Showing 1–50 of 117 results for author: Volkov, M K

Decay widths of radially excited vector mesons of the $U(3)$ nonet with production of three pseudoscalar mesons in the extended NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the extended NJL model, the decays of the first radially excited vector mesons $ρ'$,$ω'$, $φ'$ and ${K^*}'$ with production of $3P$, where $P=K,π,η$ are calculated. The box channels and the channels with intermediate vector mesons in the ground and first radially excited states are considered. The obtained results can be considered as predictions for future experiments. In the extended NJL model, the decays of the first radially excited vector mesons $ρ'$,$ω'$, $φ'$ and ${K^*}'$ with production of $3P$, where $P=K,π,η$ are calculated. The box channels and the channels with intermediate vector mesons in the ground and first radially excited states are considered. The obtained results can be considered as predictions for future experiments. △ Less

Submitted 13 August, 2026; originally announced August 2026.

Description of the process $e^+ e^- \to π^0π^0 γ$ in the extended NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The cross section of the process $e^+ e^- \to π^0π^0 γ$ is calculated in the extended NJL quark model. The vector channel with the intermediate $ρ$, $ω$, $ρ'$ and $ω'$ mesons is considered. The main contribution is given by the intermediate radially excited $ρ'$ meson. The role of the channel with the intermediate scalar meson is also discussed. The cross section of the process $e^+ e^- \to π^0π^0 γ$ is calculated in the extended NJL quark model. The vector channel with the intermediate $ρ$, $ω$, $ρ'$ and $ω'$ mesons is considered. The main contribution is given by the intermediate radially excited $ρ'$ meson. The role of the channel with the intermediate scalar meson is also discussed. △ Less

Submitted 16 June, 2026; originally announced June 2026.

Comments: 6 pages

Two-body decays of radially excited $η(1295)$ and $η(1475)$ mesons in the extended NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the extended NJL model, two-body strong decays of the radially excited $η(1295)$ and $η(1475)$ mesons are described. It is shown that the two-body decays $η(1475)\to K_0^*K, a_0π$ play a dominant role in determining the width of the radially excited meson $η(1475)$. At the same time, the decays $η(1475)\to K^*K$ make a significantly smaller contribution to the total width. It is shown that two-… ▽ More In the extended NJL model, two-body strong decays of the radially excited $η(1295)$ and $η(1475)$ mesons are described. It is shown that the two-body decays $η(1475)\to K_0^*K, a_0π$ play a dominant role in determining the width of the radially excited meson $η(1475)$. At the same time, the decays $η(1475)\to K^*K$ make a significantly smaller contribution to the total width. It is shown that two-particle decays give only a negligible contribution to the total width of the $η(1295)$. △ Less

Submitted 18 May, 2026; originally announced May 2026.

Comments: 6 pages

Chiral anomaly in the $η^{(\prime)}\toπ^+π^-γ$ and $η^{(\prime)}\toπ^+π^-l^+l^-$ decays

Authors: M. K. Volkov, A. A. Osipov, K. Nurlan, A. A. Pivovarov

Abstract: We report the presence of a flavor-violating correction to the $VAAA$-type anomaly, $δ^{(\prime)}$, induced by the surface terms of the anomalous quark triangle diagram, previously found in the $η,η'\toπ^+π^-γ$ decay amplitudes, and investigate its impact on the corresponding semileptonic decay modes of $η$ and $η'$. The magnitude of $δ^{(\prime)}$ can be set from the experimental data on the… ▽ More We report the presence of a flavor-violating correction to the $VAAA$-type anomaly, $δ^{(\prime)}$, induced by the surface terms of the anomalous quark triangle diagram, previously found in the $η,η'\toπ^+π^-γ$ decay amplitudes, and investigate its impact on the corresponding semileptonic decay modes of $η$ and $η'$. The magnitude of $δ^{(\prime)}$ can be set from the experimental data on the $η^{(\prime)}\to π^+π^-γ$ decay width. We then estimate another low-energy constant, the slope parameter $α^{(\prime)}$. The impact of different schemes for describing $η$-$η^\prime$ mixing on the value of $δ^{(\prime)}$ and $α^{(\prime)}$ is discussed. The predictions are shown to be in complete agreement with the available experimental data. △ Less

Submitted 30 June, 2026; v1 submitted 11 January, 2026; originally announced January 2026.

Comments: 25 pages, 5 figures

Decays $f_1 \to a_0 π,πππ(η)$ and $f_1 \to K K π$ in the chiral $U(3) \times U(3)$ quark NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The branching fractions of the axial vector meson decays $f_1 \to a_0 π,ππη$, $f_1 \to ρπ,πππ$ and $f_1 \to KKπ$ are calculated in the standard $U(3) \times U(3)$ quark NJL model. The intermediate channels with the states $a_0(980)π$ and $f_0(500)η$ are taken into account in the decay $f_1 \to ππη$. In the case of the scalar mesons, the $\bar{q}q$ representation as a chiral symmetric partners of t… ▽ More The branching fractions of the axial vector meson decays $f_1 \to a_0 π,ππη$, $f_1 \to ρπ,πππ$ and $f_1 \to KKπ$ are calculated in the standard $U(3) \times U(3)$ quark NJL model. The intermediate channels with the states $a_0(980)π$ and $f_0(500)η$ are taken into account in the decay $f_1 \to ππη$. In the case of the scalar mesons, the $\bar{q}q$ representation as a chiral symmetric partners of the pseudoscalar mesons is used. It is shown that the decays $f_1 \to ρπ$ and $f_1 \to3π$ occur due to the mass difference of the $u$ and $d$ quarks. All the results are obtained without using any additional arbitrary parameters and are in satisfactory agreement with the known experimental data. △ Less

Submitted 8 June, 2025; originally announced June 2025.

Comments: 8 pages

Decays $τ\to ππην_τ$ and $τ\to πηην_τ$ in the extended Nambu-Jona-Lasinio model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the framework of the extended Nambu-Jona-Lasinio model, the processes $τ\to ππη(η')ν_τ$ and $τ\to πηη(η')ν_τ$ are considered taking into account mesons in the ground and first radially excited intermediate states. It is shown that in the processes $τ\to ππη(η')ν_τ$ the vector channel is dominant, and in the processes $τ\to πηη(η')ν_τ$ the main contribution is given by the axial vector channel.… ▽ More In the framework of the extended Nambu-Jona-Lasinio model, the processes $τ\to ππη(η')ν_τ$ and $τ\to πηη(η')ν_τ$ are considered taking into account mesons in the ground and first radially excited intermediate states. It is shown that in the processes $τ\to ππη(η')ν_τ$ the vector channel is dominant, and in the processes $τ\to πηη(η')ν_τ$ the main contribution is given by the axial vector channel. The scalar meson $a_0$ plays a dominant role in processes with two $η$-mesons in the final state. The significance of the relative phase between the ground and first radially excited states for these processes is shown. The obtained results for the $τ\to ππην_τ$ process are in satisfactory agreement with the recent experimental data from BaBar and CMD-3, which differ from the averaged values given in the PDG tables. △ Less

Submitted 9 April, 2025; originally announced April 2025.

Comments: 8 pages, 3 figures

Decays $τ\to f_0(π,K) ν_τ$ and $τ\to 3 πν_τ$ accounting for the contribution of $f_0(500)$

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the $U(3) \times U(3)$ quark NJL model, $τ$ lepton decays with the production of scalar mesons $f_0(π,K])$ and neutrinos are studied, where $f_0=f_0(500), f_0(980)$. It is shown that these decays mainly occur via contact channels and channels with axial-vector mesons $a_1$, $K_1(1270)$ and $K_1(1400)$. All mesons are considered as quark-antiquark states in this case. The obtained results can be… ▽ More In the $U(3) \times U(3)$ quark NJL model, $τ$ lepton decays with the production of scalar mesons $f_0(π,K])$ and neutrinos are studied, where $f_0=f_0(500), f_0(980)$. It is shown that these decays mainly occur via contact channels and channels with axial-vector mesons $a_1$, $K_1(1270)$ and $K_1(1400)$. All mesons are considered as quark-antiquark states in this case. The obtained results can be considered as predictions for future experiments. The obtained estimates for the branching fractions of the $τ\to π^-2π^0 ν_τ$ decay taking into account the contributions of the $ρπ$ and $f_0(500)π$ states are in satisfactory agreement with experimental data. △ Less

Submitted 15 December, 2024; originally announced December 2024.

