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Parametrisation-free determination of the shape parameters for the pion electromagnetic form factor

  • B. AnanthanarayanEmail author
  • I. Caprini
  • Diganta Das
  • I. Sentitemsu Imsong
Regular Article - Theoretical Physics

Abstract

Recent data from high-statistics experiments that have measured the modulus of the pion electromagnetic form factor from threshold to relatively high energies are used as input in a suitable mathematical framework of analytic continuation to find stringent constraints on the shape parameters of the form factor at t=0. The method uses also as input a precise description of the phase of the form factor in the elastic region based on Fermi–Watson theorem and the analysis of the ππ scattering amplitude with dispersive Roy equations, and some information on the spacelike region coming from recent high precision experiments. Our analysis confirms the inconsistencies of several data on the modulus, especially from low energies, with analyticity and the input phase, noted in our earlier work. Using the data on the modulus from energies above 0.65 GeV, we obtain, with no specific parametrisation, the prediction \(\langle r_{\pi}^{2} \rangle\in(0.42,\,0.44)\ \text{fm}^{2}\) for the charge radius. The same formalism leads also to very narrow allowed ranges for the higher-order shape parameters at t=0, with a strong correlation among them.

Keywords

Form Factor Charge Radius Pion Form Factor BaBar Data Pion Electromagnetic Form Factor 
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.

Notes

Acknowledgements

IC acknowledges support from the Program Nucleu under Contract PN 09370102/2009, and from Program Idei-PCE, Contract No 121/2011. ISS acknowledges the support from Deutsche Forschungsgemeinschaft Research Unit FOR 1873 “Quark Flavour Physics and Effective Theories”, Contract No. KH 205/2-1.

