symmetry under which hadrons involving only exotic quarks can be constructed.
A light collective theta+ baryon state (with strangeness +1) was predicted via rigid-rotor collective quantization of SU(3) chiral soliton models. This paper explores the validity of this treatment. A number of rather general analyses suggest that predictions of exotic baryon properties based on this approximation do not follow from large Nc QCD. These include an analysis of the baryon's width, a comparison of the predictions with general large Nc consistency conditions of the Gervais-Sakita-Dashen-Manohar type; an application of the technique to QCD in the limit where the quarks are heavy; a …
A detailed study of the criteria for stability of the scalar potential, and the proper electroweak symmetry breaking pattern in some 3-3-1 models without exotic electric charges is presented. In this paper we concentrate in a scalar sector with three Higgs scalar triplets, with a potential that does not include the cubic term, due to the presence of a discrete symmetry. For the analysis we use, and improve, a method previously developed to study the scalar potential in the two-Higgs-doublet extension of the standard model. Our main result is to show the consistency of those 3-3-1 models withou…
I study the scalar representations of the electroweak group of the Standard Model, with a special emphasis on their chiral properties and on their behaviour by the discrete symmetries P and CP. A gauge theory for J=0 mesons naturally springs out, together with a new approach to the question of the electroweak violation of CP. When acting in the 4-dimensional space of states spanned by the special representations under scrutiny in this paper, the electric charge appears as one of the three generators of the diagonal SU(2) and its eigenvalues are consequently quantized.
Predictions for a light collective $Θ^+$ baryon state (with strangeness +1) based on the collective quantization of chiral soliton models are shown to be inconsistent with large $N_c$ QCD. The lightest strangeness +1 state to emerge from the analysis has an excitation energy which at large $N_c$ scales as $N_c^0$ while collective quantization is legitimate only for excitations which go to zero as $N_c \to \infty$. This inconsistency strongly suggests that predictions for $Θ^+$ properties based on collective quantization of chiral solitons are not valid.
The boson mass spectrum of the electro-weak \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} model with exotic electric charges is investigated by using the algebraical approach supplied by the method of exactly solving gauge models with high symmetries. Our approach predicts for the boson sector a one-parameter mass scale to be tuned in order to match the data obtained at LHC, LEP, CDF.
We obtain electric charge quantization in the context of models based on the gauge symmetry group SU(3) X SU(4) X U(1). The gauge models studied include three families to cancel out anomalies and a set of scalar fields to break spontaneously the symmetry. To show the electric charge quantization, we use clasical symmetry conditions and quantum quiral anomaly conditions.
For the particular class of \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} electro-weak models without exotic electric charges, some plausible phenomenological predictions - such as the boson mass spectrum and charges of all the fermions involved therein - are made by using the algebraical approach of the exactly solving method for gauge models with high symmetries. Along with the one-parameter resulting mass scale (to be confirmed at TeV scale in LHC, LEP, CDF and other high energy experiments) our approach predicts the exact expressions of the charges (both electric and neutral) in the fermion sector,…
The low-energy approach to electric charge quantization predicts physics beyond the minimal standard model. A model-independent approach via effective Lagrangians is used examine the possible new physics, which may manifest itself indirectly through family-lepton--number violating rare decays.
In this work we study the structure of the electromagnetic interactions and the electric charge quantization in gauge theories of electroweak interactions based on semi-simple groups. We show that in the standard model of the electroweak interactions the structure of the electromagnetic interactions is strongly correlated to the quantization pattern of the electric charges. We examine these two questions also in all possible chiral bilepton gauge models of the electroweak interactions. In all they we can explain the vectorlike nature of the electromagnetic interactions and the electric charge …
In the framework of Standard Model for the arbitrary values of Higgs and fermions fields hypercharges, taking into account parity invariance of electromagnetic interaction, expressions for the fermions charges, testifying the electric charge quantization are obtained. From the chiral anomalies cancellation condition within one family of leptons and quarks, numerical values of fermions charges, coinciding with standard values of charges have been obtained.
We consider the gauge invariant version of the Proca theory, where besides the real vector field there is also the real scalar field. We quantize the theory such that the commutator of the scalar field operator and the electric field operator is given by a predefined three-dimensional vector field, say $\cal E$ up to a global prefactor. This happens when the field operators of the gauge invariant Proca theory satisfy the proper gauge constraint. In particular, we show that $\cal E$ given by the classical Coulomb field leads to the Coulomb gauge constraint making the vector field operator diver…
The weak currents with respect to the diagonal neutral bosons $Z$,$Z^{\prime}$, and $Z^{\prime\prime}$ of a specific \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} gauge model are computed in detail for all the fermion families involved therein. Our algebraical approach, which is based on the general method of solving gauge models with high symmetries proposed several years ago by Cotăescu, recovers in a non-trivial way all the Standard Model values for current couplings of the traditional leptons and quarks, and predicts plausible values for those of the exotic fermions in the model.