Comments: 7 pages

Weak semileptonic decays of vector mesons in the NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The decay widths of $V \to K(π) l \barν_l $ are calculated within the Nambu--Jona-Lasinio model, where $V=K^*, ρ, ω, φ$ and $l=μ, e$. The results are obtained using the previously fixed model parameters without introducing any arbitrary parameters. The obtained results are considered as predictions due to the absence of experimental data. The decay widths of $V \to K(π) l \barν_l $ are calculated within the Nambu--Jona-Lasinio model, where $V=K^*, ρ, ω, φ$ and $l=μ, e$. The results are obtained using the previously fixed model parameters without introducing any arbitrary parameters. The obtained results are considered as predictions due to the absence of experimental data. △ Less

Submitted 29 October, 2024; originally announced October 2024.

Comments: 7 pages, 2 figures

Description of the processes $e^+ e^- \to π^+ π^-$ and $τ^- \to π^- π^0 ν_τ$ in the NJL model with value of the vector coupling constant $ g_ρ = 6$

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: It is shown that the processes $e^+ e^- \to π^+ π^-$ and $τ^- \to π^- π^0 ν_τ$ can be described in a unified approach in satisfactory agreement with experiment using the vector coupling constant $g_ρ = 6$. In this case, in addition to quark loops, it is also necessary to take into account meson loops corresponding to the next order in $1/N_c$. These loops must be taken into account when describing… ▽ More It is shown that the processes $e^+ e^- \to π^+ π^-$ and $τ^- \to π^- π^0 ν_τ$ can be described in a unified approach in satisfactory agreement with experiment using the vector coupling constant $g_ρ = 6$. In this case, in addition to quark loops, it is also necessary to take into account meson loops corresponding to the next order in $1/N_c$. These loops must be taken into account when describing the $γ(W) \to ρ$ transition, as well as in interaction of mesons in the final state. △ Less

Submitted 10 July, 2024; originally announced July 2024.

Comments: 10 pages, 9 figures

Description of the processes $e^+e^- \to K^+K^-π^0$ and $e^+e^- \to K^+K^-η$ within the extended NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the framework of the $U(3) \times U(3)$ extended Nambu-Jona-Lasinio model, the processes $e^+e^- \to K^+K^-π^0$ and $e^+e^- \to K^+K^-η$ are described taking into account both ground and first radially excited intermediate meson states. It is shown that channels with radially excited $φ(1680)$ meson are dominant in both processes. The influence on the results of the appearance of phase factors… ▽ More In the framework of the $U(3) \times U(3)$ extended Nambu-Jona-Lasinio model, the processes $e^+e^- \to K^+K^-π^0$ and $e^+e^- \to K^+K^-η$ are described taking into account both ground and first radially excited intermediate meson states. It is shown that channels with radially excited $φ(1680)$ meson are dominant in both processes. The influence on the results of the appearance of phase factors of radially excited intermediate states, the existence of which is indicated by experimental data, is discussed. △ Less

Submitted 9 April, 2024; originally announced April 2024.

Comments: 11 pages, 7 figures

Decays of radially excited vector mesons $ρ'$ and $ω'$ in the extended NJL model

Authors: M. K. Volkov, A. B. Arbuzov, A. A. Pivovarov, K. Nurlan

Abstract: The decay widths of $ρ' \to ππ, ωπ, ρη$, $ω' \to ρπ, ωη$ and $π' \to ρπ$ are recalculated within the extended NJL quark model. It is shown that the mass of $ρ'(1450)$ meson in the derived in the NJL model agrees with the one given in Particle Data Group tables but significantly deviates from the recent result of CMD-3 collaboration. Comparisons with earlier theoretical results are presented. The decay widths of $ρ' \to ππ, ωπ, ρη$, $ω' \to ρπ, ωη$ and $π' \to ρπ$ are recalculated within the extended NJL quark model. It is shown that the mass of $ρ'(1450)$ meson in the derived in the NJL model agrees with the one given in Particle Data Group tables but significantly deviates from the recent result of CMD-3 collaboration. Comparisons with earlier theoretical results are presented. △ Less

Submitted 30 November, 2023; originally announced November 2023.

Comments: 6 pages

The decays $τ\to [K^- K^0 π^0, K^- K^+ π^-, K^0 \bar{K^0} π^-] ν_τ$ in the NJL quark model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The $τ$ lepton decays $τ\to [K^- K^0 π^0, K^- K^+ π^-, K ^0 \bar{K^0} π^-] ν_τ$ are described in the $U(3) \times U(3)$ NJL quark model. The contact channel and intermediate channels with axial-vector, vector and pseudoscalar mesons are taken into account. It is shown that the strange scalar meson $K^*_0$ plays an important role in these processes in addition to the intermediate vector meson… ▽ More The $τ$ lepton decays $τ\to [K^- K^0 π^0, K^- K^+ π^-, K ^0 \bar{K^0} π^-] ν_τ$ are described in the $U(3) \times U(3)$ NJL quark model. The contact channel and intermediate channels with axial-vector, vector and pseudoscalar mesons are taken into account. It is shown that the strange scalar meson $K^*_0$ plays an important role in these processes in addition to the intermediate vector meson $K^*$. The obtained results are in satisfactory agreement with the recent experimental data within the experimental and theoretical uncertainties. △ Less

Submitted 11 October, 2023; originally announced October 2023.

Comments: 6 pages, 2 figures

Three-meson $τ$ decays involving kaons and $η$ mesons in the NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: Branching fractions of decays $τ\to K^0 π^- ην_τ$, $τ\to K^- π^0 ην_τ$, $τ\to K^-K^0 ην_τ$ and $τ\to K^- ηην_τ$ are calculated in the $U(3)\times U(3)$ chiral NJL quark model. The contact, vector, axial-vector and pseudoscalar channels are considered. It is shown that the axial vector channel is dominant. The obtained results are in satisfactory agreement with experiment. Branching fractions of decays $τ\to K^0 π^- ην_τ$, $τ\to K^- π^0 ην_τ$, $τ\to K^-K^0 ην_τ$ and $τ\to K^- ηην_τ$ are calculated in the $U(3)\times U(3)$ chiral NJL quark model. The contact, vector, axial-vector and pseudoscalar channels are considered. It is shown that the axial vector channel is dominant. The obtained results are in satisfactory agreement with experiment. △ Less

Submitted 18 July, 2023; originally announced July 2023.

Comments: 7 pages, 2 figures

Decays $τ\to 3K ν_τ$ in $U(3)\times U(3)$ quark NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The widths of the decays $τ\to K^- K^+ K^- ν_τ$ and $τ\to K^- K^0 \bar{K}^0 ν_τ$ are calculated in the $U(3)\times U(3)$ chiral quark NJL model. Four channels are considered: contact, axial vector, vector and pseudoscalar channels. It is shown that the dominant contribution is given by the axial vector channel with an intermediate $φ$ meson. The obtained results are in satisfactory agreement with… ▽ More The widths of the decays $τ\to K^- K^+ K^- ν_τ$ and $τ\to K^- K^0 \bar{K}^0 ν_τ$ are calculated in the $U(3)\times U(3)$ chiral quark NJL model. Four channels are considered: contact, axial vector, vector and pseudoscalar channels. It is shown that the dominant contribution is given by the axial vector channel with an intermediate $φ$ meson. The obtained results are in satisfactory agreement with the experimental data. △ Less

Submitted 16 May, 2023; originally announced May 2023.

