The pion form factor within the hidden local symmetry model

  • M. Benayoun
  • P. David
  • L. DelBuono
  • Ph Leruste
  • H. B. O'Connell
Original Paper


We analyze a pion form factor formulation which fulfills the Analyticity requirement within the Hidden Local Symmetry (HLS) Model. This implies an s-dependent dressing of the \(\rho-\gamma\) VMD coupling and an account of several coupled channels. The corresponding function \(F_\pi(s)\) provides nice fits of the pion form factor data from s=-0.25 to s=1 GeV2. It is shown that the coupling to \(K \overline{K}\) has little effect, while \(\omega \pi^0\) improves significantly the fit probability below the \(\phi\) mass. No need for additional states like \(\rho(1450)\) shows up in this invariant-mass range. All parameters, except for the subtraction polynomial coefficients, are fixed from the rest of the HLS phenomenology. The fits show consistency with the expected behaviour of \(F_\pi(s)\) at s=0 up to \({\cal O} (s^2)\) and with the phase shift data on \(\delta_1^1(s)\) from threshold to somewhat above the \(\phi\) mass. The \(\omega\) sector is also examined in relation with recent data from CMD-2.


Phase Shift Form Factor Additional State Local Symmetry Analyticity Requirement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1. J. F. De Troconiz, F. J. Yndurain, Precision determination of the pion form factor and calculation of the muon g-2, Phys. Rev. D 65, 093001, (2002), [arXiv:hep-ph/0106025]Google Scholar
  2. 2. M. Davier, S. Eidelman, A. Hocker, Z. Zhang, Confronting spectral functions from $e^+ e^-$ annihilation and tau decays: Consequences for the muon magnetic moment, Eur. Phys. J. C 27, 497, (2003), [arXiv:hep-ph/0208177]Google Scholar
  3. 3. A. Pich, J. Portoles, Vector form factor of the pion: A model-independent approach, [arXiv:hep-ph/0209224]Google Scholar
  4. 4. J. J. Sanz-Cillero, A. Pich, Rho meson properties in the chiral theory framework, Eur. Phys. J. C 27, 587, (2003), [arXiv:hep-ph/0208199]Google Scholar
  5. 5. B. Hayms, Nucl. Phys. B 64, 134, (1973)Google Scholar
  6. 6. R. Barate, [ALEPH Collaboration], Measurement of the spectral functions of vector current hadronic tau decays, Z. Phys. C 76, 15, (1997)Google Scholar
  7. 7. K. Ackerstaff, [OPAL Collaboration], Measurement of the strong coupling constant alpha(s) and the vector and axial-vector spectral functions in hadronic tau decays, Eur. Phys. J. C 7, 571, (1999), [arXiv:hep-ex/9808019]Google Scholar
  8. 8. S.D. Protopopescu, Pi Pi Partial Wave Analysis From Reactions Pi+ P $\to$ Pi+ Pi- Delta++ And Pi+ P $\to$ K+ K- Delta++ At 7.1-Gev/c, Phys. Rev. D 7, 1279, (1973)Google Scholar
  9. 9. S. Anderson, [CLEO Collaboration], Hadronic structure in the decay tau- $\to$ pi- pi0 nu/tau, Phys. Rev. D 61, 112002, (2000), [arXiv:hep-ex/9910046]Google Scholar
  10. 10. G. Ecker, J. Gasser, A. Pich, E. de Rafael, The Role Of Resonances In Chiral Perturbation Theory, Nucl. Phys. B 321, 311, (1989)Google Scholar
  11. 11. K. Hagiwara, [Particle Data Group Collaboration], Review Of Particle Physics, Phys. Rev. D 66, 010001, (2002)Google Scholar
