arXiv subjects
Publications and source records attributed to M. K. Volkov.
The process $e^{+}e^{-} \to π^{+}π^{-}$ is described in the framework of the extended NJL model. Intermediate vector mesons $ρ^0(770)$, $ω(782)$ and ρ'(1450)$ are taken into account. Our results are in satisfactory agreement with experimental data. The prediction for the process $e^{+}e^{-} \to ππ'(1300)$ is given. Here the main contribution is given by the diagram with intermediate $ρ'(1450)$ meson.
The width of the decay $τ^{-} \to π^{-} π^{0} ν_τ$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $ρ$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $ρ$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.
The process $e^+e^- \to π^0ρ$ is described in the framework of the expanded NJL model in the energy region from 0.9 GeV to 1.5 GeV. The contribution of intermediate state with vector mesons $ω(782), \,\,ϕ(1020)$, and $ω'(1420)$, where $ω'$ is the first radial excitation of $ω$ - meson was taken into account. Results obtained are in satisfactory agreement with experimental data.
Electromagnetic interactions of the ground and first radial excited states of $η$ and $η'$ mesons in the framework of the extended $U(3)\times U(3)$ NJL model are considered. The radial excitations are described with the help of polynomial form factor of the second order over the inner quark momentum. The solution of the $U_A(1)$ problem by means of 't Hooft interaction is taken into account. For diagonalization of the free Lagrangian the $4\times4$ mixing matrix is used. Two-photon decay widths of the ground $η$ and $η'$ meson are found to be in a satisfactory agreement with the experiment. Predictions for the two-photon decay widths of $η(1295)$ and $η(1475)$ are given. The probabilities of eta meson production by two-photon mechanism in $e^+e^-$ collisions and of their photoproduction on electrons are calculated.
The processes of electron-positron annihilation into $π^0γ$ and into $π'(1300)γ$ are considered within the NJL model. Intermediate vector mesons $ρ^0$, $ω$, $ρ'(1450)$, and $ω'(1420)$ are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the $π^0γ$ production are in agreement with experimental data received in the energy region 600 -- 1020 MeV.
A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted so that the physical values of the pion mass and the weak pion decay constant are obtained. The size of the 1/Nc correction to the quark condensate is carefully studied and compared with the usual local Nambu-Jona-Lasinio model. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. The model is also applied to finite temperature. We find that the 1/Nc corrections dominate the melting of the chiral condensate at low temperatures, T<100 MeV, in agreement with chiral perturbation theory. On the other hand, the relative importance of the 1/Nc corrections in the cross-over regime depends on the parameter T0 of the Polyakov loop potential. For T0=270 MeV, corresponding to a fit of lattice data for pure gluodynamics, the correction terms are large and lead to a lowering of the chiral phase transition temperature in comparison with the mean-field result. Near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme is needed to include mesonic correlations in that regime. Lowering T0 leads to a more rapid cross-over even at the mean-field level and the unstable region for the 1/Nc corrections shrinks. For T0< 220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.
Differential distributions in the $π_0π_0γ$ system created in the annihilation channel of an electron-positron collision are considered. The energy fractions of the pions (Dalitz-plot) distribution are presented in a general form and in approximation of intermediate vector mesons (excited and ordinary ones).It is pointed out that in relevant experiments the generalized polarizability of the neutral pion can be measured. Numerical illustrations are presented.
The process of electron-positron annihilation into a pair of $π^0$ and $ω$ mesons is considered in the framework of the SU(2)$\times$SU(2) Nambu--Jona-Lasinio model. Contributions of intermediate photons, $ρ(770)$ and $ρ'(1450)$ vector mesons are taken into account. It is shown that the bulk of the cross section at energies below 2 GeV is provided by the process with intermediate $ρ'(1450)$ state. The contribution due to single photon and $ρ(770)$ exchange is in agreement with the vector meson dominance model. Numerical results are compared with experimental data.
Within the framework of non-local quark model of Nambu--Jona-Lasinio type the two-photon decay of radial excited state of $π_0$-meson -- $π_0'$ -- is found to be $3.6\KeV$. The radial excitation of pion is described with the use of polynomial formfactor of second order over $\vec q^2$ where $\vec q$ is the transverse momentum, which corresponds to relative motion of quark-antiquark pair within the energy range from 0 up to $1\GeV$. The probabilities of production of $π_0'$ and $(π_0'+γ)$ states in the electron-positron colliders are estimated. The production of $π_0'$-meson in the interaction of photon with electron or muon is as well considered (Primakoff effect). The relevant total cross sections are 0.14 or $0.06\nb$.
