Method for Calculating Electromagnetic Mass Differences of Hadrons: Application to the Pion and Kaon

Thomas J. Wilcox; Richard E. Norton

doi:10.1103/PhysRevD.7.879

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Method for Calculating Electromagnetic Mass Differences of Hadrons: Application to the Pion and Kaon

Thomas J. Wilcox^* and Richard E. Norton

Department of Physics, University of California, Los Angeles, California 90024

^*The research reported here constitutes part of a dissertation to be submitted to the University of California at Los Angeles in partial fulfillment of the requirements for the degree of doctor of philosophy.

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Phys. Rev. D 7, 879 – Published 1 February, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.879

Abstract

A method is presented for the calculation of hadronic electromagnetic mass differences and is applied to the calculation of $m_{π^{\pm}} - m_{π^{0}}$ and $m_{K^{\pm}} - m_{K^{0}}$ . Our results, although far from conclusive, include an explanation of the observed sign and general magnitude of $m_{K^{\pm}} - m_{K^{0}}$ . In contrast with the familiar Cottingham approach, the method apparently fails for $m_{π^{\pm}} - m_{π^{0}}$ .

References (20)

A. Zee, Phys. Reports 3C, 129 (1972)
F. Buccella, M. Cini, M. DeMaria, and B. Tirozzi, Nuovo Cimento 64A, 927 (1969) T. Das, G. Guralnik, V. Mathur, F. Low, and J. Young, Phys. Rev. Letters 18, 759 (1967) R. Socolow, Phys. Rev. 137, B1221 (1965)
H. Harari, Phys. Rev. Letters 17, 1303 (1966)
W. Cottingham, Ann. Phys. (N.Y.) 25, 424 (1963)
M. Elitzur and H. Harari, Ann. Phys. (N.Y.) 56, 81 (1970) J. Cornwall, D. Corrigan, and R. Norton, Phys. Rev. D 3, 536 (1971)
J. Moffat and A. Wright, Phys. Rev. D 5, 75 (1972) W. Ng and P. Vinciarelli, ibid. 5, 2566 (1972) R. Brandt, W. Ng, and P. Vinciarelli, University of Maryland Technical Report No. 72-054 (unpublished)
L.-F. Li and H. Pagels, Phys. Rev. Letters 26, 1204 (1971) ibid.27, 1089 (1971) Phys. Rev. D 5, 1509 (1972)
J. Ball and F. Zachariasen, Phys. Rev. 177, 2264 (1969) T. Nagylaki, Phys. Rev. D 1, 637 (1970)
S. Adler, Phys. Rev. 139, B1638 (1965)
Omitted endnote
M. Gell-Mann and F. Zacharaisen, Phys. Rev. 124, 953 (1961)
J. Sakurai, Currents and Mesons (University of Chicago Press, Chicago, 1969)
[8]
Omitted endnote
M. Gell-Mann, D. Sharp, and W. G. Wagner, Phys. Rev. Rev. Letters 8, 261 (1962)
Particle Data Group, Rev. Mod. Phys. 43, S1 (1971) V. Barnes, talk presented at the Meson Spectroscopy Workshop, Argonne National Laboratory, 1971 (unpublished) A. Firestone, in Experimental Meson Spectroscopy, edited by C. Baltay and A. Rosenfeld (Columbia University Press, New York, 1970)
Omitted endnote
K. Kawarabayashi, S. Kitakado, and H. Yabuki, Phys. Letters 28B, 432 (1969) C. Lovelace, in Proceedings of the Argonne Conference on $π - π$ and $K - π$ Interactions, edited by F. Loeffler and E. Malamud (Argonne National Lab., Argonne, Ill., 1968), p. 562
Omitted endnote
C. K. Chen, Phys. Rev. D 5, 1464 (1972)

[c1] A. Zee, Phys. Reports 3C, 129 (1972)

[c2] F. Buccella, M. Cini, M. DeMaria, and B. Tirozzi, Nuovo Cimento 64A, 927 (1969) T. Das, G. Guralnik, V. Mathur, F. Low, and J. Young, Phys. Rev. Letters 18, 759 (1967) R. Socolow, Phys. Rev. 137, B1221 (1965)

[c3] H. Harari, Phys. Rev. Letters 17, 1303 (1966)

[c4] W. Cottingham, Ann. Phys. (N.Y.) 25, 424 (1963)

[c5] M. Elitzur and H. Harari, Ann. Phys. (N.Y.) 56, 81 (1970) J. Cornwall, D. Corrigan, and R. Norton, Phys. Rev. D 3, 536 (1971)

[c6] J. Moffat and A. Wright, Phys. Rev. D 5, 75 (1972) W. Ng and P. Vinciarelli, ibid. 5, 2566 (1972) R. Brandt, W. Ng, and P. Vinciarelli, University of Maryland Technical Report No. 72-054 (unpublished)

[c7] L.-F. Li and H. Pagels, Phys. Rev. Letters 26, 1204 (1971) ibid.27, 1089 (1971) Phys. Rev. D 5, 1509 (1972)

[c8] J. Ball and F. Zachariasen, Phys. Rev. 177, 2264 (1969) T. Nagylaki, Phys. Rev. D 1, 637 (1970)

[c9] S. Adler, Phys. Rev. 139, B1638 (1965)

[c10] Omitted endnote

[c11] M. Gell-Mann and F. Zacharaisen, Phys. Rev. 124, 953 (1961)

[c12] J. Sakurai, Currents and Mesons (University of Chicago Press, Chicago, 1969)

[c13] [8]

[c14] Omitted endnote

[c15] M. Gell-Mann, D. Sharp, and W. G. Wagner, Phys. Rev. Rev. Letters 8, 261 (1962)

[c16] Particle Data Group, Rev. Mod. Phys. 43, S1 (1971) V. Barnes, talk presented at the Meson Spectroscopy Workshop, Argonne National Laboratory, 1971 (unpublished) A. Firestone, in Experimental Meson Spectroscopy, edited by C. Baltay and A. Rosenfeld (Columbia University Press, New York, 1970)

[c17] Omitted endnote

[c18] K. Kawarabayashi, S. Kitakado, and H. Yabuki, Phys. Letters 28B, 432 (1969) C. Lovelace, in Proceedings of the Argonne Conference on $π - π$ and $K - π$ Interactions, edited by F. Loeffler and E. Malamud (Argonne National Lab., Argonne, Ill., 1968), p. 562

[c19] Omitted endnote

[c20] C. K. Chen, Phys. Rev. D 5, 1464 (1972)

Physical Review D

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Method for Calculating Electromagnetic Mass Differences of Hadrons: Application to the Pion and Kaon

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