M. K. Volkov1,a, A. A. Pivovarov1,b, K. Nurlan1,2
Keywords:
chiral Lagrangians, τ decays
Topics:
Physics
, High Energy Physics (Theory)
Abstract
In the framework of the extended Nambu–Jona-Lasinio model, the processes τ → ππη(η′)ντ and τ → πηη(η′)ντ are considered taking into account mesons in the ground and first radially excited intermediate states. It is shown that in the processes τ → ππη(η′)ντ the vector channel is dominant, and in the processes τ → πηη(η′)ντ the main contribution is given by the axial-vector channel. The scalar meson a0 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 → ππηντ 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.
Acknowledgements
The authors thank Professor A. B. Arbuzov for useful discussions. This research has beenfunded by the Science Committee of the Ministry of Science and Higher Education of theRepublic of Kazakhstan Grant No. BR24992891.
References
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[31] M. K. Volkov, A. B. Arbuzov, and D. G. Kostunin, Thee+e−→η(η′)2πprocess in the extendedNambu–Jona-Lasinio model, Physical Review C 89 (1) (2014) 015202.
[32] D. Gomez Dumm and P. Roig, Resonance chiral Lagrangian analysis ofτ−→η(′)π−π0ντdecays,Physical Review D 86 (2012) 076009.
[33] M. K. Volkov, A. A. Pivovarov, and K. Nurlan, Decaysτ→f0(π,K)ντandτ→3πντaccountingfor the contribution off0(500), European Physical Journal A 61 (3) (2025) 66.
[34] D. M. Asner et al. (CLEO Collab.), Hadronic structure in the decayτ−→ντπ−π0π0and the signof the tau-neutrino helicity, Physical Review D 61 (2000) 012002.
[2] J. Gasser and H. Leutwyler, Chiral perturbation theory: Expansions in the mass of the strangequark, Nuclear Physics B 250 (1985) 465–516.
[3] Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogywith superconductivity. 1, Physical Review 122 (1961) 345–358.
[4] T. Eguchi, A new approach to collective phenomena in superconductivity models, Physical ReviewD 14 (1976) 2755.
[5] D. Ebert and M. K. Volkov, Composite meson model with vector dominance based onU(2)invari-ant four quark interactions, Zeitschrift f ̈ur Physik C 16 (1983) 205.
[6] M. K. Volkov, Meson Lagrangians in a superconductor quark model, Annals of Physics 157 (1984)282–303.
[7] M. K. Volkov, Low-energy meson physics in the quark model of superconductivity type, SovietJournal of Particles and Nuclei 17 (1986) 186 [Fizika Elementarnykh Chastits i Atomnogo Yadra17 (1986) 433 (in Russian)].
[8] D. Ebert and H. Reinhardt, Effective chiral hadron Lagrangian with anomalies and Skyrme termsfrom quark flavor dynamics, Nuclear Physics B 271 (1986) 188.
[9] U. Vogl and W. Weise, The Nambu and Jona Lasinio model: Its implications for hadrons andnuclei, Progress in Particle and Nuclear Physics 27 (1991) 195.
[10] S. P. Klevansky, The Nambu–Jona-Lasinio model of quantum chromodynamics, Reviews of Mod-ern Physics 64 (1992) 649.
[11] T. Hatsuda and T. Kunihiro, QCD phenomenology based on a chiral effective Lagrangian, PhysicsReports 247 (1994) 221.
[12] D. Ebert, H. Reinhardt, and M. K. Volkov, Effective hadron theory of QCD, Progress in Particleand Nuclear Physics 33 (1994) 1.
[13] M. K. Volkov and A. E. Radzhabov, The Nambu–Jona-Lasinio model and its development, PhysicsUspekhi 49 (2006) 551.
[14] G. ’t Hooft, Symmetry breaking through Bell–Jackiw anomalies, Physical Review Letters 37 (1976)8–11.
[15] M. K. Volkov, M. Nagy, and V. L. Yudichev, Scalar mesons in the Nambu–Jona-Lasinio model with’t Hooft interaction, Nuovo Cimento A 112 (1999) 225–232.