$τ$ lepton decays with production of strange scalar mesons $K^*_0(700)$ and $K^*_0(1430)$ in the extended NJL model

Authors: Mikhail K. Volkov, K. Nurlan

Abstract: The branching fractions of $τ$ lepton decays with the production of strange scalar mesons both in the ground and first radially excited states $τ\to ν_τ[K^*_0(700), K^*_0(1430)]$ and $τ\to ν_τ[K^*_0(700)π, K^*_0(1430)π, K^*_0(700) K, K^*_0 (700)η]$ are calculated in the extended $U(3) \times U(3)$ chiral quark NJL model. All mesons are considered as $q\bar{q}$ systems. The obtained results should… ▽ More The branching fractions of $τ$ lepton decays with the production of strange scalar mesons both in the ground and first radially excited states $τ\to ν_τ[K^*_0(700), K^*_0(1430)]$ and $τ\to ν_τ[K^*_0(700)π, K^*_0(1430)π, K^*_0(700) K, K^*_0 (700)η]$ are calculated in the extended $U(3) \times U(3)$ chiral quark NJL model. All mesons are considered as $q\bar{q}$ systems. The obtained results should be considered as predictions for future experiments. △ Less

Submitted 24 November, 2022; originally announced November 2022.

Comments: 9 pages, 5 figures

On the decay widths of radially excited scalar meson $K^*_0(1430)$ in view of new experimental data

Authors: M. K. Volkov, K. Nurlan, A. A. Pivovarov

Abstract: Decays of scalar mesons $K^*_0(800) \to Kπ$ and $K^*_0(1430) \to Kπ, K η, K η', K_1 π$ are described in the extended $U(3 ) \times U(3)$ Nambu - Jona-Lasinio chiral quark model. The obtained results are in satisfactory agreement with the new experimental data obtained by the BaBar collaboration, which markedly differ from the existing values in the PDG. Decays of scalar mesons $K^*_0(800) \to Kπ$ and $K^*_0(1430) \to Kπ, K η, K η', K_1 π$ are described in the extended $U(3 ) \times U(3)$ Nambu - Jona-Lasinio chiral quark model. The obtained results are in satisfactory agreement with the new experimental data obtained by the BaBar collaboration, which markedly differ from the existing values in the PDG. △ Less

Submitted 19 October, 2022; originally announced October 2022.

Comments: 6 pages, 1 figure

The decay $η' \to πρ$ in the chiral NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The branching fraction of the decay $η' \to πρ$ is calculated in the chiral quark NJL model. The decay exists due to the mass difference between $u$- and $d$-quarks leading to $π^{0}-η^{'}$ mixing. Two different approaches are applied: the approximate calculation of this process taking into account the transition $π^{0}-η^{'}$ explicitly without dioganalisation and a more precise approach consisti… ▽ More The branching fraction of the decay $η' \to πρ$ is calculated in the chiral quark NJL model. The decay exists due to the mass difference between $u$- and $d$-quarks leading to $π^{0}-η^{'}$ mixing. Two different approaches are applied: the approximate calculation of this process taking into account the transition $π^{0}-η^{'}$ explicitly without dioganalisation and a more precise approach consisting in the diagonalisation of the singlet and octet states leading to the physical fields $π^{0}$, $η$ and $η^{'}$. The obtained results are in satisfactory agreement with current experimental data. △ Less

Submitted 28 July, 2022; originally announced July 2022.

The decays $τ\to a_{1} πν_τ$, $τ\to K_{1} πν_τ$ and $τ\to K_{1} K ν_τ$ in the extended $U(3)\times U(3)$ chiral NJL model

Authors: Mikhail K. Volkov, Aleksey A. Pivovarov, Kanat Nurlan

Abstract: The branching fractions of the decays $τ\to a_{1} πν_τ$, $τ\to K_{1} πν_τ$ and $τ\to K_{1} K ν_τ$ are calculated in the framework of the extended $U(3)\times U(3)$ chiral Nambu--Jona-Lasinio model. There are no experimental data for these decays in the present time, thus the obtained results are considered as predictions. The comparison of these results to the theoretical results of other authors… ▽ More The branching fractions of the decays $τ\to a_{1} πν_τ$, $τ\to K_{1} πν_τ$ and $τ\to K_{1} K ν_τ$ are calculated in the framework of the extended $U(3)\times U(3)$ chiral Nambu--Jona-Lasinio model. There are no experimental data for these decays in the present time, thus the obtained results are considered as predictions. The comparison of these results to the theoretical results of other authors is carried out. △ Less

Submitted 5 May, 2022; originally announced May 2022.

Comments: 8 pages, 4 figures

Semileptonic decays of $ρ$, $ω$, $φ$, $η$ and $η'$ mesons in ground and first radially excited states in the $U(3)\times U(3)$ NJL model

Authors: M. K. Volkov, K. Nurlan

Abstract: In the extended $U(3)\times U(3)$ NJL model, semileptonic decays of $ρ$, $ω$, $φ$, $η$ and $η'$ mesons in both the ground and first radially excited states are described. Quark loops of the anomalous type are considered, which are based on the vertex $η\to VV$. The obtained results are in satisfactory agreement with the existing experimental data. In addition, a number of predictions for experimen… ▽ More In the extended $U(3)\times U(3)$ NJL model, semileptonic decays of $ρ$, $ω$, $φ$, $η$ and $η'$ mesons in both the ground and first radially excited states are described. Quark loops of the anomalous type are considered, which are based on the vertex $η\to VV$. The obtained results are in satisfactory agreement with the existing experimental data. In addition, a number of predictions for experimentally unmeasured decays of radially excited mesons are presented. △ Less

Submitted 21 March, 2022; originally announced March 2022.

Comments: 6 pages, 2 figures

Low-energy interactions of mesons with participation of the first radially excited states in $U(3) \times U(3)$ NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The $U(3) \times U(3)$ chiral symmetric NJL model describing pseudoscalar, vector, and axial vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to describe a large number of low-energy interactions of mesons, $τ$ lepton decays into mesons and processes of meson production in electron-positron annihilations in… ▽ More The $U(3) \times U(3)$ chiral symmetric NJL model describing pseudoscalar, vector, and axial vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to describe a large number of low-energy interactions of mesons, $τ$ lepton decays into mesons and processes of meson production in electron-positron annihilations in satisfactory agreement with the experiments. In describing a number of processes, it turned out to be necessary to take into account the interactions of mesons in the final state. △ Less

Submitted 11 January, 2022; originally announced January 2022.

Comments: 62 pages, 32 figures and 8 tables

Calculation of the width of the decay $τ\to K^{-} K^{0} ν_τ$ in the extended NJL model with estimation of the contribution of the kaon final state interaction

Authors: M. K. Volkov, A. A. Pivovarov

Abstract: The branching fraction of the decay $τ\to K^{-} K^{0} ν_τ$ is calculated in the framework of the extended Nambu--Jona-Lasinio model. The contact and vector channels are considered. The contributions to this process of the $ρ$ meson in the ground and first radially excited states are taken into account in the vector channel. The obtained results are in satisfactory agreement with the experimental d… ▽ More The branching fraction of the decay $τ\to K^{-} K^{0} ν_τ$ is calculated in the framework of the extended Nambu--Jona-Lasinio model. The contact and vector channels are considered. The contributions to this process of the $ρ$ meson in the ground and first radially excited states are taken into account in the vector channel. The obtained results are in satisfactory agreement with the experimental data. Taking into account the kaon interaction in the final state results in insignificant corrections, which are not beyond the scope of the model uncertainties. △ Less

Submitted 11 August, 2021; originally announced August 2021.