In models with flat extra dimensions tiny Dirac neutrino masses can be generated via the coupling of four dimensional Standard Model fields to a higher dimensional fermion. Here we argue that, in spite of the Dirac nature of the neutrino, quantization of the electric charge can still be understood as a result of anomaly cancellation, charge conservation and naturalness requirements.
We investigate some proposals to solve the electric charge quantization puzzle, which simultaneously explain the recent measured deviation on the muon anomalous magnetic moment. For this we assess extensions of the Electro-Weak Standard Model spanning modifications on the scalar sector only. It is interesting to verify that one can have modest extensions which easily account for the solution for both problems.
This comment discusses a recent paper by Walliser and Weigel on the quantization of chiral soliton models in the context of exotic baryons. Claims made in that work are misleading due to unfortunate nomenclature. Moreover, attempts in that paper to go beyond the leading order calculations of the phase shifts are ad hoc and never justified. This comment also addresses a technical issue in that paper: the identification of the excitation energy of the pentaquark obtained via conventional rigid rotor quantization with a frequency obtained in the context of small amplitude fluctuations. The identi…
We study the minimal set of Higgs scalars, for models based on the local gauge group $SU(3)_c \otimes SU(3)_L \otimes U(1)_X$ which do not contain particles with exotic electric charges. We show that only two Higgs $SU(3)_L$ triplets are needed in order to properly break the symmetry. The exact tree-level scalar mass matrices resulting from symmetry breaking are calculated at the minimum of the most general scalar potential, and the gauge bosons are obtained, together with their couplings to the physical scalar fields. We show how the scalar sector introduced is enough to produce masses for fe…
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 generati…
We show that three SU(2) singlet neutral scalars (two CP-even and one CP-odd) in the spectrum of models based on the gauge symmetry SU(3)_c X SU(3)_L X U(1)_X, which do not contain exotic electric charges, are realistic candidates for thermally generated self-interacting dark matter in the Universe, a type of dark matter that has been recently proposed in order to overcome some difficulties of collisionless cold dark matter models at the galactic scale. These candidates arise without introducing a new mass scale in the model and/or without the need for a discrete symmetry to stabilize them, bu…
The quantization of the electrical charge in the electrodynamics and of the hypercharge in the standard model are imposed in the theory based not on theoretical arguments but on the experimental observations. In this paper we propose a quantum consistency condition in a theory where Ward identities are respected that requires the quantization of the charge within the framework of the theory without external impositions. This refers to the renormalization conditions in the background gauge field method such that to ensure a correct mathematical correspondence between the bare partition function…
Basing on the general photon eigenstate and anomaly cancellation, it is shown that the electric charge quantization in SU(3)_c X SU(3)_L X U(1)_X model with exotic particles can be obtained independently on parameters alpha and betta. The fixation of hypercharges of fermions fields by the Higgs fields and dependence of the electric charges quantization conditions from the hypercharges of Higgs fields leads to the fact that the electric charge in the considered model can be quantized and fixed only in the presence of Higgs fields. In addition, we have shown that in the considered model the clas…
I study, in the leptonic sector, the role of the $SU(2)_V$ custodial symmetry $\ti{\cal G}$ which was shown in ref. [1] to control the quantization of the electric charge in the $J=0$ mesonic sector. The electroweak theory is considered, according to ref. [2], as a purely vectorial model which interacts with a ``hidden'' sector of composite scalars. $\ti{\cal G}$ can only be a symmetry of the former if the neutrino is a Majorana particle; the latter provides a dynamical modification of the leptonic weak couplings, reconstructing those of the Standard Model with a massless Majorana neutrino.
