Skip to main content
SpringerLink
Log in

On properties of low-lying spin-1 hadron resonances

  • Published:
Physics of Particles and Nuclei Aims and scope Submit manuscript

Abstract

Properties of low-lying spin-1 hadron resonances are described in the review. It is shown how the Nambu–Jona-Lasinio model can be extended in the chiral invariant way by new tensor interactions. New mass formulas are obtained, which are not based on unitary symmetry groups but involve particles from different multiplets even with opposite parity. They all are in good agreement with experimental data. Dynamic properties of spin-1 mesons confirmed by the calculations performed using the QCD sum rule technique and the lattice calculations are understood and explained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. N. Bogoliubov and V. D. Shirkov, Introduction to the Theory of Quantized Fields (Nauka, Moscow, 1976, Wiley, N.Y., 1980).

    Google Scholar 

  2. V. G. Kadyshevskii, M. D. Mateev, and M. V. Chizhov, Theor. Math. Phys. 45, 1077 (1980).

    Article  Google Scholar 

  3. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).

  4. E. Kartan, Theory of Spinors (Inostrannaya Literatura, Moscow, 1947) [in Russian].

    Google Scholar 

  5. B. van der Waerdan, Nachr. Ges. Wiss. Gött., 100 (1929)

    Google Scholar 

  6. O. Laporte and G. E. Uhlenbeck, Phys. Rev. 37, 1380 (1931).

    Article  ADS  Google Scholar 

  7. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 124, 246 (1961).

    Article  ADS  Google Scholar 

  8. N. N. Bogoliubov, Preprint OIYaI D-781 (Joint Inst. Nucl. Res., Dubna, 1961).

    Google Scholar 

  9. N. N. Bogoliubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 1, 77 (1947).

    Google Scholar 

  10. N. N. Bogoliubov, Zh. Eksp. Teor. Fiz. 34, 58 (1958).

    MathSciNet  Google Scholar 

  11. S. P. Klevansky, Rev. Mod. Phys. 64, 649 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  12. M. K. Volkov, Fiz. Elem. Chastits At. Yadra 24, 81 (1993).

    Google Scholar 

  13. T. Hatsuda and T. Kunihiro, Phys. Rep. 247, 221 (1994).

    Article  ADS  Google Scholar 

  14. J. Bijnens, Phys. Rep. 265, 369 (1996).

    Article  ADS  Google Scholar 

  15. R. Alkofer, H. Reinhardt, and H. Weigel, Phys. Rep. 265, 139 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  16. H. Fritzsch and M. Gell-Mann, in Proceedings of the XVI International Conference on High-Energy Physics, Chicago, 1972, Ed. by J. D. Jackson and A. Roberts (National Accelerator Lab., Chicago, 1972), p. 135

  17. H. Fritzsch, M. Gell-Mann, and H. Leutwyler, Phys. Lett. B 47, 365 (1973).

    Article  ADS  Google Scholar 

  18. D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)

    Article  ADS  Google Scholar 

  19. H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973).

    Article  ADS  Google Scholar 

  20. C. M. Bender, F. Cooper, and G. Guralnik, S. Ann. Phys. 109, 165 (1977).

    Article  ADS  Google Scholar 

  21. K. Tamvakis and G. S. Guralnik, Phys. Rev. D: Part. Fields 18, 4551 (1978).

    Article  ADS  Google Scholar 

  22. F. Cooper, G. Guralnik, and N. Snyderman, Phys. Rev. Lett. 40, 1620 (1978).

    Article  ADS  Google Scholar 

  23. M. V. Chizhov, Theor. Math. Phys. 51, 458 (1982).

    Article  Google Scholar 

  24. G. ‘tHooft, Phys. Rev. Lett. 37, 8 (1976), Phys. Rev. D: Part. Fields 14, 3432 (1976).

    Article  ADS  Google Scholar 

  25. T. Eguchi and H. Sugawara, Phys. Rev. D: Part. Fields 10, 4257 (1974).

    Article  ADS  Google Scholar 

  26. E. Fermi, Z. Phys. 88, 161 (1934), Nuovo Cim. 11, 1 (1934).

    Article  ADS  Google Scholar 

  27. L. V. Avdeev and M. V. Chizhov, Phys. Lett. B 321, 212 (1994).

    Article  ADS  Google Scholar 

  28. C. Wetterich, Mod. Phys. Lett. A 23, 677 (2008).

    Article  ADS  Google Scholar 

  29. H. Leutwyler, Phys. Lett. B 96, 154 (1980).

    Article  ADS  Google Scholar 

  30. T. Eguchi, Phys. Rev. D: Part. Fields 14, 2755 (1976).

    Article  ADS  Google Scholar 

  31. W. Heisenberg, Z. Phys. 77, 1 (1932).

    Article  ADS  Google Scholar 

  32. J. Goldstone, Nuovo Cimento 19, 154 (1961)

    Article  MathSciNet  Google Scholar 

  33. J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  34. K. A. Olive et al. (Particle Data Group), Chin. Phys. C 38, 090001 (2014).

