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Nguyen Anh Ky

Publications and source records attributed to Nguyen Anh Ky.

At least 19 recordsLinked to original sources
arXiv2024

Gravitational radiation of a spherically symmetric source in $f(R)$-gravitation

It is shown that Birkhoff's theorem for the general theory of relativity is overcome in the $f(R)$-theory of gravitation. That means, the $f(R)$-theory of gravitation, unlike Einstein's general theory of relativity, does not forbid gravitational radiation from a spherically symmetric source (whether stationary or non-stationary). As a consequence, in the $f(R)$-theory a spherically symmetric gravitational deformation (e.g., collapse/expansion or pulsation) could emit gravitational waves (of tensor- and scalar polarization modes), a phenomenon impossible in the general relativity. A test model is examined and it turns out that the gravitational radiation is strongest when the surface of the deforming object is in the vicinity of the (modified) event horizon, even suddenly flares up just outside the latter. In this letter, within the $f(R)$-theory of gravitation, a gravitational wave equation and a formula for the gravitational emission power are derived. These formulae, along with searching for signals, can be used for the experimental test of the $f(R)$-theory. In general, including the spherically symmetry case, gravitational radiation of both tensor- and scalar polarization modes are allowed, although under some circumstance the contribution of scalar modes is strongly suppressed.

gr-qc↗
arXiv2023

Perturbative approach to $f(R)$-gravitation in FLRW cosmology

The $f(R)$ theory of gravitation developed perturbatively around the general theory of relativity with cosmological constant (the \text{$Λ$}CDM model) in a flat FLWR geometry is considered. As a result, a general explicit cosmological solution that can be used for any model with an arbitrary, but well-defined, $f(R)$ function (just satisfying given perturbation conditions) is derived. This perturbative solution shows how the Hubble parameter $H (t)$ depends on time (along with the cosmological constant and the matter density) to adapt to the evolution of the Universe. To illustrate, this approach is applied to some specific test models. One of these models appears to be more realistic as it could describe three phases of the Universe's evolution. Despite the fact that the perturbation is applied for a flat FLWR geometry (according to the current cosmological observation) indicates that the obtained solution can mainly describe the evolution of the late Universe, it may also work for an early Universe. As a next step, the present method can be applied to the case with a more general FLRW geometry to increase the precision of the description of different stages in the evolution of the Universe. Finally, it is shown that in a desription of the Universe's evolution the perturbative $f(R)$-theory can be considered as an effective GR with the cosmological constant $Λ$ replaced by an effective parameter $ Λ_{eff}[ρ(t)] $. This trick leads to a simpler way of solving an $f(R)$-theory regardless its specific form.

gr-qc↗
arXiv2019

Testing the $f(R)$-theory of gravity

A procedure of testing the $f(R)$-theory of gravity is discussed. The latter is an extension of the general theory of relativity (GR). In order this extended theory (in some variant) to be really confirmed as a more precise theory it must be tested. To do that we first have to solve an equation generalizing Einstein's equation in the GR. However, solving this generalized Einstein's equation is often very hard, even it is impossible in general to find an exact solution. It is why the perturbation method for solving this equation is used. In a recent work \cite{Ky:2018fer} a perturbation method was applied to the $f(R)$-theory of gravity in a central gravitational field which is a good approximation in many circumstances. There, perturbative solutions were found for a general form and some special forms of $f(R)$. These solutions may allow us to test an $f(R)$-theory of gravity by calculating some quantities which can be verified later by the experiment (observation). In \cite{Ky:2018fer} an illustration was made on the case $f(R)=R+λR^2$. For this case, in the present article, the orbital precession of S2 orbiting around Sgr A* is calculated in a higher-order of approximation. The $f(R)$-theory of gravity should be also tested for other variants of $f(R)$ not considered yet in \cite{Ky:2018fer}. Here, several representative variants are considered and in each case the orbital precession is calculated for the Sun--Mercury- and the Sgr A*--S2 gravitational systems so that it can be compared with the value observed by a (future) experiment. Following the same method of \cite{Ky:2018fer} a light bending angle for an $f(R)$ model in a central gravitational field can be also calculated and it could be a useful exercise.

physics.gen-ph↗
arXiv2018

Perturbative solutions of the $f(R)$-theory of gravity in a central gravitational field and some applications

