Skip to main content
SpringerLink
Log in

Vector and axial-vector correlators in a non-local chiral quark model

  • theoretical physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

Abstract.

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic \(\tau \) decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic \( {\rm\pi}^{\pm}- {\rm\pi}^{0}\) mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be \( {\rm\chi}^{\prime}(0)\approx (50 \mathrm{MeV})^{2}\). In addition, the fulfillment of the Crewther theorem is demonstrated.

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. R. Barate et al. [ALEPH Collaboration], Eur. Phys. J. C 4, 409 (1998)

    Article  Google Scholar 

  2. K. Ackerstaff et al. [OPAL Collaboration], Eur. Phys. J. C 7, 571 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. T. Das, V.S. Mathur, S. Okubo, Phys. Rev. Lett. 18, 761 (1967)

    Article  Google Scholar 

  5. T. Das, G.S. Guralnik, V.S. Mathur, F.E. Low, J.E. Young, Phys. Rev. Lett. 18, 759 (1967)

    Article  Google Scholar 

  6. J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. K.G. Chetyrkin, S. Narison, V.I. Zakharov, Nucl. Phys. B 550, 353 (1999)

    Article  Google Scholar 

  9. P. Boucaud, A. Le Yaouanc, J.P. Leroy, J. Micheli, O. Pene, J. Rodriguez-Quintero, Phys. Rev. D 63, 114003 (2001)

    Article  Google Scholar 

  10. M. Davier, L. Girlanda, A. Hocker, J. Stern, Phys. Rev. D 58, 096014 (1998)

    Article  Google Scholar 

  11. B.L. Ioffe, K.N. Zyablyuk, Nucl. Phys. A 687, 437 (2001)

    Article  Google Scholar 

  12. B.V. Geshkenbein, hep-ph/0206094

  13. T. Schafer, E.V. Shuryak, Phys. Rev. Lett. 86, 3973 (2001)

    Article  Google Scholar 

  14. S.P. Klevansky, R.H. Lemmer, hep-ph/9707206

  15. E. de Rafael, Analytic approaches to kaon physics, Plenary talk at 20th International Symposium on Lattice Field Theory (LATTICE 2002), Boston, Massachusetts, 24-29 June 2002, hep-ph/0210317

  16. I.V. Anikin, A.E. Dorokhov, L. Tomio, Phys. Part. Nucl. 31, 509 (2000) [Fiz. Elem. Chast. Atom. Yadra 31, 1023 (2000)]

    Google Scholar 

  17. S.V. Mikhailov, A.V. Radyushkin, Sov. J. Nucl. Phys. 49, 494 (1989) [Yad. Fiz. 49, 794 (1988)]

    Google Scholar 

  18. A.E. Dorokhov, S.V. Esaibegian, S.V. Mikhailov, Phys. Rev. D 56, 4062 (1997)

    Article  Google Scholar 

  19. D. Diakonov, V.Y. Petrov, Nucl. Phys. B 272, 457 (1986)

    Article  Google Scholar 

  20. J. Terning, Phys. Rev. D 44, 887 (1991)

    Article  Google Scholar 

  21. H. Ito, W. Buck, F. Gross, Phys. Rev. C 43, 2483 (1991)

    Article  Google Scholar 

  22. C.D. Roberts, A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994)

    Article  Google Scholar 

  23. R.D. Bowler, M.C. Birse, Nucl. Phys. A 582, 655 (1995)

    Article  Google Scholar 

  24. A.E. Dorokhov, L. Tomio, Phys. Rev. D 62, 014016 (2000)

    Article  Google Scholar 

  25. W. Broniowski, Mesons in non-local chiral quark models, in Hadron Physics: Effective theories of low energy QCD, Coimbra, Portugal, September 1999, AIP Conference Proceedings 508, 380 (1999), edited by A.H. Blin, B. Hiller, M.C. Ruivo, C.A. Sousa, E. van Beveren, AIP, Melville, New York, hep-ph/9911204

    Google Scholar 

  26. W. Broniowski, Gauging non-local quark models, talk presented at the Mini-Workshop on Hadrons as Solitons, Bled, Slovenia, 6-17 July 1999, hep-ph/9909438

  27. B. Golli, W. Broniowski, G. Ripka, Phys. Lett. B 437, 24 (1998)

    Article  Google Scholar 

  28. M. Praszałowicz, A. Rostworowski, Phys. Rev. D 64, 074003 (2001)

    Article  Google Scholar 

  29. I.V. Anikin, A.E. Dorokhov, L. Tomio, Phys. Lett. B 475, 361 (2000)

    Article  Google Scholar 

  30. A.E. Dorokhov, JETP Letters, 77, 63 (2003) [Pisma ZhETF 77, 68 (2003)]

    Google Scholar 

  31. R.D. Ball, G. Ripka, in Many Body Physics (Coimbra 1993), edited by C. Fiolhais, M. Fiolhais, C. Sousa, J.N. Urbano (World Scientific, Singapore 1993)

  32. E.R. Arriola, L.L. Salcedo, Phys. Lett. B 450, 225 (1999)

    Article  Google Scholar 

  33. D. Diakonov, Prog. Part. Nucl. Phys. 36, 1 (1996)

    Article  Google Scholar 

  34. J. Bijnens, C. Bruno, E. de Rafael, Nucl. Phys. B 390, 501 (1993)

    Article  Google Scholar 

  35. C. Christov, A. Blotz, H. Kim, P. Pobylitsa, T. Watabe, Th. Meissner, E. Ruiz Arriola, K. Goeke, Prog. Part. Nucl. Phys. 37, 1 (1996)

