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 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.
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 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.
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…
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.
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 …
text of abstract It is showed that the eletric charge quantization is unconnected to Majorana neutrino in the non-universal generations leptoquark-bilepton flavordynamics which includes the right-handed neutrino and an explicit U(1) factor in the gauge semisimple group.
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 first review the three known chiral anomalies in four dimensions and then use the anomaly free conditions to study the uniqueness of quark and lepton representations and charge quantizations in the standard model. We also extend our results to theory with an arbitrary number of color. Finally, we discuss the family problem.
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.
Under the assumption that there exists a local gauge horizontal symmetry $G_H$ wich allows only for a top quark mass at tree level, we look for the constraints that charge quatization and the family structure of the standard model imposes on that symmetry.
We propose that the physics beyond the standard Weinberg-Salam model is such that matter and the CP conjugate anti-matter fields have the same set of charges with respect to the various force groups (upto ordering). We show that this CP-like symmetry leads to an understanding of family replication. We use anomaly constraints to infer the fermion spectra that lead to automatic electric charge quantization. We also find that the unification of coupling constants is possible at $M_{U} = 2 \times 10^{15} GeV$.
After proving, in a previous paper, that the electric charge quantization occurs as a natural consequence in renormalizable $SU(3)_c \otimes SU(n)_{L} \otimes U(1)_{Y}$ gauge models, we take here a step further within the same paradigm in order to obtain the precise weak charges quantization. To this end a viable boson mass spectrum yields first, once a proper parametrization in the Higgs sector is employed. Hence, by diagonalizing the neutral bosons mass matrix, the quantized neutral weak charge operators are obtained. The Standard Model phenomenology is entirely recovered, as its scale ($v_{…
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 quantization conditions which come from the requirement of the singlevaluedness of the odderon wave function are formulated and solved numerically in the 4 dimensional space of the odderon charge q3 and the conformal weight h. It turns out that these conditions are fulfilled along one dimensional curves parametrized by a discrete set of values of Re(h) in 3 dimensional subspace (Im(h),Im(q3),Re(q3)). The odderon energy calculated along these curves corresponds in all cases to the intercept lower than 1.
In a minimal extension of the Standard Model, in which new neutral fermions have been introduced, we show that the requirement of vanishing anomalies fixes the hypercharges of all fermions uniquely. This naturally leads to electric charge quantization in this minimal scenario which has features similar to the Standard Model: invariance under the gauge group $SU(2)_L\otimes U(1)_Y$, conservation of the total lepton number and masslessness for the ordinary neutrinos. Such minimal models might arise as low-energy realizations of some heterotic superstring models or $SO(10)$ grand unified theories…
We examine the issue of magnetic charge quantization in the presence of black holes. It is pointed out that quantization of magnetic charge can lead to the mass quantization for magnetically charged black holes. We also discuss some implications for the experimental searches of magnetically charged black holes.
We show a possibility for the charge quantization of the standard model (SM) particles. If a global symmetry makes the three copies of a generation and supersymmetry (SUSY) relates the Higgs boson to a lepton, all the charges of the SM particles can be quantized through gauge-anomaly cancellation. In the minimal model realizing the possibility, the gravitino mass around the Planck-scale is needed to generate the SM couplings through (quantum) supergravity. Much below the Planck-scale, the SM is obtained as the effective theory. Interestingly, if the gaugino masses are generated through anomaly…
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, depen…
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.
The influence of electric stochastic fields on the relativistic charged particles is investigated in the gauge invariant path integral formalism. Using the cumulant expansion one finds the exponential relaxation of the charge Green's function both for spinless and Dirac charges.
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…
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…
We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, $ω^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun's equation, and we find that the charge as well as the energy must be quantized and state dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun's equation.
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 investigate the consistency conditions for matter fields coupled to the four-dimensional (${\cal N} = 1$ supersymmetric) $\mathbb{CP}(1)$ nonlinear sigma model (the coset space $SU(2)_G/U(1)_H$). We find that consistency requires that the $U(1)_H$ charge of the matter be quantized, in units of half of the $U(1)_H$ charge of the Nambu-Goldstone (NG) boson, if the matter has a nonsingular kinetic term and the dynamics respect the full group $SU(2)_G$. We can then take the linearly realized group $U(1)_H$ to comprise the weak hypercharge group $U(1)_Y$ of the Standard Model. Thus we have charg…
We investigate charge quantization in the Standard Model (SM) through a $\mathbb{CP}^2$ nonlinear sigma model (NLSM), $SU(3)_G/(SU(2)_H \times U(1)_H)$, and a $\mathbb{CP}^3$ model, $SU(4)_G/(SU(3)_H \times U(1)_H)$. We also generalize to any $\mathbb{CP}^k$ model. Charge quantization follows from the consistency and dynamics of the NLSM, without a monopole or Grand Unified Theory, as shown in our earlier work on the $\mathbb{CP}^1$ model (arXiv:1309.0692). We find that representations of the matter fields under the unbroken non-abelian subgroup dictate their charge quantization under the $U(1…
The contribution of crossed gluon fields in flux tubes connecting quarks to the proton spin is calculated. The calculations are performed following non-perturbative Heisenberg's quantization technique. In our approach a proton is considered as consisting of three quarks connected by three flux tubes. The flux tubes contain color longitudinal electric and transversal electric and magnetic fields. The transversal fields causes the appearance of the angular momentum density. The dimensionless relation between the angular momentum and the mass of the gluon fields is obtained. The contribution to p…
If photon mass is not exactly zero, though arbitrary small, electric charge would not be conserved in interaction of charged particles with black holes. Manifestations of such mechanism of electric charge non-conservation are discussed.
The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed.