Exact solutions of an $ f(R) $-theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a non-static central field are not easy at all. There are, however, approximation methods of finding a solution in a central field which is not necessarily static. It is shown in this article that an approximate solution of an $f(R)$-theory in a general central field, which is not necessary to be static, can be found perturbatively around a solution of the Einstein equation in the general theory of relativity. In particular, vacuum solutions are found for $f(R)$ of general and some special forms. Further, applications to the investigation of a planetary motion and light's propagation in a central field are presented. An effect of an $f(R)$-gravity is also estimated for the SgrA*--S2 system. The latter gravitational system is much stronger than the Sun--Mercury system, thus the effect could be much stronger and, thus, much more measurable.

gr-qc↗
arXiv2017

A see-saw scenario of an $A_4$ flavour symmetric standard model

A see-saw scenario for an $A_4$ flavour symmetric standard model is presented. The latter, compared with the standard model, has an extended field content adopting now an additional $A_4$ symmetry structure (along with the standard model symmetry). As before, the see-saw mechanism can be realized in several models of different types depending on different ways of neutrino mass generation corresponding to the introduction of new (heavy in general) fields with different symmetry structures. In the present paper, a general description of all these see-saw types is made with a more detailed investigation on type-I models, while for type-II and type-III models a similar strategy can be followed. As within the original see-saw mechanism, the symmetry structure of the standard model fields decides the number and the symmetry structure of the new fields. In a model considered here, the scalar sector consists of three standard-model-Higgs-like iso-doublets ($SU_L(2)$-doublets) forming together an $A_4$-triplet, and three iso-singlets transforming as three singlets (1,$1^{'}$ and $1^{''}$) of $A_4$. In the lepton sector, the three left-handed lepton iso-doublets form an $A_4$-triplet, while the three right-handed charged leptons are either $A_4$-singlets in one version of the model, or components of an $A_4$-triplet in another version. To generate neutrino masses through, say, the type-I see-saw mechanism, it is natural to add four right-handed neutrino multiplets, including one $A_4$-triplet and three $A_4$-singlets. For an interpretation, the model is applied to deriving some physics quantities such as neutrinoless double beta decay effective mass $|\langle m_{ee}\rangle|$, CP violation phase $δ_{CP}$ and Jarlskog parameter $J_{CP}$, which can be verified experimentally.

hep-ph↗
arXiv2016

A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry

A model of a neutrino mixing with an $A_4\times Z_3\times Z_4$ flavour symmetry is suggested. In addition to the standard model fields, the present model contains six new fields which transform under different representations of $A_4\times Z_3\times Z_4$. The model is constructed to slightly deviate from a tri-bi-maximal model in agreement with the current experimental data, thus, all analysis can be done in the base of the perturbation method. Within this model, as an application, a relation between the mixing angles ($θ_{12}, θ_{23}, θ_{13}$) and the Dirac CP-violation phase ($δ_{CP}$) is established. This relation allows a prediction of $δ_{CP}$ and the Jarlskog parameter ($J_{CP}$). The predicted value $δ_{CP}$ is in the 1$σ$ region of the global fit for both the normal- and inverse neutrino mass ordering and gives $J_{CP}$ to be within the bound $|J_{CP}|\leq 0.04$. For an illustration, the model is checked numerically and gives values of the neutrino masses (of the order of 0.1 eV) and the mixing angle $θ_{13}$ (about $9^\circ$) very close to the current experimental data.

hep-ph↗
arXiv2015

Was the Higgs boson discovered?

The standard model has postulated the existence of a scalar boson, named the Higgs boson. This boson plays a central role in a symmetry breaking scheme called the Brout-Englert-Higgs mechanism (or the Brout-Englert-Higgs-Guralnik-Hagen-Kibble mechanism, for completeness) making the standard model realistic. However, until recently at least, the 50-year-long-sought Higgs boson had remained the only particle in the standard model not yet discovered experimentally. It is the last but very important missing ingredient of the standard model. Therefore, searching for the Higgs boson is a crucial task and an important mission of particle physics. For this purpose, many theoretical works have been done and different experiments have been organized. It may be said in particular that to search for the Higgs boson has been one of the ultimate goals of building and running the LHC, the world's largest and most powerful particle accelerator, at CERN, which is a great combination of science and technology. Recently, in the summer of 2012, ATLAS and CMS, the two biggest and general-purpose LHC collaborations, announced the discovery of a new boson with a mass around 125 GeV. Since then, for over two years, ATLAS, CMS and other collaborations have carried out intensive investigations on the newly discovered boson to confirm that this new boson is really the Higgs boson (of the standard model). It is a triumph of science and technology and international cooperation. Here, we will review the main results of these investigations following a brief introduction to the Higgs boson within the theoretical framework of the standard model and Brout-Englert-Higgs mechanism as well as a theoretical and experimental background of its search. This paper may attract interest of not only particle physicists but also a broader audience.