Radiative decays $π^0({π^0}')\toγ+γ$, ${π^0}'\toρ^0(ω)+γ$, ${ρ^0}'(ω')\toπ^0+γ$, and ${ρ^0}'(ω')\to{π^0}'+γ$ are considered in the framework of the non-local SU(2)$\times$SU(2) NJL model. Radially excited mesons are described with the help of polynomial form factor $f({k^\bot}^2)$, where $k^\bot$ is the quark momentum transverse to the external meson momentum. In spite of mixing of the ground and excited meson states in this model, the decay widths of $π^0\toγ+γ$ and $ρ^0(ω)\toπ^0+γ$ are found to be in good agreement with experimental data as in the standard local NJL model. Our predictions for decay widths of radially excited mesons can be verified in future experiments.
We describe application of Bogoliubov compensation principle to calculation of non-perturbative contribution in the electroweak theory and QCD. We obtain unique solutions of compensation equations, which impose strong restrictions on parameters of theories and on functional dependence of corresponding form-factors. We calculate value of running gauge electroweak coupling $α_w(M_W)=0.0374$, that differs from the experimental value less than by 10%. We derive effective Nambu-Jona-Lasinio interaction from fundamental QCD and express its parameters in terms of initial QCD parameters: $α_s$ at low-momenta and current mass of light quarks. This leads to satisfactory description of low-mass hadron physics.
We calculate the contribution of semi-hadronic states with pseudoscalar $P=π^0, η$ and scalar ($σ$(550))meson accompanied with real photon as an intermediate state of a heavy photon to the anomalous magnetic moment of muon. We consider the intermediate states with $π_0$ and $σ$ as a hadrons in frames of Nambu-Jona-Lasinio model. The contribution of $π_0γ$ state is in agreement with results obtained in previous theoretical considerations as well as with experimental data $a_μ^{π_0γ}\approx 4.5 \times 10^{-10}$, besides we estimate $a_μ^{ηγ}=0.7 \times 10^{-10}, a_μ^{σγ} \sim 1.5 \times 10^{-11}, a_μ^{π^+π^-γ} \sim 3.2 \times 10^{-10}.$ We discass as well the LbL mechanism with $a_μ^{lbl}=10.5 \cdot 10^{-10}.$
A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted to the physical values of the pion mass and the weak pion decay constant. The size of the 1/Nc correction to the quark condensate is carefully studied in the nonlocal and the usual local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. It is also found that the 1/Nc corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition point.
The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/N_c$ approximation) are taken into account. We show that quark loop contribution dominates, because the meson loops strongly conceal each other. The sigma-pole contribution $(m^2_σ-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_π^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated for the COMPASS experiment.
Meson correlation functions are studied in the model with four-fermion interaction Lagrangian. We demonstrate that despite the singular character of system mean energy and corresponding quark condensate found out the meson observables are finite, quite well identified and compatible with experimental energy scale. It allows one to use the similar model Hamiltonians for describing the nonequilibrium features of quark/hadron systems which reveal themselves in studying ultrarelativistic heavy ion collisions. The analytical results for meson correlation functions in the Keldysh model are given.
The cross sections of the scalar meson $f_0(980)$, $a_0(980)$ and $σ(600)$ production in collision of electron and positron beams were calculated. The two-photon decays of the scalar mesons, obtained in the framework of the Nambu-Jona-Lasinio model, were used. The quark and meson loops were taken into account.
The two-photon decay widths of scalar mesons σ(600), f_0(980) and a_0(980) as well a_0 -> ρ(ω)γand f_0 -> ρ(ω)γare calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/Nc -approximation where Nc is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f_0 decay the K-loop contribution turns out to play the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a_0 -> ρ(ω)γand f_0 -> ρ(ω)γwidths are given.
Using the description of the subprocess $γγ^*\to S(P)$ in terms of local Nambu-Jona-Lasinio model we calculate the cross sections of photoproduction of scalar and pseudoscalar mesons in high energy photon-lepton collisions processes. The dependence on the transversal momentum and the total cross sections in Weizsaecker-Williams approximation are presented.