The second-class current decays $τ\to πη(η') ν_τ$ in the NJL model including the interaction of mesons in the final state

Authors: M. K. Volkov, K. Nurlan, A. A. Pivovarov

Abstract: The effect of the interaction of mesons in the final state is additionally considered within the description of $τ\to πη(η') ν_τ$ decays. This interaction is taken into account at the level of production of intermediate pions. One of them, in turn, might be transited into $η$ or $η'$ mesons. Our results do not exceed the experimentally established branching fractions, and they are in agreement wit… ▽ More The effect of the interaction of mesons in the final state is additionally considered within the description of $τ\to πη(η') ν_τ$ decays. This interaction is taken into account at the level of production of intermediate pions. One of them, in turn, might be transited into $η$ or $η'$ mesons. Our results do not exceed the experimentally established branching fractions, and they are in agreement with the results of other theoretical studies. △ Less

Submitted 10 July, 2021; originally announced July 2021.

Comments: 9 pages, 2 figures

The decay $τ\to K^{-} ην_τ$ in the extended Nambu-Jona-Lasinio model taking into account the meson interaction in the final state

Authors: M. K. Volkov, A. A. Pivovarov

Abstract: The branching fraction of the decay $τ\to K^{-} ην_τ$ has been calculated by using the extended Nambu-Jona-Lasinio model taking into account the meson interaction in the final state. The contact term and the channel with the intermediate ground $K^{*}(892)$ and first radially excited state $K^{*}(1410)$ have been calculated. For the purpose of describing the meson interaction in the final state, t… ▽ More The branching fraction of the decay $τ\to K^{-} ην_τ$ has been calculated by using the extended Nambu-Jona-Lasinio model taking into account the meson interaction in the final state. The contact term and the channel with the intermediate ground $K^{*}(892)$ and first radially excited state $K^{*}(1410)$ have been calculated. For the purpose of describing the meson interaction in the final state, the triangle diagram with three mesons has been considered. The cutoff parameter of divergent integrals of the meson loop is equal to the appropriate parameter used in our previous work to describe the decay $τ\to K^{-} π^{0} ν_τ$. Thereby, the present work does not set any additional arbitrary parameters. The obtained results are in satisfactory agreement with the experimental data. △ Less

Submitted 8 July, 2021; originally announced July 2021.

$1/N_c$ approximation and universality of vector mesons

Authors: M. K. Volkov, A. A. Osipov, A. A. Pivovarov, K. Nurlan

Abstract: In this work, we argue that the observed differences in the value of the vector coupling constant extracted from the decays $ρ\to ππ$ ($g_ρ = 6.0$), $ρ\to l^+l^-$ ($g_ρ = 5.0 $) and $ω\to l^+ l^-$ ($g_ρ = 5.7$), where $l=e,μ$, are an indication of the important role played by the $1/N_c$ corrections in the description of these processes. We show that an emission of a photon by charged meson loops… ▽ More In this work, we argue that the observed differences in the value of the vector coupling constant extracted from the decays $ρ\to ππ$ ($g_ρ = 6.0$), $ρ\to l^+l^-$ ($g_ρ = 5.0 $) and $ω\to l^+ l^-$ ($g_ρ = 5.7$), where $l=e,μ$, are an indication of the important role played by the $1/N_c$ corrections in the description of these processes. We show that an emission of a photon by charged meson loops in the $ρ^0, ω,φ\toγ$ transitions is a key process that allows to describe above vector meson decays into two leptons with a single value $g_ρ= 6.0$. Our result supports the idea of universality of neutral vector mesons and clarifies the role of accounting of $1/N_c$ corrections to its fulfilment. △ Less

Submitted 4 August, 2021; v1 submitted 5 May, 2021; originally announced May 2021.

Comments: 9 pages, 2 figuras, the version accepted for publication in Physical Review D

Journal ref: Phys. Rev. D 104, 034021 (2021)

Fixing the vector coupling constant $g_ρ= 5.0$ in the NJL model and final-state interactions in processes $ρ\to e^+e^-[μ^+μ^-]$, $ρ\to π^+π^-$, $τ\to π^-π^0ν_τ$, and $e^+e^-\toπ^+π^-$

Authors: M. K. Volkov, A. B. Arbuzov, K. Nurlan, A. A. Pivovarov

Abstract: The possibility to use the width of the decay $ρ\to e^{+}e^{-}$ to fix the input parameter $g_ρ=5.0$ of the $SU(2) \times SU(2)$ chiral-symmetric Nambu--Jona-Lasinio model is discussed. It is shown that for a consistent simultaneous description of the processes $ρ\to e^{+}e^{-}$, $ρ\to π^{+}π^{-}$, $τ^{-} \to π^{-}π^{0} ν_τ$, and $e^{+}e^{-} \to π^{+}π^{-}$ can be constructed. Taking into account… ▽ More The possibility to use the width of the decay $ρ\to e^{+}e^{-}$ to fix the input parameter $g_ρ=5.0$ of the $SU(2) \times SU(2)$ chiral-symmetric Nambu--Jona-Lasinio model is discussed. It is shown that for a consistent simultaneous description of the processes $ρ\to e^{+}e^{-}$, $ρ\to π^{+}π^{-}$, $τ^{-} \to π^{-}π^{0} ν_τ$, and $e^{+}e^{-} \to π^{+}π^{-}$ can be constructed. Taking into account the interaction of pions in the final state appears to be important. The obtained theoretical results for the considered processes are in a satisfactory agreement with experimental data. △ Less

Submitted 5 November, 2020; v1 submitted 4 November, 2020; originally announced November 2020.

Comments: 4 pages, 6 figures, misprints are corrected

Processes $τ^- \to π^- π^0 ν_τ$ and $e^{+}e^{-} \to π^{+} π^{-}$ in the chiral NJL model with final state interactions taken into account

Authors: M. K. Volkov, A. B. Arbuzov, A. A. Pivovarov

Abstract: The processes $τ^- \to π^- π^0 ν_τ$ and $e^{+}e^{-} \to π^{+} π^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $ρ$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The resul… ▽ More The processes $τ^- \to π^- π^0 ν_τ$ and $e^{+}e^{-} \to π^{+} π^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $ρ$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data. △ Less

Submitted 23 October, 2020; v1 submitted 9 October, 2020; originally announced October 2020.

Comments: 8 pages, 8 figures, formula (10) is corrected, numerical results are slightly changed

On the mixing angle of the vector mesons $ω(782)$ and $φ(1020)$

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the present work, the mixing angle of the vector $ω(782)$ and $φ(1020)$ mesons is estimated in the framework of Nambu--Jona-Lasinio model. The decay $φ\to π^{0} γ$ is considered as a basic process to determine this angle. The obtained value is compared with the results of the other authors. Besides, the width of the decay $φ\to 3π$ and the cross-section of the process $e^{+}e^{-} \to π^{0} φ$ a… ▽ More In the present work, the mixing angle of the vector $ω(782)$ and $φ(1020)$ mesons is estimated in the framework of Nambu--Jona-Lasinio model. The decay $φ\to π^{0} γ$ is considered as a basic process to determine this angle. The obtained value is compared with the results of the other authors. Besides, the width of the decay $φ\to 3π$ and the cross-section of the process $e^{+}e^{-} \to π^{0} φ$ are calculated by using this angle. △ Less

Submitted 2 May, 2020; originally announced May 2020.

Account for axial vector mesons in the $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays

Authors: A. A. Osipov, A. A. Pivovarov, M. K. Volkov, M. M. Khalifa

Abstract: The rates and spectra of the anomalous $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays are calculated. The approach is based on the effective meson Lagrangian obtained in the Nambu-Jona-Lasinio model with vector and axial-vector mesons by integrating out quark fields. The resulting action is affected by mixing between members of pseudoscalar $J^{PC}=0^{-+}$ and axial-vector $1^{++}$ nonets that violates… ▽ More The rates and spectra of the anomalous $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays are calculated. The approach is based on the effective meson Lagrangian obtained in the Nambu-Jona-Lasinio model with vector and axial-vector mesons by integrating out quark fields. The resulting action is affected by mixing between members of pseudoscalar $J^{PC}=0^{-+}$ and axial-vector $1^{++}$ nonets that violates some low-energy theorems. In this note we point out that a gauge covariant procedure to diagonalize this mixing allows for consistent description of the $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays. △ Less

Submitted 7 March, 2020; originally announced March 2020.

