Charge Symmetry and Charge Independence

  • K. K. Seth
Conference paper


Symmetry principles occupy a hallowed place in physics, indeed in all human culture. At the level at which we believe in a friendly and benevolent Nature, we believe in symmetries. Symmetries appeal to our sense of logic, order, and beauty. Nuclear physicists are very fond of pointing out that isospin (T) invariance was the first ‘internal’ symmetry (as distinguished from space-time symmetries) to be postulated[1], initially for nucleons, and soon after for mesons as well. Isospin invariance leads to the principle of charge independence (CI) which may be stated as:

Hadronic forces are invariant under rotations in isospin space, or
$$ \left[ {{H_{{hadr}}},\vec{T}} \right] = 0 $$

Obviously, we can formulate a weaker principle, i.e., charge symmetry (CS), which is contained in charge independence, but states:

Hadronic forces are invariant under rotations by 180°in isospin space, or,
$$ \left[ {{H_{{hadr}}},{e^{{i\pi {T_2}}}}} \right] = 0 $$

This is equivalent to the statement that a system with hadronic forces only is invariant if mesons and baryons in it (π+, π-,⋯, n, p,⋯) are all replaced by their charge symmetric counterparts (π+, π-,⋯, p, n,⋯) in the same space-spin states. It may be noted[2] that since apparent charge symmetry effects (e.g., equality of π+ and π- masses) may arise as a consequence of another unrelated invariance principle (TCP, in this case), it is clearly not enough to just test CS breaking (CSB). Charge independence breaking (CIB) must be also studied.