  12. 12. G. Gounaris, J. Sakurai, Finite Width Corrections To The Vector Meson Dominance Prediction For Rho $\to$ E+ E-, Phys., Rev. Lett. 21, 244, (1968)Google Scholar
  13. 13. L. M. Barkov, Electromagnetic Pion Form-Factor In The Timelike Region, Nucl. Phys. B 256, 365, (1985)Google Scholar
  14. 14. A. Quenzer , Pion Form-Factor From 480-MeV To 1100-MeV, Phys. Lett. B 76, 512, (1978)Google Scholar
  15. 15. R. R. Akhmetshin, [CMD-2 Collaboration], Measurement of e+ e- $\to$ pi+ pi- cross section with CMD-2 around rho-meson, Phys. Lett. B 527, 161, (2002), [arXiv:hep-ex/0112031]Google Scholar
  16. 16. M. Benayoun, S. Eidelman, K. Maltman, H. B. O'Connell, B. Shwartz and A. G. Williams, New results in rho0 meson physics, Eur. Phys. J. C 2, 269, (1998), [arXiv:hep-ph/9707509]Google Scholar
  17. 17. M. Bando, T. Kugo, K. Yamawaki, Nonlinear Realization And Hidden Local Symmetries, Phys. Rept. 164, 217, (1988)Google Scholar
  18. 18. M. Benayoun, H. B. O'Connell, Isospin symmetry breaking within the HLS model: A full ($\rho$, $\omega$, $\Phi$) mixing scheme, Eur. Phys. J. C 22, 503, (2001), [arXiv:nucl-th/0107047]Google Scholar
  19. 19. C. D. Froggatt, J. L. Petersen, Phase Shift Analysis Of Pi+ Pi- Scattering Between 1.0-Gev And 1.8-Gev Based On Fixed Momentum Transfer Analyticity, Nucl. Phys. B 129, 89, (1977)Google Scholar
  20. 20. T. Fujiwara, T. Kugo, H. Terao, S. Uehara, K. Yamawaki, Nonabelian Anomaly And Vector Mesons As Dynamical Gauge Bosons Of Hidden Local Symmetries, Prog. Theor. Phys. 73, 926, (1985)Google Scholar
  21. 21. M. Benayoun, L. DelBuono, S. Eidelman, V.N. Ivanchenko, H.B. O'Connell, Radiative decays, nonet symmetry and SU(3) breaking, Phys. Rev. D 59, 114027, (1999), [arXiv:hep-ph/9902326]Google Scholar
  22. 22. M. Benayoun, L. DelBuono, Ph. Leruste, H. B. O'Connell, An effective approach to VMD at one loop order and the departures from ideal mixing for vector mesons, Eur. Phys. J. C 17, 303, (2000), [arXiv:nucl-th/0004005]Google Scholar
  23. 23. M. Benayoun, L. DelBuono, H. B. O'Connell, VMD, the WZW Lagrangian and ChPT: The third mixing angle, Eur. Phys. J. C 17, 593, (2000), [arXiv:hep-ph/9905350]Google Scholar
  24. 24. M. Benayoun, H. B. O'Connell, SU(3) breaking and hidden local symmetry, Phys. Rev. D 58, 074006, (1998), [arXiv:hep-ph/9804391]Google Scholar
  25. 25. M. Benayoun, H. B. O'Connell, A. G. Williams, Vector meson dominance and the rho meson, Phys. Rev. D 59, 074020, (1999), [arXiv:hep-ph/9807537]Google Scholar
  26. 26. H. B. O'Connell, B. C. Pearce, A. W. Thomas, A. G. Williams, Constraints on the momentum dependence of $\rho\!-\!\omega$ mixing, Phys. Lett. B 336, 1, (1994), [arXiv:hep-ph/9405273]Google Scholar
  27. 27. M. N. Achasov, Recent results from SND detector at VEPP-2M, [arXiv:hep-ex/0010077]Google Scholar
  28. 28. M. Bando, T. Kugo, K. Yamawaki, On The Vector Mesons As Dynamical Gauge Bosons Of Hidden Local Symmetries, Nucl. Phys. B 259, 493, (1985)Google Scholar
  29. 29. A. Bramon, A. Grau, G. Pancheri, Radiative vector meson decays in SU(3) broken effective chiral Lagrangians, Phys. Lett. B 344, 240, (1995)Google Scholar
