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For the quantum quartic anharmonic oscillator with the Hamiltonian H = (p²+x²)/2+λx4, which is one of the traditional quantum-mechanical and quantum-field-theory models, we study summation of its factorially divergent perturbation series by the proposed method of averaging of the corresponding Padé approximants. Thus, for the first time, we are able to construct the Padé-type approximations that possess correct asymptotic behaviour at infinity with a rise of the coupling constant λ. The approach gives very essential theoretical and applicatory-computational advantages in applications of the given method. We also study convergence of the applied approximations and calculate by the proposed method the ground state energy E0(λ) of the anharmonic oscillator for a wide range of variation of the coupling constant λ. [ABSTRACT FROM AUTHOR]

Quantum chromodynamics (QCD) running coupling constant αs and its dependence on the energy scale renormalization parameter μ are studied in the energy range of μ ≲ 25 GeV based on the five-loop calculations according to QCD renormalization group equation. Position of the Landau pole μ ≡ Λ = 664.9 MeV of the αs(μ) dependence (QCD scale parameter Λ) is calculated in the five-loop order for the first time. Energy dependence αs(μ) of the running coupling constant in the given energy range is very well described by the proposed simple one-pole formula. [ABSTRACT FROM AUTHOR]

Simple relations connecting the strange quark mass to the splittings of the light hyperon masses were obtained on the basis of the phenomenological quark model compatible with the present-day theory of strong interactions, i.e. with quantum chromodynamics (QCD). Strange quark mass ms 89.5 ± 19.5 MeV, calculated in the proposed approach, is in good agreement with the modern evaluations and calculations of this quantity, mainly obtained by the lattice QCD methods. [ABSTRACT FROM AUTHOR]

Simple relations between the masses of the two lightest up and down quarks were obtained on the basis of the simple physically based model compatible with the present-day theory of strong interactions, i.e. with quantum chromodynamics. Relations between the u- and d- quark masses, on one hand, and nucleon and pion masses, on the other hand, are also established. The u- and d-quark masses mu = 1,903 MeV, md = 4,594 MeV, calculated with the help of the obtained relations, are in very good agreement with the modern evaluations and calculations of these quantities. The average of the u and d quark masses mud = 3,248 MeV, obtained in the proposed approach, is also in good agreement with previous calculations. [ABSTRACT FROM AUTHOR]

Charge dependence of the pion-nucleon coupling constants and the 1 0 S -state low-energy nucleon-nucleon scattering parameters are studied on the basis of the Yukawa meson theory. The charge independence breaking effect in the pionnucleon coupling constants is entirely explained by the mass difference between the charged and the neutral pions and by the mass difference between the proton and the neutron. Using of well-known pseudovector pion-nucleon coupling constant   0 2 0.0749 7 pp f   , which characterize the proton-proton nuclear interaction, we calculate the charged   2 0.0802 7 c f  and the neutral   2 0 f  0.0750 7 pion-nucleon coupling constants, and also the pion-nucleon coupling constant   0 2 0.0751 7 nn f   , which characterize the neutron-neutron nuclear interaction. With the help of the obtained coupling constants, we also calculate values of the low-energy np- and nn-scattering parameters, which appear to be in good agreement with the experiment. [ABSTRACT FROM AUTHOR]

Charge independence breaking (CIB) in the pion-nucleon coupling constant and the nucleon-nucleon scattering length is considered on the basis of the Yukawa meson theory. CIB effect in these quantities is almost entirely explained by the mass difference between the charged and the neutral pions. Therewith charge splitting of the pionnucleon coupling constant is almost the same as charge splitting of the pion mass. Calculated difference between the proton-proton and the neutron-proton scattering length in this case comprises ~90% of the experimental value. [ABSTRACT FROM AUTHOR]

On the basis of the Yukawa potential we study the pion-nucleon coupling constants for the neutral and charged pions assuming that nuclear forces at low energies are mainly determined by the exchange of virtual pions. We obtain the charged pseudovector pion-nucleon coupling constant f²π0=0,0749(7) by making the use of experimental low-energy scattering parameters for the singlet pp- and np-scattering, and also by use of the neutral pseudovector pion-nucleon coupling constant f²π± = 0,0804(7). Corresponding value of the charged pseudoscalar pion-nucleon coupling constant g²π±/4π= 14,55(13) is also determined. This calculated value of the charged pseudoscalar pion-nucleon coupling constant is in fully agreement with the experimental constant g²π±/4π= 14,52(26) obtained by the Uppsala Neutron Research Group. Our results show considerable charge splitting of the pion-nucleon coupling constant. [ABSTRACT FROM AUTHOR]