hep-ph↗
arXiv2012

Representations of quantum superalgebra Uq[gl(2|1)] in a coherent state basis and generalization

The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum superalgebras, except $U_q[osp(1|2)]$, one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely $U_q[gl(2|1)]$, in constructing $q$--boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified into typical and nontypical representations. This construction leads to a more general class of $q$--boson-fermion realizations and finite-dimensional representations of $U_q[gl(2|1)]$ and, thus, at $q=1$, of $gl(2|1)$. Both $gl(2|1)$ and $U_q[gl(2|1)]$ have found different physics applications, therefore, it is meaningful to construct their representations.

math-ph↗
arXiv2006

Scalar sextet in the 331 model with right-handed neutrinos

A Higgs sextet is introduced in order to generate Dirac and Majorana neutrino masses in the 331 model with right-handed neutrinos. As will be seen, the present sextet introduction leads to a rich neutrino mass structure. The smallness of neutrino masses can be achieved via, for example, a seesaw limit. The fact that the masses of the charged leptons are not effected by their new Yukawa couplings to the sextet is convenient for generating small neutrino masses.

hep-ph↗
arXiv2005

A three-parametric deformation of GL(1/1)

A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra $U[gl(1/1)]$.

hep-th↗
arXiv2005

A two-parametric deformation of U[sl(2)], its representations and complex "spin"

A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters. Interestingly that finite-dimensional representations of $U_{pq}[sl(2)]$ allow arbitrary complex "spins" (i.e., not necessary they to be integral or half-integral numbers), unlike those in the classical and one-parametric deformation cases.

math.QA↗
arXiv2005

Comments related to reading "Static quantities of the $W$ boson in the $SU_L(3)\times U_X(1)$ model with right-handed neutrinos"

Comments related to reading the paper "Static quantities of the $W$ boson in the $SU_L(3)\times U_X(1)$ model with right-handed neutrinos", hep-ph/0312308 (by J. L. Garcia-Luna et al) are given. They do not concern the main results of the paper but a statement there about the Higgs sector of the 331 model with right-handed neutrinos. The scalar sextet introduced here may help us to generate neutrino masses in an acceptable range.

hep-ph↗
arXiv2003

Some deformations of U[sl(2)] and their representations

Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters.

math.QA↗
arXiv2003

Finite-dimensional representations of U_q[gl(2/1)] in a basis of U_q[gl(2)\oplus gl(1)]

The quantum superalgebra $U_q[gl(2/1)]$ is given as both a Drinfel'd--Jimbo deformation of $U[gl(2/1)]$ and a Hopf superalgebra. Finite--dimensional representations of this quantum superalgebra are constructed and investigated in a basis of its even subalgebra $U_q[gl(2)\oplus gl(1)]$. The present method for constructing representations of a quantum superalgebra combines previously suggested ones for the cases of superalgebras and quantum superalgebras, and, therefore, has an advantage in comparison with the latter.

math.QA↗
arXiv2001

Irreducible representations of Upq[gl(2/2)]

The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical ones according to a proposition proved in the present paper. This proposition is a nontrivial deformation from the one for the classical superalgebra gl(2/2), unlike the case of one-parametric deformations.

math.QA↗
arXiv2000

The Higgs sector in the minimal 3-3-1 model with the most general lepton-number conserving potential

The Higgs sector of the minimal 3 - 3 - 1 model with three triplets and one sextet is investigated in detail under the most general lepton--number conserving potential. The mass spectra and multiplet decompostion structure are explicitly given in a systematic order and a transparent way allowing they to be easily checked and used in further investigations. A previously arising problem of inconsistent signs of f_{2} is also automatically solved.

hep-ph↗
arXiv2000

Bounds on masses of new gauge bosons in the 3 - 3 -1 models

Contribution from new gauge bosons in the 3 - 3 - 1 models to the anomalous magnetic moment of the muon, mass difference of the kaon system and rare kaon decay are calculated and numerically estimated. Bounds on masses of new gauge bosons: bileptons and Z' are derived.

hep-ph↗