Local Discrete Symmetries Research Articles

Mass Generation of the Scalars Bosons in a Left-Right Symmetric Model with two Bidoublets

The search for new Physics justified by new discoverys, motivate among others, the realization of new models called Extensions of the Standard Model (ESM) which must include at low energy the Standar Model. (SM) The electroweak symmetry group SU(2) L ⊗ U(1) Y to the gauge group with left-right symmetry SU(2) L ⊗ SU(2) R ⊗ U(1) B − L ⊗ 𝒫, represents one of the minimal extensions of the SM, in which 𝒫 is a parity discrete symmetry such that left-right coupling constants satisfied gL = gR , and according to the hierarchy in the symmetry breaking (conditions that must be met by the vacuum expectation values introduced in the model) allow to obtain the SM. The aim of this work is to identify the Higgs boson of the SM, considering a more general scalar potential that must respect all the symmetries (local gauge invariant, discrete symmetries and Lorentz invariant) established in the model. We will take into account those previous works about the hierarchy conditions and certain approximations that must satisfy the vacuum expectation values for obtain greater simplicity in the caculations of scalar masses of the model.

Loop currents in two-leg ladder cuprates

New phases with broken discrete Ising symmetries are uncovered in quantum materials with strong electronic correlations. The two-leg ladder cuprate Sr14−xCaxCu24O41 hosts a very rich phase diagram where, upon hole doping, the system exhibits a spin liquid state ending to an intriguing ordered magnetic state at larger Ca content. Using polarized neutron diffraction, we report here the existence of short range magnetism in this material for two Ca contents, whose origin cannot be ascribed to Cu spins. This magnetism develops exclusively within the two-leg ladders with a diffraction pattern at forbidden Bragg scattering, which is the hallmark of loop current-like magnetism breaking both time-reversal and parity symmetries. Our discovery shows local discrete symmetry breaking in a one dimensional spin liquid system as theoretically predicted. It further suggests that a loop current-like phase could trigger the long range magnetic order reported at larger doping in two-leg ladder cuprates.

Self-interacting scalar dark matter with local Z3 symmetry

We construct a self-interacting scalar dark matter (DM) model with local discrete Z3 symmetry that stabilizes a weak scale scalar dark matter X. The model assumes a hidden sector with a local U(1)X dark gauge symmetry, which is broken spontaneously into Z3 subgroup by nonzero VEV of dark Higgs field ϕX (⟨ϕX⟩≠0). Compared with global Z3 DM models, the local Z3 model has two new extra fields: a dark gauge field Z′ and a dark Higgs field ϕ (a remnant of the U(1)X breaking). After imposing various constraints including the upper bounds on the spin-independent direct detection cross section and thermal relic density, we find that the scalar DM with mass less than 125 GeV is allowed in the local Z3 model, in contrary to the global Z3 model. This is due to new channels in the DM pair annihilations open into Z′ and ϕ in the local Z3 model. Most parts of the newly open DM mass region can be probed by XENON1T and other similar future experiments. Also if ϕ is light enough (a few MeV ≲mϕ≲ O(100) MeV), it can generate a right size of DM self-interaction and explain the astrophysical small scale structure anomalies. This would lead to exotic decays of Higgs boson into a pair of dark Higgs bosons, which could be tested at LHC and ILC.

Naturally light invisible axion in models with large local discrete symmetries

We show that by introducing appropriate local ${Z}_{N}(N>~13)$ symmetries in electroweak models it is possible to implement an automatic Peccei-Quinn symmetry, at the same time keeping the axion protected against gravitational effects. Although we consider here only an extension of the standard model and a particular 3-3-1 model, the strategy can be used in any kind of electroweak model. An interesting feature of this 3-3-1 model is that if we add (i) right-handed neutrinos, (ii) the conservation of the total lepton number, and (iii) a ${Z}_{2}$ symmetry, the ${Z}_{13}$ and the chiral Peccei-Quinn ${U(1)}_{\mathrm{PQ}}$ symmetries are both accidental symmetries in the sense that they are not imposed on the Lagrangian but are just a consequence of the particle content of the model, its gauge invariance, renormalizability, and Lorentz invariance. In addition, this model has no domain wall problem.

Gauge symmetry and supersymmetry breaking by discrete symmetry

We study the principles of the gauge symmetry and supersymmetry breaking due to the local or global discrete symmetries on the extra space manifold. We show that the gauge symmetry breaking by Wilson line is the special case of the discrete symmetry approach where all the discrete symmetries are global and act freely on the extra space manifold. As applications, we discuss the N=2 supersymmetric SO(10) and E 8 breaking on the spacetime M 4× A 2 and M 4× D 2, and point out that similarly one can study any N=2 supersymmetric SO( M) breaking. We also comment on the one-loop effective potential, the possible questions and generalization.

Local discrete symmetry in the brane neighborhood

With the ansatz that there exist local or global discrete symmetries in the special branes' neighborhoods, we can construct the extra dimension models with only zero modes, or the models which have large extra dimensions and arbitrarily heavy KK modes because there is no simple relation between the mass scales of extra dimensions and the masses of KK states. In addition, the bulk gauge symmetry and supersymmetry can be broken on the special branes for all the modes, and in the bulk for the zero modes by local and global discrete symmetries. To be explicit, we discuss the supersymmetric SU(5) model on $M^4\times S^1/Z_2$ in which there is a local $Z_2'$ symmetry in the special 3-brane neighborhood along the fifth dimension.