    Article  Google Scholar 

  35. M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968).

    Article  ADS  Google Scholar 

  36. S. L. Adler, Phys. Rev. 177, 2426 (1969)

    Article  ADS  Google Scholar 

  37. J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).

    Article  ADS  Google Scholar 

  38. S. Weinberg, Phys. Rev. Lett. 18, 507 (1967).

    Article  ADS  Google Scholar 

  39. S. S. Gershtein and Ya. B. Zel’dovich, Zh. Eksp. Teor. Fiz. 29, 698 (1955).

    Google Scholar 

  40. R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958).

    Article  ADS  MathSciNet  Google Scholar 

  41. H. J. Lipkin, Phys. Lett. B 72, 249 (1977).

    Article  ADS  Google Scholar 

  42. H. J. Lipkin, Nucl. Phys. B (Proc. Suppl.) 115, 117 (2003).

    Article  ADS  Google Scholar 

  43. J. M. Link et al., (FOCUS Collaboration), Phys. Lett. B 535, 43 (2002).

    Article  ADS  Google Scholar 

  44. S. Dimopoulos and H. Georgi, Nucl. Phys. A. 193, 150 (1981).

    Article  Google Scholar 

  45. M. V. Chizhov, Fiz. Elem. Chastits At. Yadra 26, 1322 (1995).

    Google Scholar 

  46. J. Gasser and H. Leutwyler, Ann. Phys. (N. Y., NY, U. S.), 158, 142 (1984).

    Article  ADS  Google Scholar 

  47. G. Ecker, J. Gasser, A. Pich, and E. de Rafael, Nucl. Phys. B 321, 311 (1989).

    Article  ADS  Google Scholar 

  48. G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Phys. Lett. B 223, 425 (1989).

    Article  ADS  Google Scholar 

  49. D. Kalafatis, Phys. Lett. B 313, 115 (1993).

    Article  ADS  Google Scholar 

  50. V. I. Ogievetskii and I. V. Polubarinov, Yad. Fiz. 4, 216 (1966).

    Google Scholar 

  51. U. Kalb and P. Ramon, Phys. Rev. D: Part. Fields 9, 2273 (1974)

    Article  ADS  Google Scholar 

  52. E. Cremmer and J. Scherk, Nucl. Phys. B 72, 117 (1974).

    Article  ADS  Google Scholar 

  53. A. Salam, Unification of Fundamental Forces: the First of the (1988) Dirac Memorial Lectures (Cambridge Univ., 1990).

    Book  MATH  Google Scholar 

  54. M. V. Chizhov, Phys. Lett. B 104, 449 (1981).

    Article  ADS  Google Scholar 

  55. M. V. Chizhov, Phys. Lett. B 113, 159 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  56. J. D. Bjorken, Ann. Phys. (N. Y., NY, U. S.) 24, 174 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  57. I. Bialynicki-Birula, Phys. Rev. 130, 465 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  58. A. V. Chizhov and M. V. Chizhov, Phys. Lett. B 125, 190 (1983).

    Article  ADS  Google Scholar 

  59. D. I. Kazakov and D. V. Shirkov, in High Energy Particle Interactions: Proceedings of the Conference, Smolenice, 1975, Ed. by D. Krupa and J. Pišút (VEDA, Bratislava, 1976).

  60. W. Zimmermann, Comm. Math. Phys. 97, 211 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  61. M. V. Chizhov, JINR Commun. E, 2-84-257 (Joint Inst. Nucl. Res., Dubna, 1984).

    Google Scholar 

  62. M. V. Chizhov, Extended Abstract of Cand. Sci. Dissertation, R2-82-112 (Joint Inst. Nucl. Res., Dubna, 1982)

    Google Scholar 

  63. M. V. Chizhov, Preprint OIYaI R2-84-172 (Joint Inst. Nucl. Res., Dubna, 1984).

    Google Scholar 

  64. L. V. Avdeev and M. V. Chizhov, Phys. Lett. B 145, 397 (1984)

    Article  ADS  Google Scholar 

  65. L. V. Avdeev and M. V. Chizhov, Phys. Lett. B 184, 363 (1987).

    Article  ADS  Google Scholar 

  66. J. Wess and B. Zumino, Phys. Lett. B 49, 52 (1974).

    Article  ADS  Google Scholar 

  67. M. V. Chizhov, arXiv:hep-ph/0107025.

  68. L. D. Faddeev and V. N. Popov, Phys. Lett. B 25, 29 (1967).

    Article  ADS  Google Scholar 

  69. C. N. Yang and R. L. Mills, Phys. Rev. 96, 191 (1954).

    Article  ADS  Google Scholar 

  70. K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16, 255 (1966), Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)

