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A. P. Martynenko

Publications and source records attributed to A. P. Martynenko.

At least 19 recordsLinked to original sources
arXiv2026

Rydberg states of muonic helium in quantum electrodynamics

The variational method is used to study the energy levels of muonic helium $(\mu^{-} \, e^{-} \, He)$ with an electron in the ground state and a muon in an excited state with principal and orbital quantum numbers $n \sim l+1 \sim 14$. The variational wave functions are chosen in the Gaussian form. The matrix elements of the Hamiltonian in the nonrelativistic approximation, as well as corrections for the vacuum polarization and relativism, are calculated analytically. A series of energies of the Rydberg muon states is obtained, which can be studied experimentally.

hep-ph↗
arXiv2026

Weak Interaction Contribution to the Muonium Hyperfine Structure in the Standard Model

The contribution of the weak interaction to the hyperfine splitting of the ground state of muonium is investigated. The amplitudes of the one- and two-quantum exchange determined by the Z and W bosons are calculated. One-loop corrections in the photon and Z boson propagators and their contribution to the hyperfine structure of the spectrum are obtained.

hep-ph↗
arXiv2026

Few-particle lepton bound states in variational approach

The energy levels of the ground states of the three-particle and four-particle bound states of leptons in quantum electrodynamics are calculated. For the calculation, the variational method with Gaussian basis functions is used. The hyperfine structure of the spectrum is taken into account due to the pairwise spin-spin interaction of particles.

hep-ph↗
arXiv2025

Heavy tetraquarks in the hyperspherical approach

Within the quark model and hyperspherical method, the bound states of four heavy quarks and antiquarks (tetraquarks) are investigated. In hyperradial approximation, the Schroedinger equation is reduced to a one-dimensional equation after averaging over angles in hyperspace. This equation is solved numerically and analytically within the variational method. The hyperfine structure of the spectrum is calculated. To increase the accuracy of the calculation, corrections to the energy levels from the QCD generalization of the Breit Hamiltonian are taken into account.

hep-ph↗
arXiv2025

Production of heavy tetraquarks in rare exclusive decays of the Higgs boson

The relativistic quark model is used to study the processes of heavy tetraquark $(cc\bar{c}\bar{c})$ production in the Higgs boson decay. We consider quark-gluon, ZZ-boson, and quark-gluon loop decay mechanisms with the production of a fully charmed tetraquark. Relativistic interaction amplitudes are constructed and decay widths are calculated taking into account relativistic corrections in the decay amplitude connected with the relative motion of quarks and antiquarks.

hep-ph↗
arXiv2025

Mass spectrum of heavy tetraquarks in variational approach

Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. Numerical calculation of the energy levels of tetraquarks is performed using a program in the Matlab system. Hyperfine structure of the spectrum is calculated. To increase the accuracy of the calculation, relativistic corrections are taken into account.

hep-ph↗
arXiv2025

Production of heavy quark bound states in rare exclusive decays of Higgs boson

The processes of pair production of S- and P- wave charmonium, as well as the production of the tetraquark (cc \bar{c} \bar{c}) in the Higgs boson decays are investigated within the framework of relativistic quark model. Relativistic decay amplitudes are constructed and decay widths are calculated taking into account relativistic corrections both in the decay amplitude and in the wave function of bound heavy quarks.

hep-ph↗
arXiv2024

Hadronic light-by-light scattering contribution to 1S-2S transition in muonium

We study hadronic light-by-light scattering contribution to the energy interval (1S-2S) in muonium. Various amplitudes of interaction of a muon and an electron are constructed, in which the effect of hadronic scattering of light-by-light is determined using the transition form factor of two photons into a meson. Their contributions to the particle interaction operator in the case of S-states are obtained in integral form, and to the energy spectrum in numerical form. The contributions of pseudoscalar, scalar, axial vector mesons are taken into account.

hep-ph↗
arXiv2024

Production of dileptonic bound states in the Higgs boson decay

The production of single and paired lepton bound states in the decay of the Higgs boson has been studied. We explore different decay mechanisms that contribute significantly to the decay width. The decay widths are calculated taking into account relativistic corrections in the decay amplitude and in the wave function of the bound state of leptons.