  30. 30. H. B. O'Connell, B. C. Pearce, A. W. Thomas, A. G. Williams, Rho - omega mixing, vector meson dominance and the pion form-factor, Prog. Part. Nucl. Phys. 39, 201 (1997), [arXiv:hep-ph/9501251]Google Scholar
  31. 31. F. Klingl, N. Kaiser, W. Weise, Effective Lagrangian approach to vector mesons, their structure & decays, Z. Phys. A 356 (1996) 193 [arXiv:hep-ph/9607431]Google Scholar
  32. 32. D. Melikhov, O. Nachtmann, T. Paulus, The pion form factor at timelike momentum transfers in a dispersion approach, [arXiv:hep-ph/0209151]Google Scholar
  33. 33. R. Kaiser, H. Leutwyler, Pseudoscalar decay constants at large N(c), [arXiv:hep-ph/9806336]Google Scholar
  34. 34. J. L. Goity, A. M. Bernstein, B. R. Holstein, The decay $\pi^0 \to \gamma \gamma$ to next to leading order in chiral perturbation theory, Phys. Rev. D 66, 076014, (2002), [arXiv:hep-ph/0206007]Google Scholar
  35. 35. S. Gardner, H. B. O'Connell, $\rho\!-\!\omega$ mixing and the pion form factor in the time-like region, Phys. Rev. D 57, 2716 (1998) [Erratum-ibid. D 62, 019903 (2000)] [arXiv:hep-ph/9707385]Google Scholar
  36. 36. J. Gasser, H. Leutwyler, Chiral Perturbation Theory To One Loop, Annals Phys. 158, 142, (1984)Google Scholar
  37. 37. J. Bijnens, G. Colangelo, P. Talavera, The vector and scalar form factors of the pion to two loops, JHEP 9805, 014, (1998), [arXiv:hep-ph/9805389]Google Scholar
  38. 38. T. Hannah, The inverse amplitude method and chiral perturbation theory to two loops, Phys. Rev. D 55, 5613, (1997), [arXiv:hep-ph/9701389]Google Scholar
  39. 39. T. N. Truong, When is it possible to use perturbation technique in field theory?, [arXiv:hep-ph/0006302]Google Scholar
  40. 40. S. R. Amendolia, [NA7 Collaboration], A Measurement Of The Space - Like Pion Electromagnetic Form-Factor, Nucl. Phys. B 277, 168, (1986)Google Scholar
  41. 41. E. B. Dally, Elastic Scattering Measurement Of The Negative Pion Radius, Phys. Rev. Lett. 48, 375, (1982)Google Scholar
  42. 42. B. Costa de Beauregard, T.N. Pham, B. Pire, T.N. Truong, Inelastic Effect Of The Omega Pi0 Channel On The Pion Form-Factor, Phys. Lett. B 67, 213, (1977)Google Scholar
  43. 43. M. Bando, T. Kugo, K. Yamawaki, On The Vector Mesons As Dynamical Gauge Bosons Of Hidden Local Symmetries, Nucl. Phys. B 259, 493, (1985)Google Scholar
  44. 44. G. 't Hooft, How Instantons Solve The U(1) Problem, Phys. Rept. 142, 357 (1986)Google Scholar
  45. 45. G. Morpurgo, General Parametrization Of The V $\to$ P Gamma Meson Decays, Phys. Rev. D 42, 1497, (1990)Google Scholar
  46. 46. T. Feldmann, Quark structure of pseudoscalar mesons, Int. J. Mod. Phys. A 15, 159, (2000), [arXiv:hep-ph/9907491]Google Scholar
  47. 47. T. Feldmann, P. Kroll, Mixing of pseudoscalar mesons, Phys. Scripta T 99, 13, (2002), [arXiv:hep-ph/0201044]Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • M. Benayoun
    • 1
    • 2
  • P. David
    • 2
  • L. DelBuono
    • 2
  • Ph Leruste
    • 2
  • H. B. O'Connell
    • 3
  1. 1.Laboratoire Européen pour la Recherche NucléaireCERNGenève 23Switzerland
  2. 2.Laboratoire Européen pour la Recherche NucléaireLPNHE des Universités Paris VI et VII-IN2P3ParisFrance
  3. 3.Laboratoire Européen pour la Recherche NucléaireFermilabBataviaUSA

Personalised recommendations