We study an electroweak gauge extension of the standard model, so called 3-4-1 model, which does not contain exotic electric charges and it is anomaly free. We discuss phenomenological constraints of the model and compute all the corrections to the muon magnetic moment. Mainly, we discuss different mass regimes and their impact on this correction, deriving for the first time direct limits on the masses of the neutral fermions and charged vector bosons. Interestingly, the model could address the reported muon anomalous magnetic moment excess, however it would demands a rather low scale of symme…
In gauge theories like the standard model, the electric charges of the fermions can be heavily constrained from the classical structure of the theory and from the cancellation of anomalies. We argue that the anomaly conditions are not quite as well motivated as the classical constraints, since it is possible that new fermions could exist which cancel potential anomalies. For this reason we examine the classically allowed electric charges of the known fermions and we point out that the electric charge of the tau neutrino is classically allowed to be non-zero. The experimental bound on the elect…
Experimentally it has been known for a long time that the electric charges of the observed particles appear to be quantized. An approach to understanding electric charge quantization that can be used for gauge theories with explicit $U(1)$ factors -- such as the standard model and its variants -- is pedagogically reviewed and discussed in this article. This approach uses the allowed invariances of the Lagrangian and their associated anomaly cancellation equations. We demonstrate that charge may be de-quantized in the three-generation standard model with massless neutrinos, because differences …
We argue that magnetic and electric charges of the Reissner-Nordstrom black hole are quantized in CP conserving theories. Dequantization phenomenon occurs when CP is broken either explicitly or effectively, and, as a result, pure magnetic black holes are not possible. Two examples illustrating this phenomenon are discussed. One is the electric charge induced by the neutral pion field in a magnetically charged black hole, and another is the electric charge induced due to the massive spin-two field emerging from possible higher curvature terms.
We prove that - even at a low TeV scale - the canonical seesaw mechanism can be naturally implemented in the exact solution of a particular 3-3-1 gauge model, since a very small alteration $ε$ in the parameter matrix of the Higgs sector is taken into account. Therefore, this new parameter can act as an appropriate mass source for neutrinos, while - due to the main parameter $a$ - all the previously achieved results in the exact solution of the model are recovered. Moreover, this mathematical artifice does separate the boson mass spectrum from the neutrino mass issue, hence giving more flexibil…
A detailed analysis of $Z^{'0}Z^{'0}$, $K^{+}K^{-}$ and $K^{0}\bar{K}^{0}$ pair production in $e^{+}e^{-}$ collisions is presented by using helicity amplitudes. The trilinear bosons couplings in the $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ models without exotic electric charges are also calculated. We carry out the mentioned analysis for two models, one of them is a one family model which is an $E_6$ subgroup \cite{b1} and the other one is a three family model with right handed neutrinos\cite{b2,b3}. These models do not contain exotic electric charges. For them, we give explicit formulae a…
In the context of the standard model the quantization of the electric charge occurs only family by family. When we consider the three families together with massless neutrinos the electric charge is not quantized any more. Here we show that a chiral bilepton gauge model based on the gauge group SU(3)_C X SU(3)_L X U(1)_N explains the quantization of the electric charge when we take into account the three families of fermions. This result does not depend on the neutrino masses. Charge quantization occurs either the neutrinos are massless or Dirac or Majorana massive fields.
We present an extension of the Standard Model to the local gauge group $SU(3)_c\otimes SU(4)_L\otimes U(1)_X$ with a family non-universal treatment and anomalies canceled among the three families in a nontrivial fashion. The mass scales, the gauge boson masses, and the masses for the spin 1/2 particles in the model are analyzed. The neutral currents coupled to all neutral vector bosons in the model are studied, and particular values of the parameters are used in order to simplify the mixing between the three neutral currents present in the theory, mixing which is further constrained by experim…
In this research, we propose a modified version of the 3-3-1 model, incorporating a type I+II seesaw mechanism and Z4 discrete symmetry, as a framework for investigating lepton flavor-violating (LFV) decays. This model successfully yields the left-handed neutrinos mass square difference in the eV scale, with specific values of mass square differences; and generates mixing angles that align with experimental data. Furthermore, we develop SARAH and SPheno algorithms tailored for our modified model, enabling us to estimate the magnitude of LFV observables. Our calculations indicate favorable resu…
I study the scalar representations of the electroweak group of the Standard Model, which is a subgroup of the chiral group U(N)L x U(N)R with N flavours, for N even, with a special emphasis on their chiral properties and on their behaviour by the discrete symmetries P and CP. They exhaust the $2N^2$ scalar and pseudoscalar degrees of freedom of the chiral group, for which a SU(2)L x U(1) renormalizable, anomaly-free gauge theory naturally springs out. It is shown to have a global diagonal SU(2)V symmetry independently of the value of the hypercharge coupling, which becomes local at the limit w…
The uniqueness of the hypercharge assignments in the three fermion families leptoquark-bilepton $SU(3)_C \times SU(4)_L \times U(1)_N$ model is established. Although the gauge group contains an explicit U(1) factor, freedom from triangle anomalies combined with the requirement of nonvanishing charged fermion masses uniquely fix the electric charges of all fermions independently of the neutrinos being massless or not. The electric-charge quantization, family replication, and the existence of three colors are interwoven.
Models with fermions in bifundamental representations can lead naturally to family unification as opposed to family replication. Such models typically predict (exotic) color singlet states with fractional electric charge, and magnetic monopoles with multiple Dirac charge. The exotics may be at the TeV scale, and relatively light magnetic monopoles (greater than about 10^7 GeV) can be present in the galaxy with abundance near the Parker bound. We focus on three family SU(4)XSU(3)XSU(3) models.