Comments: 8 pages, 6 figuras

Journal ref: Phys. Rev. D 101, 094031 (2020)

The decay $τ\to K^{*0}(892) K^- ν_τ$ in the extended NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the extended Nambu -- Jona-Lasinio model, the decay width of $τ\to K^{*0}(892) K^- ν_τ$ is calculated. The contributions from the contact diagram and diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that axial-vector and vector channel with a contact diagram give a dominant contribution to… ▽ More In the extended Nambu -- Jona-Lasinio model, the decay width of $τ\to K^{*0}(892) K^- ν_τ$ is calculated. The contributions from the contact diagram and diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that axial-vector and vector channel with a contact diagram give a dominant contribution to the decay width. The obtained results for the decay width $τ\to K^{*0}(892) K^- ν_τ$ are in satisfactory agreement with experimental data. A prediction for differential distribution over the invariant mass of the meson pair $K^{*0}(892) K^-$ is given. △ Less

Submitted 20 December, 2019; originally announced December 2019.

Comments: 7 pages, 3 figures

The decay $τ\to K^{*-}(892) ην_τ$ in the NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: The decay width $τ\to K^{*-}(892) ην_τ$ was calculated in the Nambu--Jona-Lasinio model. Four channels were taken into account: the contact channel (the final states are directly producted from lepton current without any intermediate meson states), the axial-vector channel with two intermediate physical states $K_{1}(1270)$ and $K_{1}(1400)$, the vector channel with intermediate $K^{*}(892)$ meson… ▽ More The decay width $τ\to K^{*-}(892) ην_τ$ was calculated in the Nambu--Jona-Lasinio model. Four channels were taken into account: the contact channel (the final states are directly producted from lepton current without any intermediate meson states), the axial-vector channel with two intermediate physical states $K_{1}(1270)$ and $K_{1}(1400)$, the vector channel with intermediate $K^{*}(892)$ meson and the pseudoscalar channel with intermediate $K$ meson. It is shown that the first two channels give the dominant contribution to the decay width. Of the remaining two channels, the pseudoscalar channel plays a more prominent role. The final result is in satisfactory agreement with experimental data. Prediction for the differential decay width is presented. △ Less

Submitted 26 November, 2019; originally announced November 2019.

Comments: 4 pages, 3 figures

The decays $τ\to [ω(782), φ(1020)] K^{-} ν_τ$ in the extended NJL model

Authors: M. K. Volkov, A. A. Pivovarov, K. Nurlan

Abstract: In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $τ\to [ω(782), φ(1020)] K^{-} ν_τ$ were calculated. The intermediate channels with axial vector ($K_{1}(1270)$, $K_{1}(1400)$ and $K_{1}(1650)$), vector ($K^{*}(892)$ and $K^{*}(1410)$) and pseudoscalar ($K$ and $K(1460)$) mesons were considered. The results for these processes are in satisfactory agreement with the exper… ▽ More In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $τ\to [ω(782), φ(1020)] K^{-} ν_τ$ were calculated. The intermediate channels with axial vector ($K_{1}(1270)$, $K_{1}(1400)$ and $K_{1}(1650)$), vector ($K^{*}(892)$ and $K^{*}(1410)$) and pseudoscalar ($K$ and $K(1460)$) mesons were considered. The results for these processes are in satisfactory agreement with the experimental data. △ Less

Submitted 3 September, 2019; v1 submitted 7 July, 2019; originally announced July 2019.

The decays $τ\rightarrow (K, K(1460))ν_τ$ and the value of the weak decay coefficients ${F}_{K}$ and ${{F}_{{K}^{'}}}$ in the extended NJL model

Authors: M. K. Volkov, K. Nurlan, A . A. Pivovarov

Abstract: In the extended NJL model, the decay widths of $τ\rightarrow (K, K(1460))ν_τ$, $(K, K(1460))\rightarrow μν_μ$ are calculated. The contributions from intermediate axial-vector mesons ${K}_{1}(1270)$, ${K}_{1}(1400)$ and the first radially excited state ${K}_{1}(1650)$ are taken into account. Estimates for the weak decay coefficients ${F}_{K}$ and ${{F}_{{K}^{'}}}$ are given. Predictions are made fo… ▽ More In the extended NJL model, the decay widths of $τ\rightarrow (K, K(1460))ν_τ$, $(K, K(1460))\rightarrow μν_μ$ are calculated. The contributions from intermediate axial-vector mesons ${K}_{1}(1270)$, ${K}_{1}(1400)$ and the first radially excited state ${K}_{1}(1650)$ are taken into account. Estimates for the weak decay coefficients ${F}_{K}$ and ${{F}_{{K}^{'}}}$ are given. Predictions are made for the width of $τ\rightarrow K(1460)ν_τ$ decay and ${{F}_{{K}^{'}}}$ constant. △ Less

Submitted 16 June, 2019; originally announced June 2019.

Comments: 8 pages, 4 figures

The tetraquark $K_{1}(1400)$ in the decays $τ\to [ω(782), φ(1020)] K^{-} ν_τ$

Authors: M. K. Volkov, Aleksey A. Pivovarov, K. Nurlan

Abstract: In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $τ\to [ω(782), φ(1020)] K^{-} ν_τ$ were calculated. The intermediate strange quark-antiquark mesons in both the ground and the first radially excited states were taken into account. The meson $K_{1}(1400)$, being a possible candidate for the role of the tetraquark meson, was also taken into account as an intermediate stat… ▽ More In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $τ\to [ω(782), φ(1020)] K^{-} ν_τ$ were calculated. The intermediate strange quark-antiquark mesons in both the ground and the first radially excited states were taken into account. The meson $K_{1}(1400)$, being a possible candidate for the role of the tetraquark meson, was also taken into account as an intermediate state. The result for the process $τ\to ω(782) K^{-} ν_τ$ is in satisfactory agreement with the experimental data. Simultaneously, the result for the decay $τ\to φ(1020) K^{-} ν_τ$ is in agreement with the experimental data with precision $1.3 σ$. △ Less

Submitted 25 June, 2019; v1 submitted 2 March, 2019; originally announced March 2019.

Comments: Another explanation of the nature of the physical state $K_{1}(1400)$ was found

Decay rates $f_{1}(1285)\to ρ^{0}π^{+} π^{-}$ and $a_{1}(1260)\toωπ^{+}π^{-}$ in the Nambu -- Jona-Lasinio model

Authors: A. A. Osipov, A. A. Pivovarov, M. K. Volkov

Abstract: The anomalous decays $f_1(1285)\toρ^0π^+π^-$ and $a_1(1260)\toωπ^+π^-$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu -- Jona-Lasinio model. We consider the Lagrangian with $U(2)_L\times U(2)_R$ chiral symmetric four quark interactions. The theory is bosonized and corresponding effective meson vertices are obtained in the leading order of $1/N_c$ a… ▽ More The anomalous decays $f_1(1285)\toρ^0π^+π^-$ and $a_1(1260)\toωπ^+π^-$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu -- Jona-Lasinio model. We consider the Lagrangian with $U(2)_L\times U(2)_R$ chiral symmetric four quark interactions. The theory is bosonized and corresponding effective meson vertices are obtained in the leading order of $1/N_c$ and derivative expansions. The uncertainties related with the surface terms of anomalous quark triangle diagrams are fixed by the corresponding symmetry requirements. We make a numerical estimate of the decay widths $Γ(f_1(1285)\toρ^0π^+π^-)=2.78\, \mbox{MeV}$ and $Γ(a_1(1260)\toωπ^+π^-)=87\, \mbox{keV}$. Our result on the $f_1(1285)\toρ^0π^+π^-$ decay rate is in a good agreement with experiment. It is shown that a strong suppression of the $a_1(1260)\toωππ$ decay is a direct consequence of destructive interference between box and triangle anomalies. △ Less

Submitted 28 May, 2018; originally announced May 2018.