    Article  Google Scholar 

  36. E. Witten, Phys. Rev. Lett. 51, 2351 (1983)

    Article  MathSciNet  Google Scholar 

  37. C. Caso et al. [Particle Data Group Collaboration], Eur. Phys. J. C 3, 1 (1998)

    Google Scholar 

  38. S.R. Amendolia et al. [NA7 Collaboration], Nucl. Phys. B 277, 168 (1986)

    Article  Google Scholar 

  39. S. Narison, QCD spectral sum rules, Lecture notes in physics, Vol. 26 (World Scientific, Singapore 1989)

  40. E.V. Shuryak, Nucl. Phys. B 203, 93 (1982)

    Article  Google Scholar 

  41. E.V. Shuryak, Nucl. Phys. B 203, 116 (1982)

    Article  Google Scholar 

  42. S. Narison, V.I. Zakharov, Phys. Lett. B 522, 266 (2001)

    Article  MATH  Google Scholar 

  43. S. Mandelstam, Annals Phys. 19, 1 (1962)

    MATH  Google Scholar 

  44. D. Diakonov, V.Y. Petrov, Sov. Phys. JETP 62, 204 (1985) [Zh. Eksp. Teor. Fiz. 89, 361 (1985)]

    Google Scholar 

  45. B. Holdom, R. Lewis, Phys. Rev. D 51, 6318 (1995)

    Article  Google Scholar 

  46. K. Yamawaki, V.I. Zakharov, hep-ph/9406373

  47. S. Peris, E. de Rafael, Nucl. Phys. B 500, 325 (1997)

    Article  Google Scholar 

  48. H. Pagels, S. Stokar, Phys. Rev. D 20, 2947 (1979)

    Article  Google Scholar 

  49. J.S. Ball, T.W. Chiu, Phys. Rev. D 22, 2542 (1980)

    Article  Google Scholar 

  50. L. Stodolsky, P. van Baal, V.I. Zakharov, Phys. Lett. B 552, 214 (2003)

    Article  MATH  Google Scholar 

  51. D. Dudal, H. Verschelde, R.E. Browne, J.A. Gracey, hep-th/0302128

  52. A.E. Dorokhov, N.I. Kochelev, Y.A. Zubov, Int. J. Mod. Phys. A 8, 603 (1993)

    Google Scholar 

  53. R.L. Jaffe, A. Manohar, Nucl. Phys. B 337, 509 (1990)

    Article  Google Scholar 

  54. A.E. Dorokhov, W. Broniowski, Phys. Rev. D 65, 094007 (2002)

    Article  Google Scholar 

  55. D.V. Shirkov, I.L. Solovtsov, Phys. Rev. Lett. 79, 1209 (1997)

    Article  Google Scholar 

  56. S.B. Gerasimov, Meson structure constants in a model of the quark diagrams, JINR-E2-11693, 1978

  57. V.A. Petrunkin, Sov. J. Part. Nucl. 12, 278 (1981) [Fiz. Elem. Chast. Atom. Yadra 12, 692 (1981)]

    Google Scholar 

  58. M.K. Volkov, Sov. J. Part. Nucl. 17, 185 (1981) [Fiz. Elem. Chast. Atom. Yadra 17, 433 (1986)]

    Google Scholar 

  59. M.V. Terentev, Yad. Fiz. 16, 162 (1972) [Sov. J. Nucl. Phys. 16, 87 (1972)]

    Google Scholar 

  60. U. Burgi, Nucl. Phys. B 479, 392 (1996)

    Article  Google Scholar 

  61. S.P. Klevansky, R.H. Lemmer, C.A. Wilmot, Phys. Lett. B 457, 1 (1999)

    Article  Google Scholar 

  62. M. Knecht, S. Peris, E. de Rafael, Phys. Lett. B 443, 255 (1998)

    Article  Google Scholar 

  63. V.A. Andrianov, S.S. Afonin, Phys. Atom. Nucl. 65, 1862 (2002) [Yad. Fiz. 65, 1913 (2002)]

    Article  Google Scholar 

  64. B.L. Ioffe, hep-ph/9811217

  65. V.A. Novikov, M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Phys. Lett. B 86, 347 (1979)

    Article  Google Scholar 

  66. G. Veneziano, Nucl. Phys. B 159, 213 (1979)

    Article  MathSciNet  Google Scholar 

  67. R.J. Crewther, Phys. Lett. B 70, 349 (1977)

    Article  Google Scholar 

  68. K. Kawarabayashi, N. Ohta, Nucl. Phys. B 175, 477 (1980)

    Article  Google Scholar 

  69. B.L. Ioffe, A.G. Oganesian, Phys. Rev. D 57, 6590 (1998)

    Article  Google Scholar 

  70. G.M. Shore, G. Veneziano, Phys. Lett. B 244, 75 (1990)

    Article  Google Scholar 

  71. K. Fukushima, K. Ohnishi, K. Ohta, Phys. Rev. C 63, 045203 (2001)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 , Dubna, Russia

    A. E. Dorokhov

  2. Instituto de Fisica Teorica, Universidade Estudial Paulista, 01405-900 , Sao Paulo SP, Brazil

    A. E. Dorokhov

  3. The H. Niewodniczański Institute of Nuclear Physics, 31342, Cracow, Poland

    W. Broniowski

Authors
  1. A. E. Dorokhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Broniowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Dorokhov.

Additional information

Received: 9 May 2003, Revised: 22 September 2003, Published online: 4 November 2003

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dorokhov, A.E., Broniowski, W. Vector and axial-vector correlators in a non-local chiral quark model. Eur. Phys. J. C 32, 79–96 (2003). https://doi.org/10.1140/epjc/s2003-01386-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2003-01386-x

Keywords

Search

Navigation