Mass Difference Final State Interaction Pion Exchange Charge Symmetry Charge Independence 
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.
    W. Heisenberg: Z. Phys. 77 (1932) 1.MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    E. M. Henley in Isospin in Nuclear Physics, ed. D. Wilkinson, (North Holland, Amsterdam 1969) Ch. 2.Google Scholar
  3. 3.
    S. Weinberg: Trans. N.Y. Acad. Sci. 38 (1977) 185Google Scholar
  4. 3a.
    see however. D. Kaplan and A. V. Manohar: Phys. Rev. Lett. 56 (1986) 2004.ADSCrossRefGoogle Scholar
  5. 4.
    E. M. Henley, G. A. Miller in Mesons in Nuclei, eds. M. Rho and D. Wilkinson, (North Holland, Amsterdam. 1979) vol. I. p. 405.Google Scholar
  6. 5.
    E. M. Henley in Proc.Nucl. Theory Summer Workshop, Sante Barbara. (1981) ed. G. F. Bertsch. (World Scientific. Singapore. 1981) Ch. 1.Google Scholar
  7. 6.
    E. G. Adelberger in Symmetries in Nucl. Structure, eds. K. Abrahams, K. Allart and A. E. L. Dieperink. (Plenum Press, N.Y., 1982). p. 55.Google Scholar
  8. 7.
    W. T. H. van Oers, Comments Nucl. Part. Phys. 10 (1982) 251.Google Scholar
  9. 8.
    S. Schlomo: Rep. Prog. Phys. 41 (1978) 66.Google Scholar
  10. 9.
    P. U. Sauer and H. Walliser: J. Phys. G3 (1977) 1513.ADSGoogle Scholar
  11. 10.
    J. M. Allen and H. Fiedelday: Nucl. Phys. A260 (1976) 213.ADSGoogle Scholar
  12. 11.
    M. Rahman and G. A. Miller: Phys. Rev. C27 (1983) 917.ADSGoogle Scholar
  13. 12.
    B. Gibioud et. al.: Phys. Rev. Lett. 42 (1979) 1508ADSCrossRefGoogle Scholar
  14. 12a.
    Phys. Lett. 103B (1981) 9. At the symposium we were informed that this group at SIN has done a new experiment in which the γ’s as well as neutrons were detected. The results of the new experiment are stated to be consistent with those of the older one.ADSGoogle Scholar
  15. 13.
    R. M. Salter et al.: Nucl. Phys. A254 (1975) 241.ADSGoogle Scholar
  16. 14.
    D. W. Glasgow et al: Prot. Int.Conf. on Nucl. Data for basic and applied Science, Santa Fe (1985), to be published by in Radiation Effects; also D. W. Glasgow, priv.comm.Google Scholar
  17. 15.
    P. C. McNamee et al.: Nucl. Phys. A249 (1975) 483ADSGoogle Scholar
  18. 15a.
    ibid., A287 (1977) 381ADSGoogle Scholar
  19. 15b.
    J. L. Friar and B. F. Gibson: Phys. Rev. C17 (1978) 1752.ADSGoogle Scholar
  20. 16.
    A. W. Thomas, P. Bickerstaff and A. Gersten: Phys. Rev. D24 (1981) 2539.ADSGoogle Scholar
  21. 17.
    R. A. Brandenburg, S. A. Coon and P. U. Sauer: Nucl. Phys. A294 (1978) 305.ADSGoogle Scholar
  22. 18.
    S. A. Coon and M. D. Scadron: Phys. Rev. C26 (1982) 562ADSGoogle Scholar
  23. 18a.
    S. A. Coon in Proc. Workshop on Charge Symmetry, TRIUMF Report TRI-81–3 (1981).Google Scholar
  24. 19.
    H. Baier, W. Bentz, Ch. Hajduk and P. U. Sauer: Nucl. Phys. A386 (1982) 460.ADSGoogle Scholar
  25. 20.
    J. L. Friar and B. F. Gibson: Ann. Rev. Nucl. Sci. 34 (1984) 403.ADSCrossRefGoogle Scholar
  26. 21.
    J. M. Greben and A. W. Thomas: Phys. Rev. C30 (1984) 1021.ADSGoogle Scholar
  27. 21a.
    V. Koch and G. A. Miller: Phys. Rev. C31 (1985) 602.ADSGoogle Scholar
  28. 22.
    E. Pedroni et al.: Nucl. Phys. A300 (1978) 321.ADSGoogle Scholar
  29. 23.
    B. Balestri et al.: Nucl. Phys. A392 (1983) 217.ADSGoogle Scholar
  30. 24.
    T. G. Masterson et al.: Phys. Rev. Lett. 47 (1981) 220ADSCrossRefGoogle Scholar
  31. 24a.
    Phys. Rev. C26 (1982) 2091ADSGoogle Scholar
  32. 24b.
    Phys. Rev. C30 (1984) 2010.ADSGoogle Scholar
  33. 25.
    J. Frölich, and B. Saghai: Nucl. Phys. A435 (1985) 738.ADSGoogle Scholar
  34. 26.