Comments: 10 pages, 6 figuras

Journal ref: Phys. Rev. D 98, 014037 (2018)

Low energy process $e^{+}e^{-} \rightarrow K^{+} K^{-}$ in the extended Nambu-Jona-Lasinio model

Authors: M. K. Volkov, K. Nurlan, A. A. Pivovarov

Abstract: In the extended Nambu-Jona-Lasinio model, the process of production of charged kaon pair on colliding electron-positron beams in the energy interval 1 - 1.7 GeV is described. In studying of this process, we take into account the contact terms when the pairs $K^{+}$ $K^{-}$ are generated by an intermediate photon, and processes with intermediate vector mesons $ρ$, $ω$ and $φ$ in the ground and in t… ▽ More In the extended Nambu-Jona-Lasinio model, the process of production of charged kaon pair on colliding electron-positron beams in the energy interval 1 - 1.7 GeV is described. In studying of this process, we take into account the contact terms when the pairs $K^{+}$ $K^{-}$ are generated by an intermediate photon, and processes with intermediate vector mesons $ρ$, $ω$ and $φ$ in the ground and in the first radially excited states. The results obtained here are compared with experimental data recently received in Novosibirsk and in Stanford. △ Less

Submitted 25 March, 2018; originally announced March 2018.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. C 98, 015206 (2018)

Anomalous decay $f_1(1285)\toπ^+π^-γ$ in the Nambu - Jona-Lasinio model

Authors: A. A. Osipov, M. K. Volkov

Abstract: Using the Nambu--Jona-Lasinio model with the $U(2)\times U(2)$ chiral symmetric effective four-quark interactions, we derive the amplitude of the radiative decay $f_1(1285) \toπ^+π^-γ$, find the decay width $Γ(f_1\toπ^+π^-γ)=346\,\mbox{keV}$ and obtain the spectral di-pion effective mass distribution. It is shown that in contrast to the majority of theoretical estimates (which consider the… ▽ More Using the Nambu--Jona-Lasinio model with the $U(2)\times U(2)$ chiral symmetric effective four-quark interactions, we derive the amplitude of the radiative decay $f_1(1285) \toπ^+π^-γ$, find the decay width $Γ(f_1\toπ^+π^-γ)=346\,\mbox{keV}$ and obtain the spectral di-pion effective mass distribution. It is shown that in contrast to the majority of theoretical estimates (which consider the $a_1(1260)$ meson exchange as the dominant one), the most relevant contribution to this process comes out from the $ρ^0$-resonance exchange related with the triangle $f_1ρ^0γ$ anomaly. The spectral function is obtained to be confronted with the future empirical data. △ Less

Submitted 24 January, 2018; originally announced January 2018.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. D 97, 074020 (2018)

$τ\to f_1 (1285)π^{-} ν_τ$ decay in the extended Nambu -- Jona-Lasinio model

Authors: M. K. Volkov, A. A. Pivovarov, A. A. Osipov

Abstract: Within the framework of the extended Nambu -- Jona-Lasinio model, we calculate the matrix element of the $τ\to f_1(1285) π^{-} ν_τ$ decay, obtain the invariant mass distribution of the $f_1π$ -system and estimate the branching ratio Br$(τ\to f_1 π^{-}ν_τ)=4.0\times 10^{-4}$. The two types of contributions are considered: the contact interaction, and the axial-vector $I^G(J^{PC})=1^-(1^{++})$ reson… ▽ More Within the framework of the extended Nambu -- Jona-Lasinio model, we calculate the matrix element of the $τ\to f_1(1285) π^{-} ν_τ$ decay, obtain the invariant mass distribution of the $f_1π$ -system and estimate the branching ratio Br$(τ\to f_1 π^{-}ν_τ)=4.0\times 10^{-4}$. The two types of contributions are considered: the contact interaction, and the axial-vector $I^G(J^{PC})=1^-(1^{++})$ resonance exchange. The latter includes the ground $a_1(1260)$ state, and its first radially excited state, $a_1(1640)$. The corrections caused by the $π-a_1$ transitions are taken into account. Our estimate is in a good agreement with the latest empirical result Br$(τ\to f_1 π^{-} ν_τ)=(3.9\pm 0.5)\times 10^{-4}$. The distribution function obtained for the decay $τ\to f_1(1285) π^{-} ν_τ$ shows a clear signal of $a_1(1640)$ resonance which should be compared with future experimental data including our estimate of the decay width $Γ(a_1(1640) \to f_1 π)=14.1\,\mbox{MeV}$. △ Less

Submitted 28 March, 2018; v1 submitted 9 January, 2018; originally announced January 2018.

Comments: 9 pages, 5 figures, has been accepted for publication in the European Physical Journal A - "Hadrons and Nuclei"

Journal ref: Eur. Phys. J. A 54, 61 (2018)

Production of $ρ(770)$, $η$ pairs in the decays $ρ(1450)\rightarrow ρ(770)η$, $τ\rightarrow ρ(770)ην_τ$, and in the process of $e^{+}e^{-} \rightarrow ρ(770)η$ in the Extended Nambu - Jona-Lasinio model

Authors: M. K. Volkov, K. Nurlan, A . A. Pivovarov

Abstract: Production of $ρ(770)$, $η$ pairs at colliding of electron-positron beams and in the decays $ρ(1450)\rightarrow ρ(770)η$, $τ\rightarrow ρ(770)ην_τ$ is calculated in the framework of the Nambu - Jona-Lasinio model. In the process of electron-positron annihilation and the $τ$ - lepton decay the contributions of the intermediate $ρ(770)$ vector meson in the ground and first radially excited state are… ▽ More Production of $ρ(770)$, $η$ pairs at colliding of electron-positron beams and in the decays $ρ(1450)\rightarrow ρ(770)η$, $τ\rightarrow ρ(770)ην_τ$ is calculated in the framework of the Nambu - Jona-Lasinio model. In the process of electron-positron annihilation and the $τ$ - lepton decay the contributions of the intermediate $ρ(770)$ vector meson in the ground and first radially excited state are taken into account. The theoretical prediction for the decay $τ\rightarrow ρ(770)ην_τ$ is given. The obtained results for other processes are in satisfactory agreement with the experimental data. △ Less

Submitted 27 November, 2017; originally announced November 2017.

Comments: 7 pages,6 figures

The production of the $f_1(1285) γ$ and $a_1(1260) γ$ in colliding $e^{+}e^{-}$-beams in threshold domain

Authors: M. K. Volkov, A. A. Pivovarov, A. A. Osipov

Abstract: The processes $e^{+}e^{-}\!\to\! (f_1(1285), a_1(1260))γ$ in threshold domain are considered in the framework of the extended Nambu--Jona-Lasinio model. The channels with the ground $ρ(770)$, $ω(782)$ and radially excited $ρ(1450)$, $ω(1420)$ intermediate meson states are taken into account. It is shown that in the process $e^{+}e^{-}\to f_1(1285)γ$, the probability of the subprocesses with $ρ$-me… ▽ More The processes $e^{+}e^{-}\!\to\! (f_1(1285), a_1(1260))γ$ in threshold domain are considered in the framework of the extended Nambu--Jona-Lasinio model. The channels with the ground $ρ(770)$, $ω(782)$ and radially excited $ρ(1450)$, $ω(1420)$ intermediate meson states are taken into account. It is shown that in the process $e^{+}e^{-}\to f_1(1285)γ$, the probability of the subprocesses with $ρ$-mesons significantly exceeds the probability of the subprocesses with $ω$-mesons, whereas, in the process $e^{+}e^{-} \to a_1(1260) γ$, $ρ$- and $ω$-channels give approximately equal contributions. The mechanism of this effect is discussed. The radiative decay widths of $ρ(1450)\!\to\! f_{1}(1285)γ$, $ω(1420)\!\to\! f_{1}(1285)γ$, $ρ(1450)\!\to\! a_1(1260)γ$ and $ω(1420)\!\to\! a_1(1260)γ$ are calculated. △ Less

Submitted 9 July, 2017; v1 submitted 4 June, 2017; originally announced June 2017.