hep-ph↗
arXiv2023

Contribution of hadronic light-by-light scattering to the hyperfine structure of muonium

The contribution of hadronic scattering of light-by-light to the hyperfine structure of muonium is calculated using experimental data on the transition form factors of two photons into a hadron. The amplitudes of interaction between a muon and an electron with horizontal and vertical exchange are constructed. The contributions due to the exchange of pseudoscalar, axial vector, scalar and tensor mesons are taken into account.

hep-ph↗
arXiv2023

Energy levels of mesonic helium in quantum electrodynamics

On the basis of variational method we study energy levels of pionic helium $(π-e-He)$ and kaonic helium $(K-e-He)$ with an electron in ground state and a meson in excited state with principal and orbital quantum numbers $n\sim l+1\sim 20$. Variational wave functions are taken in the Gaussian form. Matrix elements of the basic Hamiltonian and corrections to vacuum polarization and relativism are calculated analytically in a closed form. We calculate some bound state energies and transition frequencies which can be studied in the experiment.

hep-ph↗
arXiv2023

The light-by-light contribution to the muon anomalous magnetic moment from the axial-vector mesons exchanges within the nonlocal quark model

The contribution of axial-vector mesons to the muon's anomalous magnetic moment through a light-by-light process is considered within a nonlocal quark model. The model is based on a four-quark interaction with scalar--pseudoscalar and vector--axial-vector sectors. While the transverse component of the axial-vector corresponds to a spin-1 particle, the unphysical longitudinal component is mixed with a pseudoscalar meson. The model parameters are re-fitted to the pion properties in the presence of pi-a_1 mixing. The obtained estimation for the light-by-light contribution of a_1+f_1 mesons is (3.6+-1.8)*10^{-11}.

hep-ph↗
arXiv2022

Relativistic corrections to paired production of charmonium and bottomonium in decays of the Higgs boson

Rare decay process of the Higgs boson into a pair of $J/Ψ$ and $Υ$ particles is studied within perturbative Standard Model and relativistic quark model. The relativistic corrections connected with the relative motion of quarks are calculated in the production amplitude and the wave functions of the bound states. Numerical values of the decay widths of the Higgs boson are obtained, which can be used for comparison with experimental data.

hep-ph↗
arXiv2022

Ground state hyperfine structure of light muon-electron ions

The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.

hep-ph↗
arXiv2021

Higgs boson decay to the pair of S- and P-wave $B_c$ mesons

We investigate the rare production of the pair of $S-$ and $P-$ wave $B_c$-meson in the Higgs boson decay in the perturbative Standard Model and relativistic quark model. Relativistic amplitudes and decay widths are constructed with the account of the relative motion of heavy quarks forming $B_c$ mesons. When constructing the Higgs boson decay amplitudes, the method of projection operators on the $S-$ and $P-$wave states of quarks is used. Relativistic corrections are expressed in terms of special relativistic parameters and are calculated numerically in the quark model. The dependence of the decay widths of the Higgs boson on various sources of relativistic corrections is investigated.

hep-ph↗
arXiv2021

Higgs boson decay to paired $B_c$: relativistic and one-loop corrections

The exclusive decays of the Higgs boson to $B_c B_c$ and $B_c^\ast B_c^\ast$ pairs are studied. The hard parts of the decay amplitudes are estimated within the perturbative Standard Model up to one-loop corrections. The soft fusion of heavy quarks to the quarkonium is described in framework of the relativistic quark model.

hep-ph↗
arXiv2021

Low-lying electron energy levels in three-particle electron-muon ions $(μe Li)$, $(μe Be)$, $(μe B)$

The electron Lamb shift $(2P-2S)$ and the energy interval $(2S-1S)$ in muon-electron ions of lithium, beryllium, and boron have been calculated within the framework of the perturbation theory method for the fine structure constant and the electron-muon mass ratio. The corrections of the first and second orders of the perturbation theory, which include the effects of vacuum polarization, nuclear structure and recoil, are taken into account. The obtained analytical results in perturbation theory are compared with the results of calculations within the variational approach. The obtained values for the Lamb shift $(2P-2S)$ and the interval $(2S-1S)$ can be used for comparison with future experimental data and verification of quantum electrodynamics.

physics.atom-ph↗