    M. Th. Kankhasayev et al.: Phys. Lett. (submitted). Dubna preprint. E4–85–612 (1985).Google Scholar
  35. 27.
    B. M. K. Nefkens et al.: Phys. Rev. Lett. 52 (1984) 735.ADSCrossRefGoogle Scholar
  36. 28.
    Y. E. Kim: Phys. Rev. Lett. 53 (1984) 1508.ADSCrossRefGoogle Scholar
  37. 29.
    S. Barshay: Phys. Rev. C31 (1985) 2133.ADSGoogle Scholar
  38. 30.
    C. Pillai et al.: Bull.Amer. Phys. Soc. 31 (1986) 800. abst. DH2.Google Scholar
  39. 31.
    Yu. K. Akimov et al.: Sov. Phys. JETP 14 (1962) 512.Google Scholar
  40. 32.
    The Saturne Collaboration (unpublished), as reported by A. Stetz. Bull.Amer. Phys. Soc. 31 (1986) 848. abst. Hb4.Google Scholar
  41. 33.
    C. Y. Cheung: Phys. Lett. 119B (1982) 47.ADSGoogle Scholar
  42. 34.
    S. A. Coon, B. M. Preedom: Phys. Rev. C33 (1986) 605.ADSGoogle Scholar
  43. 35.
    C. L. Hollas, et al.: Phys. Rev. C24 (1981) 1561.ADSGoogle Scholar
  44. 36.
    C. Y. Cheung, E. M. Henley and G. A. Miller: Phys. Rev. Lett. 43 (1979) 1215ADSCrossRefGoogle Scholar
  45. 36a.
    Nucl. Phys. A348 (1980) 365.ADSGoogle Scholar
  46. 37.
    L. Wolfenstein: Ann. Rev. Nucl. Sci. 6 (1956) 43ADSCrossRefGoogle Scholar
  47. 38.
    L. Wolfenstein: Ann. Rev. Nucl. Sci. 6 (1956) 43.ADSCrossRefGoogle Scholar
  48. 39.
    C. Y. Cheung, E. M. Henley and G. A. Miller: Nucl. Phys. A348 (1980) 365ADSGoogle Scholar
  49. 39a.
    ibid. A305 (1978) 342.ADSGoogle Scholar
  50. 40.
    A. Gersten: Phys. Rev. C24 (1981) 2174ADSGoogle Scholar
  51. 40a.
    ibid. C18 (1978) 2252.ADSGoogle Scholar
  52. 41.
    L. Ge and J. P. Svenne: Phys. Rev. C33 (1986) 417.ADSGoogle Scholar
  53. 42.
    S. E. Vigdor et al.: Proc.Vth Internat. Symp. on Polarization Phenomena in Nucl.Phys. (Santa Fe. 1980).Google Scholar
  54. 42a.
    AIP Conf.Proc. 69 (1981) 1455ADSCrossRefGoogle Scholar
  55. 42b..
    also L. D. Knutson et al.: IUCF Scientific and Technical Report (1985) 12.Google Scholar
  56. 43.
    R. Abegg. et al.: Phys. Rev. Lett. 56 (1986) 2571; Proc. 6th Internat.Symp. on Polarization Phenomena in Nucl. Phys., Osaka, (1985).ADSCrossRefGoogle Scholar
  57. 43a.
    J. Phys. Soc. Japan. 55 (1986) 369.Google Scholar
  58. 44.
    G. A. Miller, A. W. Thomas, A. G. Williams: Phys. Rev. Lett. 56 (1986) 2567.ADSCrossRefGoogle Scholar
  59. 45.
    R. P. Bickerstaff and A. W. Thomas: Phys. Rev. D25 (1982) 1869.ADSGoogle Scholar
  60. 46.
    S. Godfrey and N. Isgur: University of Toronto Preprint TRI-PP-85–110 (Dec. 1985).Google Scholar
  61. 47.
    H. P. Noyes: Ann. Rev. Nucl. Sc. 22 (1972) 465.ADSCrossRefGoogle Scholar
  62. 48.
    C. Y. Cheung and R. Machleidt: contributed paper PANIC X, Heidelberg (1984) C13.Google Scholar
  63. 49.
    A. M. L. Messiah: Phys. Rev. 86 (1952) 432ADSCrossRefGoogle Scholar
  64. 49a.
    M. Ruderman: Phys. Rev. 87 (1952) 383.ADSCrossRefGoogle Scholar
  65. 50.
    For references to these experiments and a critical discussion of their limitations, see M. Artuso: Ph.D.dissertation, Northwestern University (1986), unpublished.Google Scholar
  66. 51.
    D. Harting et al.: Phys. Rev. Lett. 3 (1959) 52ADSCrossRefGoogle Scholar
  67. 51b.
    Phys. Rev. 119 (1960) 1716.ADSCrossRefGoogle Scholar
  68. 52.
    M. Artuso. K. K. Seth, B. Parker, R. Soundranayagam and D. Barlow, to be published.Google Scholar
  69. 53.
    H. S. Kohler: Phys. Rev. 118 (1969) 1345.ADSCrossRefGoogle Scholar
  70. 54.
    J. M. Laget and J. F. LeColley: contributed paper,PANIC X, Heidelberg (1984) E21; J. M. Laget: priv. comm.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • K. K. Seth
    • 1
  1. 1.Northwestern UniversityEvanstonUSA

Personalised recommendations