[16] M. K. Volkov, A. A. Pivovarov, and K. Nurlan, Description of the decayτ→Kππντin the NJL-type chiral quark model, Physical Review D 107 (11) (2023) 116009.
[17] M. K. Volkov, A. A. Pivovarov, and K. Nurlan, Three-mesonτdecays involving kaons andηmesonsin the NJL model, Physical Review D 109 (1) (2024) 016016.
[18] M. K. Volkov, A. A. Pivovarov, and K. Nurlan, Decaysτ→3Kντin theU(3)×U(3)quark NJLmodel, European Physical Journal A 595 (7) (2023) 17.
[19] J. P. Lees et al. (BaBar Collab.), Study of the processe+e−→π+π−ηusing initial state radiation,Physical Review D 97 (2018) 052007.
[20] S. S. Gribanov, A. S. Popov, R. R. Akhmetshin, A. N. Amirkhanov, A. V. Anisenkov, V. M. Aul-chenko, V. S. Banzarov, N. S. Bashtovoy, D. E. Berkaev, A. E. Bondar, et al. Measurement of thee+e−→ηπ+π−cross section with the CMD-3 detector at the VEPP-2000 collider, Journal ofExperimental and Theoretical Physics 01 (2020) 112.
[21] S. Navas et al. (Particle Data Group), Review of particle physics, Physical Review D 110 (3)(2024) 030001.
[22] V. Cherepanov and S. Eidelman, Decaysτ→η(η′)π−π0ντand CVC, Nuclear Physics B: Proceed-ings Supplements 218 (2011) 231–236.
[23] V. M. Aulchenko et al. (SND Collab.), Measurement of thee+e−→ηπ+π−cross section in thecenter-of-mass energy range 1.22–2.00 GeV with the SND detector at the VEPP-2000 collider,Physical Review D 91 (5) (2015) 052013.
[24] M. K. Volkov and C. Weiss, A chiral Lagrangian for excited pions, Physical Review D 56 (1997)221–229.
[25] M. K. Volkov, The pseudoscalar and vector excited mesons in theU(3)×U(3)chiral model, Physicsof Atomic Nuclei 60 (1997) 1920–1929.
[26] M. K. Volkov and A. B. Arbuzov, Meson production processes in electron–positron collisions andtau-lepton decays within the extended Nambu–Jona-Lasinio model, Physics Uspekhi 60 (7) (2017)643–666.
[27] M. K. Volkov, A. A. Pivovarov, and K. Nurlan, Low-energy interactions of mesons with partici-pation of the first radially excited states inU(3)×U(3)NJL model, Symmetry 14 (2) (2022)308.
[28] M. N. Achasov, A. Y. Barnyakov, K. I. Beloborodov, A. V. Berdyugin, D. E. Berkaev, A. G. Bogdan-chikov, A. A. Botov, T. V. Dimova, V. P. Druzhinin, V. B. Golubev, et al. Measurement of thee+e−→ηπ+π−cross section with the SND detector at the VEPP-2000 collider, Physical Re-view D 97 (1) (2018) 012008.
[29] K. Inami et al. (Belle Collab.), Precise measurement of hadronic tau-decays with an eta meson,Physics Letters B 672 (2009) 209–218.
[30] S. Arteaga, L. Y. Dai, A. Guevara, and P. Roig, Physical Review D 106 (9) (2022) 096016.
[31] M. K. Volkov, A. B. Arbuzov, and D. G. Kostunin, Thee+e−→η(η′)2πprocess in the extendedNambu–Jona-Lasinio model, Physical Review C 89 (1) (2014) 015202.
[32] D. Gomez Dumm and P. Roig, Resonance chiral Lagrangian analysis ofτ−→η(′)π−π0ντdecays,Physical Review D 86 (2012) 076009.
[33] M. K. Volkov, A. A. Pivovarov, and K. Nurlan, Decaysτ→f0(π,K)ντandτ→3πντaccountingfor the contribution off0(500), European Physical Journal A 61 (3) (2025) 66.
[34] D. M. Asner et al. (CLEO Collab.), Hadronic structure in the decayτ−→ντπ−π0π0and the signof the tau-neutrino helicity, Physical Review D 61 (2000) 012002.