Probing the desert with ultra-energetic neutrinos from the sun and the earth

Realistic superstring models generically give rise to exotic matter states, which arise due to the “Wilson-line” breaking of the non-Abelian unifying gauge symmetry. Often such states are protected by a gauge or local discrete symmetry and therefore may be stable or meta-stable. We study the possibility of a flux of high energy neutrinos coming from the sun and the earth due to the annihilation of such exotic string states. We also discuss the expected flux for other heavy stable particles – like the gluino LSP. We comment that the detection of ultra-energetic neutrinos from the sun and the earth imposes model independent constraints on the high energy cutoff, as for example in the recently entertained TeV scale Kaluza–Klein theories. We therefore propose that improved experimental resolution of the energy of the muons in neutrino detectors together with their correlation with neutrinos from the sun and the center of the earth will serve as a probe of the desert in Gravity Unified Theories.

Advances in old-fashioned heterotic string model building

I review findings of various research groups regarding perturbative heterotic string model building in the last 12 months. Attention is given to recent studies of extra U(1)'s and local discrete symmetries (LDS's) in generic string models. Issues covered include the role of U(1)'s and LDS's in limiting proton decay, developments in classification of models containing anomalous U(1), and possible complications resulting from kinetic mixing between observable and hidden sector U(1)'s. Additionally, recent string-derived and string-inspired models are briefly reviewed.

Exotic leptoquarks from superstring-derived models

The H1 and ZEUS collaborations have recently reported a significant excess of e + p → e + jet events at high- Q 2. While there exists insufficient data to conclusively determine the origin of this excess, one possibility is that it is due to a new leptoquark at mass scale around 200 GeV. We examine the type of leptoquark states that exists in superstring-derived standard-like models, and show that, while these models may contain the standard leptoquark states which exist in Grand Unified Theories, they also generically contain new and exotic leptoquark states with fractional lepton number, ± 1 2 . In contrast to the traditional GUT-type leptoquark states, the couplings of the exotic leptoquarks to the Standard Model states are generated after the breaking of U(1) B− L . This important feature of the exotic leptoquark states may result in local discrete symmetries which forbid some of the undesired leptoquark couplings. We examine these couplings in several models and study the phenomenological implications. The flavor symmetries of the superstring models are found to naturally suppress leptoquark flavor-changing processes.

Meeting the constraint of neutrino—Higgsino mixing in gravity unified theories

In gravity unified theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B - L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive ν L- H mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of ν L- H mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.

Local discrete symmetries from superstring derived models

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.

On detecting discrete Cheshire charge

We analyze the charges carried by loops of string in models with non-abelian local discrete symmetry. The charge on a loop has no localized source, but can be detected by means of the Aharonov-Bohm interaction of the loop with another string. We describe the process of charge detection, and the transfer of charge between point particles and string loops, in terms of gauge-invariant correlation functions.

Do cosmic strings determine the number of generations?

What distinguishes the generations above the electroweak scale? We propose a model where three families of leptons and the electroweak bosons are assigned to the irreducible representations of the local binary tetrahedral group of order 24, a discrete subgroup of SU (2), and the local discrete symmetry Z 3. The scattering cross sections of leptons off the cosmic strings associated with the elements of the local discrete symmetry distinguish the members of the lepton families. The possible relevance of the cosmic strings to E 8 unification and the families of quarks are discussed.

Remarks on local discrete symmetry

It is pointed out that discrete symmetries left unbroken after a spontaneous Higgs condensation remain as global symmetries in the low-energy effective theory. The global nature of these discrete symmetries makes the associated charges physical so that they may become “quantum hair” for black holes as has been suggested recently. It is also emphasized that to obtain a theory with a local discrete symmetry G, one must not only introduce sectors in the Hilbert space corresponding to G-twisted boundary conditions, but should also project out G non-invariant states in each sector to preserve the local G gauge invariance. Explicit examples discussed here include a Z N model with two scalars and the SO(3) → O(2) model with Alice strings.

Local discrete symmetry and quantum-mechanical hair

A charge operator is constructed for a quantum field theory with an abelian discrete gauge symmetry, and a non-local order parameter is formulated that specifies how the gauge symmetry is realized. If the discrete gauge symmetry is manifest, then the charge inside a large region can be detected at the boundary of the region, even in a theory with no massless gauge fields. This long-range effect has no classical analog; it implies that a black hole can in principle carry “quantum-mechanical hair”. If the gauge group is nonabelian, then a charged particle can transfer charge to a loop of cosmic string via the nonabelian Aharonov-Bohmeffect. The string loop can carry charge even though there is no localized source of charge anywhere on the string or in its vicinity. The “total charge” in a closed universe must vanish, but, if the gauge group is nonabelian and the universe is not simply connected, then the “total charge” is not necessarily the same as the sum of all point charges contained in the universe.

Continuum limit of lattice gauge theories in the context of renormalized perturbation theory

It is shown that in spite of the modifications introduced by Wilson and Polyakov, the gauge theory on a lattice in the Abelian case in the limit of zero lattice spacing has the same renormalized S matrix as quantum electrodynamics, to all orders in the renormalized coupling constant. Apparently nonrenormalizable vertices contained in the lattice Lagrangian contribute to mass, wave-function, and coupling-constant renormalizations, but do not contribute to the ''finite parts'' as a result of being multiplied by additional powers of lattice spacing. It is crucial for this renormalizability that the lattice theory respects local gauge symmetry and discrete symmetries and has the correct ''classical continuum limit.'' The results that in a renormalizable field theory divergences are contained in the first few terms of the Taylor series expansion of the Green's functions about the external momenta, and that these divergences are mild, play an important role in our proof. Umklapp processes characteristic of the lattice regularization do not have any observable consequences in the continuum limit. Thus Wilson's lattice action is well suited for nonperturbative considerations of gauge theories.