In the context of 331 models we analyze the phenomenology of exotic $T$ quarks with electric charge 2/3. We establish bounds for the corresponding masses and mixing angles and study the decay modes $T\to bW$, $tZ$ and $qH$. It is found that the decays into scalars are strongly dependent on the model parameters, and can be the dominant ones in a scenario with approximate flavor symmetry.
The mass splittings for the Majorana neutrinos in the exact solution of a particular 3-3-1 gauge model are computed here in detail. Since both $\sin^{2}θ_{13}\simeq0$ and the mass splittings ratio $r_Δ\simeq0.033$ are taken into account, the analytical calculations seem to predict an inverted mass hierarchy and a mixing matrix with a texture based on a very close approximation to the bi-maximal mixing. The resulting formulas for the mass squared differences can naturally accomodate the available data if the unique free parameter ($a$) gets very small values ($\sim10^{-15}$). Consequently, the …
A general covariant quantization of superparticle, Green-Schwarz superstring and a supermembrane with manifest supersymmetry and duality symmetry is proposed. This quantization provides a natural quantum mechanical description of curved BPS-type backgrounds related to the ultra-short supersymmetry multiplets. Half-size commuting and anticommuting Killing spinors admitted by such backgrounds in quantum theory become truncated $κ$-symmetry ghosts. The symmetry of Killing spinors under dualities transfers to the symmetry of the spectrum of states. GS superstring in the generalized semi-light-cone…
The embedding in SU(4)xSU(3)xSU(3) of the well studied gauge groups SU(4)xSU(2)xSU(2) and SU(3)xSU(3)xSU(3) naturally leads to family unification as opposed to simple family replication. An inescapable consequence is the predicted existence of (exotic)color singlet states that carry fractional electric charge. The corresponding magnetic monopoles carry multiple Dirac magnetic charge, can be relatively light (\sim 10^{7}-10^{13}GeV), and may be present in the galaxy not far below the Parker bound.
We carry a systematic study of possible extensions of the standard model based on the gauge group SU(3)_c X SU(4)_L X U(1)_X. We consider both models with particles with exotic electric charges and models which do not contain exotic electric charges neither in the gauge boson sector nor in the fermion sector. For the first case an infinite number of models can, in principle, be constructed, while the restriction to non-exotic electric charges only allows for eight different anomaly-free models. Four of them are three-family models in the sense that anomalies cancel by an interplay between the …
At variational level in the framework of dimensional reduced 'U_e(1)\times U_g(1)' electromagnetism it is considered an anyon Landau-Ginzburg Chern-Simons model for the fractional Hall effect. The collective gauge fields are due to pseudo-photons (...). We show that the model contains both magnetic vortexes due to the internal photons (interpreted as quasi-particles) and electric vortexes due to the internal pseudo-photons (interpreted as quasi-holes) that account for the anyon quantized magnetic flux and fractional electric charges, respectively. The effective magnetic flux is the only effect…
We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry breaking terms. In this way, we recover the standard vacuum of QCD with $N_f$ flavors and $N_c$ colors when $N_f < N_c$. However, for $N_f \geq N_c$, we find new exotic states---new vacua with spontaneously broken baryon number for $N_f = N_c$, and a vacuum state with unbroken chiral symmetry for $N_f > N_c$. These exotic vacua contain massless composite fermions and, in some cases, dynamically generated gauge bosons. In particular Seiberg's electric-magnetic d…
The nonperturbative quantization technique à la Heisenberg is applied for non-Abelian gauge theories. The operator Yang-Mills equation is written, which on the corresponding averaging gives an infinite set of equations for all Green functions. We split all degrees of freedom into two groups: in the former, we have $A^a_μ\in \mathcal G \subset SU(N)$, and in the second group we have coset degrees of freedom $SU(N) / \mathcal G$. Using such splitting and some assumptions about 2- and 4-point Green functions, we truncate the infinite set of equations to two equations. The first equation is for th…
The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a …
Heavy long-lived multi-charged leptons (MCLs) are predicted by various new physics models. These hypothetical MCLs can form bound states, due to their high electric charges and long life times. In this work, we propose a novel strategy of searching for MCLs through their bound state productions and decays. By utilizing LHC-8 TeV data in searching for resonances in the diphoton channel, we exclude the masses of isospin singlet heavy leptons with electric charge $|q|\geq 6$ (in units of electron charge) lower than $\sim$1.2 TeV, which are much stronger than the corresponding 8 TeV LHC bounds fro…