Comments: Accepted for publication in IJMPA

The anomalous decay $f_1(1285)\toργ$ and related processes

Authors: A. A. Osipov, A. A. Pivovarov, M. K. Volkov

Abstract: We work out the low-energy expansion of the anomalous $f_1(1285)\toργ$ decay amplitude by using the Nambu--Jona-Lasinio model with $U(2)\times U(2)$ chiral symmetric four-quark interactions in the one-quark-loop approximation. The related processes $f_1(1285)\toωγ$, $a_1(1260)\toωγ$, and $a_1(1260)\toργ$, are also considered. An effective meson Lagrangian responsible for $f_1ργ$, $f_1ωγ$, $a_1ργ$… ▽ More We work out the low-energy expansion of the anomalous $f_1(1285)\toργ$ decay amplitude by using the Nambu--Jona-Lasinio model with $U(2)\times U(2)$ chiral symmetric four-quark interactions in the one-quark-loop approximation. The related processes $f_1(1285)\toωγ$, $a_1(1260)\toωγ$, and $a_1(1260)\toργ$, are also considered. An effective meson Lagrangian responsible for $f_1ργ$, $f_1ωγ$, $a_1ργ$ and $a_1ωγ$ interactions is found. The predicted radiative decay widths, $Γ_{f_1\toρ^0γ}=311\ \mbox{keV}$, $Γ_{f_1\toωγ}=34.3\ \mbox{keV}$, $Γ_{a_1\toρ^0γ}=26.8\ \mbox{keV}$, $Γ_{a_1\toωγ}=238\ \mbox{keV}$, allow an experimental test of the hypothesis that $f_1(1285)$ and $a_1(1260)$-mesons have a quark-antiquark nature. At present, only the $f_1(1285)\toργ$ decay has been measured. Our result is in remarkably good agreement with the recent data of CLAS Collaboration $Γ_{f_1\toρ^0γ}=453\pm 177\ \mbox{keV}$, but disagrees with the PDG-based estimate of $Γ_{f_1\toρ^0γ}=1326\pm 313\ \mbox{keV}$. The calculations presented require a minimum of theoretical input, and are shown to be consistent with the non-renormalization theorems of QCD. △ Less

Submitted 20 August, 2017; v1 submitted 16 May, 2017; originally announced May 2017.

Comments: 7 pages, 1 figure, appear in Physical Review D

Journal ref: Phys. Rev. D 96, 054012 (2017)

The decays $τ\to ν_τ (K^{*}(892), K^{*}(1410), K_1(1270), K_1(1650), a_1(1260), a_1(1640))$ in the Extended Nambu-Jona-Lasinio Model

Authors: M. K. Volkov, K. Nurlan

Abstract: The decays $τ\to ν_τ (K^{*}(892), K^{*}(1410), K_1(1270), K_1(1650), a_1(1260), a_1(1640))$ in the extended NJL model are calculated. The results obtained for the decays are $τ\to ν_τ (K^{*}(892), K^{*}(1410), K_1(1270))$ in a satisfactory agreement with the experimental data. There are no experimental data for other types of decay. Therefore, the obtained results should be considered as predictio… ▽ More The decays $τ\to ν_τ (K^{*}(892), K^{*}(1410), K_1(1270), K_1(1650), a_1(1260), a_1(1640))$ in the extended NJL model are calculated. The results obtained for the decays are $τ\to ν_τ (K^{*}(892), K^{*}(1410), K_1(1270))$ in a satisfactory agreement with the experimental data. There are no experimental data for other types of decay. Therefore, the obtained results should be considered as predictions for further experiments. △ Less

Submitted 27 December, 2016; originally announced December 2016.

Comments: 6 pages, 2 figures

The processes $e^{+}e^{-} \rightarrow K^{\pm} (K^{*\mp}(892), K^{*\mp}(1410))$ and $e^{+}e^{-} \rightarrow (η, η^{'}(958)) (φ(1020), φ(1680))$ in the extended Nambu-Jona-Lasinio model

Authors: M. K. Volkov, A. A. Pivovarov

Abstract: The processes $e^{+}e^{-} \rightarrow K^{\pm} K^{*\mp}(892)$ and $e^{+}e^{-} \rightarrow ηφ(1020)$ are calculated in the framework of the extended Nambu-Jona-Lasinio model. The intermediate vector mesons $ρ(770), ω(782), φ(1020)$ and their first radially-excited states are taken into account. The obtained results are in satisfactory agreement with the experimental data. The predictions for the cro… ▽ More The processes $e^{+}e^{-} \rightarrow K^{\pm} K^{*\mp}(892)$ and $e^{+}e^{-} \rightarrow ηφ(1020)$ are calculated in the framework of the extended Nambu-Jona-Lasinio model. The intermediate vector mesons $ρ(770), ω(782), φ(1020)$ and their first radially-excited states are taken into account. The obtained results are in satisfactory agreement with the experimental data. The predictions for the cross sections of the reactions $e^{+}e^{-} \rightarrow K^{\pm} K^{*\mp}(1410)$, $e^{+}e^{-} \rightarrow η^{'}(958) φ(1020)$ and $e^{+}e^{-} \rightarrow ηφ(1680)$ were made. △ Less

Submitted 1 August, 2016; originally announced August 2016.

Comments: 9 pages, 9 figures

The decay $τ\rightarrow K^{0}K^{-}ν_τ$ in the extended Nambu-Jona-Lasinio model

Authors: M. K. Volkov, A. A. Pivovarov

Abstract: The full and differential widths of the decay $τ\rightarrow K^{0}K^{-}ν_τ$ are calculated in the framework of the extended Nambu-Jona-Lasinio model. The contributions of the subprocesses with the intermediate vector mesons $ρ$(770) and $ρ$(1450) are taken into account. The obtained results are in satisfactory agreement with the experimental data. The full and differential widths of the decay $τ\rightarrow K^{0}K^{-}ν_τ$ are calculated in the framework of the extended Nambu-Jona-Lasinio model. The contributions of the subprocesses with the intermediate vector mesons $ρ$(770) and $ρ$(1450) are taken into account. The obtained results are in satisfactory agreement with the experimental data. △ Less

Submitted 11 November, 2016; v1 submitted 21 March, 2016; originally announced March 2016.

Comments: 6 pages, 3 figures

The decays $τ\rightarrow (η,η') K^{-} ν_τ$ in the extended Nambu-Jona-Lasinio model

Authors: M. K. Volkov, A. A. Pivovarov

Abstract: The decays $τ\rightarrow (η,η') K^{-} ν_τ$ are described in the framework of the extended Nambu-Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channels, the subprocesses with intermediate $K^{*}(892)$ and $K^{*}(1410)$ mesons play the main role. In the scalar channels, the subprocesses with intermed… ▽ More The decays $τ\rightarrow (η,η') K^{-} ν_τ$ are described in the framework of the extended Nambu-Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channels, the subprocesses with intermediate $K^{*}(892)$ and $K^{*}(1410)$ mesons play the main role. In the scalar channels, the subprocesses with intermediate $K_{0}^{*}(800)$ and $K_{0}^{*}(1430)$ mesons are taken into account. Scalar channels play a less important role in calculation of the full width of the decay $τ\rightarrow (η,η') K^{-} ν_τ$. The obtained results are in satisfactory agreement with the experimental data. △ Less

Submitted 15 February, 2017; v1 submitted 16 February, 2016; originally announced February 2016.