References

  1. 1.
    S.R. Amendolia et al. (NA7 Collaboration), Nucl. Phys. B 277, 168 (1986) ADSCrossRefGoogle Scholar
  2. 2.
    C.N. Brown, C.R. Canizares, W.E. Cooper, A.M. Eisner, G.J. Feldmann, C.A. Lichtenstein, L. Litt, W. Loceretz, V.B. Montana, F.M. Pipkin, Phys. Rev. D 8, 92 (1973) ADSCrossRefGoogle Scholar
  3. 3.
    C.J. Bebek et al., Phys. Rev. D 17, 1693 (1978) ADSCrossRefGoogle Scholar
  4. 4.
    T. Horn et al. (Jefferson Lab F(pi)-2 Collaboration), Phys. Rev. Lett. 97, 192001 (2006). nucl-ex/0607005 ADSCrossRefGoogle Scholar
  5. 5.
    G.M. Huber et al. (Jefferson Lab Collaboration), Phys. Rev. C 78, 045203 (2008). 0809.3052 [nucl-ex] ADSCrossRefGoogle Scholar
  6. 6.
    B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 103, 231801 (2009). 0908.3589 [hep-ex] ADSCrossRefGoogle Scholar
  7. 7.
    F. Ambrosino et al. (KLOE Collaboration), Phys. Lett. B 670, 285 (2009). 0809.3950 [hep-ex] ADSCrossRefGoogle Scholar
  8. 8.
    F. Ambrosino et al. (KLOE Collaboration), Phys. Lett. B 700, 102 (2011). 1006.5313 [hep-ex] ADSCrossRefGoogle Scholar
  9. 9.
    R.R. Akhmetshin et al. (CMD-2 Collaboration), JETP Lett. 84, 413 (2006) [Pis’ma Zh. Eksp. Teor. Fiz., 84, 491 (2006)]. hep-ex/0610016 ADSCrossRefGoogle Scholar
  10. 10.
    R.R. Akhmetshin et al. (CMD-2 Collaboration), Phys. Lett. B 648, 28 (2007). hep-ex/0610021 ADSCrossRefGoogle Scholar
  11. 11.
    M. Fujikawa et al. (Belle Collaboration), Phys. Rev. D 78, 072006 (2008). 0805.3773 [hep-ex] ADSCrossRefGoogle Scholar
  12. 12.
    B. Ananthanarayan, G. Colangelo, J. Gasser, H. Leutwyler, Phys. Rep. 353, 207 (2001). hep-ph/0005297 ADSCrossRefzbMATHGoogle Scholar
  13. 13.
    G. Colangelo, J. Gasser, H. Leutwyler, Nucl. Phys. B 603, 125 (2001). hep-ph/0103088 ADSCrossRefGoogle Scholar
  14. 14.
    I. Caprini, G. Colangelo, H. Leutwyler, Eur. Phys. J. C 72, 1860 (2012). 1111.7160 [hep-ph] ADSCrossRefGoogle Scholar
  15. 15.
    R. Kaminski, J.R. Pelaez, F.J. Yndurain, Phys. Rev. D 77, 054015 (2008). 0710.1150 [hep-ph] ADSCrossRefGoogle Scholar
  16. 16.
    R. Garcia-Martin, R. Kaminski, J.R. Pelaez, J. Ruiz de Elvira, F.J. Yndurain, Phys. Rev. D 83, 074004 (2011). 1102.2183 [hep-ph] ADSCrossRefGoogle Scholar
  17. 17.
    S. Ciulli, C. Pomponiu, I. Sabba-Stefanescu, Phys. Rep. 17, 133 (1975) ADSCrossRefGoogle Scholar
  18. 18.
    G. Abbas, B. Ananthanarayan, I. Caprini, I.S. Imsong, S. Ramanan, Eur. Phys. J. A 45, 389 (2010). 1004.4257 [hep-ph] ADSCrossRefGoogle Scholar
  19. 19.
    I. Caprini, Eur. Phys. J. C 13, 471 (2000). hep-ph/9907227 ADSCrossRefGoogle Scholar
  20. 20.
    B. Ananthanarayan, I. Caprini, I.S. Imsong, Phys. Rev. D 83, 096002 (2011). 1102.3299 [hep-ph] ADSCrossRefGoogle Scholar
  21. 21.
    B. Ananthanarayan, I. Caprini, I.S. Imsong, Phys. Rev. D 85, 096006 (2012). 1203.5398 [hep-ph] ADSCrossRefGoogle Scholar
  22. 22.
    B. Ananthanarayan, I. Caprini, D. Das, I.S. Imsong, Eur. Phys. J. C 72, 2192 (2012). 1209.0379 [hep-ph] ADSCrossRefGoogle Scholar
  23. 23.
    G. Colangelo, M. Finkemeier, R. Urech, Phys. Rev. D 54, 4403 (1996). hep-ph/9604279 ADSCrossRefGoogle Scholar
  24. 24.
    J. Bijnens, G. Colangelo, P. Talavera, J. High Energy Phys. 9805, 014 (1998). hep-ph/9805389 ADSGoogle Scholar
  25. 25.
    J. Bijnens, P. Talavera, J. High Energy Phys. 0203, 046 (2002). hep-ph/0203049 ADSCrossRefGoogle Scholar
  26. 26.
    P. Maris, P.C. Tandy, Phys. Rev. C 61, 045202 (2000). nucl-th/9910033 ADSCrossRefGoogle Scholar
  27. 27.
    S. Aoki et al. (JLQCD Collaboration TWQCD Collaboration), Phys. Rev. D 80, 034508 (2009). 0905.2465 [hep-lat] ADSCrossRefGoogle Scholar
  28. 28.
    J.F. de Troconiz, F.J. Yndurain, Phys. Rev. D 71, 073008 (2005). hep-ph/0402285 ADSCrossRefGoogle Scholar
  29. 29.
    P. Masjuan, S. Peris, J.J. Sanz-Cillero, Phys. Rev. D 78, 074028 (2008). 0807.4893 [hep-ph] ADSCrossRefGoogle Scholar
  30. 30.
    T.N. Truong. hep-ph/9809476
  31. 31.
    R. Barate et al. (ALEPH Collaboration), Z. Phys. C 76, 15 (1997) CrossRefGoogle Scholar
  32. 32.
    G.J. Gounaris, J.J. Sakurai, Phys. Rev. Lett. 21, 244 (1968) ADSCrossRefGoogle Scholar
  33. 33.
    N.N. Meiman, Sov. Phys. JETP 17, 830 (1963) MathSciNetzbMATHGoogle Scholar
  34. 34.
    P. Duren, Theory of H p Spaces (Academic Press, New York, 1970) zbMATHGoogle Scholar
  35. 35.
    S. Anderson et al. (CLEO Collaboration), Phys. Rev. D 61, 112002 (2000). hep-ex/9910046 ADSCrossRefGoogle Scholar
  36. 36.
    H. Leutwyler. hep-ph/0212324
  37. 37.
    C. Hanhart, Phys. Lett. B 715, 170 (2012). 1203.6839 [hep-ph] ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • B. Ananthanarayan
    • 1
    Email author
  • I. Caprini
    • 2
  • Diganta Das
    • 3
  • I. Sentitemsu Imsong
    • 4
  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia
  2. 2.Horia Hulubei National Institute for Physics and Nuclear EngineeringBucharest-MagureleRomania
  3. 3.Institute of Mathematical SciencesTaramaniIndia
  4. 4.Theoretische Physik 1, Naturwissenschaftlich-Technische FakultätUniversität SiegenSiegenGermany

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