    Article  ADS  Google Scholar 

  71. J. J. Sakurai, Phys. Rev. Lett. 17, 552 (1966).

    Article  ADS  Google Scholar 

  72. T. A. Armstrong et al., “(WA76 Collaboration),” Phys. Lett. B 228, 536 (1989).

    Article  ADS  Google Scholar 

  73. L. J. Reinders, H. R. Rubinstein, and S. Yazaki, Nucl. Phys. B 196, 125 (1982).

    Article  ADS  Google Scholar 

  74. C. Amsler et al. (Particle Data Group), Phys. Lett. B 667, 1 (2008).

    Article  ADS  Google Scholar 

  75. M. R. Pennington, arXiv:0711.1435[hep-ph].

  76. C. McNeile and C. Michael (UKQCD Collaboration), Phys. Rev. D: Part. Fields 74, 014508 (2006)

    ADS  Google Scholar 

  77. R. Frigory, Ch. Gattringer, C. B. Lang, M. Limmer, T. Maurer, D. Mohler, A. Schäfer, arXiv:0709.4582[hep-lat].

  78. F. E. Close and A. Kirk, Z. Phys. C 76, 469 (1997).

    Article  Google Scholar 

  79. A. P. Bakulev and S. V. Mikhailov, Phys. Lett. B 436, 351 (1998).

    Article  ADS  Google Scholar 

  80. A. Abele et al. (Crystal Barrel Collaboration), Phys. Lett. B 415, 280 (1997).

    Google Scholar 

  81. D. Aston, et al. (LASS Collaboration), Phys. Lett. B 201, 573 (1988).

    Article  ADS  Google Scholar 

  82. C. G. Callan, R. Dashen, and D. J. Gross, Phys. Rev. D: Part. Fields 17, 2717 (1978).

    Article  ADS  Google Scholar 

  83. A. E. Dorokhov, JETP Lett. 77, 63 (2003).

    Article  ADS  Google Scholar 

  84. G. V. Efimov, M. A. Ivanov, R. Kh. Muradov, and M. M. Solomonovich, Pis’ma Zh. Eksp. Teor. Fiz. 34, 230 (1981).

    Google Scholar 

  85. D. Becirevic, V. Lubicz, F. Mescia, and C. Tarantino, JHEP 05, 007 (2003)

    Article  ADS  Google Scholar 

  86. V. M. Braun, T. Burch, C. Gattringer, M. Göckeler, G. Lacagnina, S. Schaefer, and A. Schäfer, Phys. Rev. D: Part. Fields 68, 054501 (2003).

  87. C. Rohrhofer, M. Pak, and L. Ya. Glozman, arXiv:1603.04665[hep-lat].

  88. O. Catà and V. Mateu, Phys. Rev. D: Part. Fields 77, 116009 (2008).

    Article  ADS  Google Scholar 

  89. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B 147, 385 (1979)

    Article  ADS  Google Scholar 

  90. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B 147, 448 (1979).

    Article  ADS  Google Scholar 

  91. P. Ball and V. M. Braun, Phys. Rev. D: Part. Fields 54, 2182 (1996).

    Article  ADS  Google Scholar 

  92. V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112, 173 (1984).

    Article  ADS  Google Scholar 

  93. V. M. Belyaev and Ya. I. Kogan, Yad. Fiz. 40, 1035 (1984).

    Google Scholar 

  94. A. P. Bakulev and S. V. Mikhailov, Eur. Phys. J. 17, 129 (2000).

    Article  ADS  Google Scholar 

  95. N. S. Craigie and J. Stern, Phys. Rev. D: Part. Fields 26, 2430 (1982).

    Article  ADS  Google Scholar 

  96. K. Jansen, C. McNeile, C. Michael, and C. Urbach, Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 80, 054510 (2009).

    Article  Google Scholar 

  97. K. Jansen, C. McNeile, C. Michael, and C. Urbach, Phys. Lett. B 690, 491 (2010).

    Article  ADS  Google Scholar 

  98. NICA White Paper. http://theor0.jinr.ru/twikicgi/view/NICA/WebHome.

Download references

Author information

Authors and Affiliations

  1. Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, Dubna, 141980, Russia

    M. V. Chizhov

  2. Centre for Space Research and Technologies, Faculty of Physics, Sofia University, Sofia, 1164, Bulgaria

    M. V. Chizhov

Authors
  1. M. V. Chizhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. V. Chizhov.

Additional information

Dedicated to the blessed memory of my teacher Vladimir Georgievich Kadyshevsky

Original Russian Text © M.V. Chizhov, 2017, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2017, Vol. 48, No. 2.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chizhov, M.V. On properties of low-lying spin-1 hadron resonances. Phys. Part. Nuclei 48, 243–266 (2017). https://doi.org/10.1134/S1063779617020034

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063779617020034

Search

Navigation