Comments: 8 pages, 4 figures

The decay $τ\rightarrow K^{-}π^{0}ν_τ$ in the Nambu-Jona-Lasinio model

Authors: M. K. Volkov, A. A. Pivovarov

Abstract: In this paper, the width of the decay $τ\rightarrow K^{-}π^{0}ν_τ$ is calculated in the framework of the Nambu-Jona-Lasinio model. The contributions of the intermediate vector $K^{*}(892)$ and scalar $K_{0}^{*}(800)$ mesons are taken into account. It is shown that the main contribution to the width of this decay is given by the subprocesses with the intermediate $W$-boson and vector $K^{*}(892)$ m… ▽ More In this paper, the width of the decay $τ\rightarrow K^{-}π^{0}ν_τ$ is calculated in the framework of the Nambu-Jona-Lasinio model. The contributions of the intermediate vector $K^{*}(892)$ and scalar $K_{0}^{*}(800)$ mesons are taken into account. It is shown that the main contribution to the width of this decay is given by the subprocesses with the intermediate $W$-boson and vector $K^{*}(892)$ meson. The scalar channel with the intermediate $K_{0}^{*}(800)$ meson gives an insignificant contribution. In Appendix, it is shown that the contribution of the subprocess with the intermediate ${K^{*}}'(1410)$ meson is negligible as well. The obtained results are in satisfactory agreement with the experimental data. △ Less

Submitted 11 November, 2016; v1 submitted 26 November, 2015; originally announced November 2015.

Comments: 7 pages, 3 figures

Decays of $τ\rightarrow ρ(770) (ρ'(1450)) ν_τ$ and $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ in the extended Nambu - Jona- Lasinio model

Authors: A. I. Ahmadov, Yu. L. Kalinovsky, M. K. Volkov

Abstract: In the extended Nambu - Jona - Lasinio model the decay widths $τ\rightarrow ρ(770) (ρ'(1450)) ν_τ$ and $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ are studied in the quark one -loop approximation. Our estimations of the decay widths $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ are in satisfactory agreement with experimantal data. In the paper, the decay widths… ▽ More In the extended Nambu - Jona - Lasinio model the decay widths $τ\rightarrow ρ(770) (ρ'(1450)) ν_τ$ and $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ are studied in the quark one -loop approximation. Our estimations of the decay widths $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ are in satisfactory agreement with experimantal data. In the paper, the decay widths $τ\rightarrow ρ(770) (ρ'(1450)) ν_τ$ are also calculated. △ Less

Submitted 4 March, 2018; v1 submitted 8 June, 2015; originally announced June 2015.

Comments: 7 pages, 2 figures

The decay $τ\to (π, π') ν_τ$ in the Nambu - Jona-Lasinio model

Authors: A. I. Ahmadov, M. K. Volkov

Abstract: In the Nambu - Jona-Lasinio model the decay widths $τ\to (π, π'(1300)) ν_τ$ were calculated. For the calculation of the decay width $τ\to πν_τ$ the standard NJL model was used with taking into account the intermediate axial-vector meson and the extended Nambu - Jona-Lasinio model with the intermediate $a_1(1260)$ and $a_1'(1647)$ mesons. These results are in good agreement with each other. For the… ▽ More In the Nambu - Jona-Lasinio model the decay widths $τ\to (π, π'(1300)) ν_τ$ were calculated. For the calculation of the decay width $τ\to πν_τ$ the standard NJL model was used with taking into account the intermediate axial-vector meson and the extended Nambu - Jona-Lasinio model with the intermediate $a_1(1260)$ and $a_1'(1647)$ mesons. These results are in good agreement with each other. For the calculation of the decay width $τ\to π' ν_τ$ extended Nambu - Jona-Lasinio model was used. The results are in satisfactory agreement with the experimental data. Numerical estimates for the constant $F_π$ and $F_{π'}$ are also in satisfactory agreement with both the experimental values for $F_π$ and the results obtained by calculations on the lattice. △ Less

Submitted 4 June, 2015; v1 submitted 13 April, 2015; originally announced April 2015.

Comments: 14 pages, 4 figures

The decay $τ\rightarrow f_1 πν_τ$ in the Nambu--Jona-Lasinio model

Authors: A. V. Vishneva, M. K. Volkov, D. G. Kostunin

Abstract: The width of the decay $τ\rightarrow f_1 πν_τ$ has recently been measured by the BaBar experiment. The estimation of this width is given in the framework of the NJL model with the axial-vector mesons. Prediction is in agreement with the experimental data. It is shown that the $π-a_1$ transition contribution plays an important role and allows us to bring the NJL prediction to the data. The width of the decay $τ\rightarrow f_1 πν_τ$ has recently been measured by the BaBar experiment. The estimation of this width is given in the framework of the NJL model with the axial-vector mesons. Prediction is in agreement with the experimental data. It is shown that the $π-a_1$ transition contribution plays an important role and allows us to bring the NJL prediction to the data. △ Less

Submitted 12 March, 2018; v1 submitted 5 May, 2014; originally announced May 2014.

Comments: 3 pages, 3 figures

Journal ref: Eur.Phys.J. A50, 137 (2014)

Radially Excited Axial-Vector Mesons in the extended Nambu--Jona-Lasinio model

Authors: A. V. Vishneva, M. K. Volkov

Abstract: The first radial excitations of axial-vector mesons are considered in the framework of the extended $U(3)\times U(3)$ Nambu--Jona-Lasinio model. We calculate the mass spectrum of $a_1$, $f_1$, and also strange axial-vector mesons. For description of radially excited states we used the form factors of polynomial type of the second order in transverse quark momentum. For the ground- and the excited-… ▽ More The first radial excitations of axial-vector mesons are considered in the framework of the extended $U(3)\times U(3)$ Nambu--Jona-Lasinio model. We calculate the mass spectrum of $a_1$, $f_1$, and also strange axial-vector mesons. For description of radially excited states we used the form factors of polynomial type of the second order in transverse quark momentum. For the ground- and the excited-state mesons consisting of light quarks we have calculated the widths of a number of strong and radiative decays. We got satisfactory agreement with experimental data for the ground states. A set of predictions for the excited states of mesons is given. △ Less

Submitted 23 May, 2014; v1 submitted 6 March, 2014; originally announced March 2014.

Comments: 6 pages, 2 figures, 1 table

Radiative decays of radially excited pseudoscalar mesons in the extended Nambu--Jona-Lasinio model

Authors: A. V. Vishneva, M. K. Volkov

Abstract: In the extended NJL model the radiative decay widths of the radially excited states of the pseudoscalar $π$, $η$, and $η'$ mesons are calculated. The predictions for the decay widths of the processes $π(1300)\longrightarrow(ρ^0,ω)γ$, $η(1295)\longrightarrow(ρ^0,ω,φ)γ$, and $η(1475)\longrightarrow(ρ^0,ω,φ)γ$ are given. Nowadays, there are no solid experimental data for these processes. The comparis… ▽ More In the extended NJL model the radiative decay widths of the radially excited states of the pseudoscalar $π$, $η$, and $η'$ mesons are calculated. The predictions for the decay widths of the processes $π(1300)\longrightarrow(ρ^0,ω)γ$, $η(1295)\longrightarrow(ρ^0,ω,φ)γ$, and $η(1475)\longrightarrow(ρ^0,ω,φ)γ$ are given. Nowadays, there are no solid experimental data for these processes. The comparison of the results obtained in the framework of the standard and the extended NJL models for decays of the ground states of mesons is given. It is shown that these calculations correspond to each other and are also in satisfactory agreement with experimental data. This allows one to expect that the extended NJL can give reliable predictions for the excited states of mesons. △ Less

Submitted 30 December, 2013; v1 submitted 5 December, 2013; originally announced December 2013.

Comments: 6 pages, 1 figure, 4 tables