Continuum Contributions to the Pion Radius

STEPHEN BLAHA

doi:10.1103/PhysRev.178.2167

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Continuum Contributions to the Pion Radius

STEPHEN BLAHA

The Rockefeller University, New York, New York 10021

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Phys. Rev. 178, 2167 – Published 25 February, 1969

DOI: https://doi.org/10.1103/PhysRev.178.2167

Abstract

We calculate continuum contributions to the mean-square radius of the pion. The calculation is based on the assumption of vector dominance of the hadronic electromagnetic current. Vector dominance is introduced through the use of field-current identities which relate the $γ π π$ form factor to the $ρ π π$ form factor. Then we assume dispersion and elastic unitarity equations in order to determine the $ρ π π$ form factor. In particular, the $π π$ interaction used in the elastic unitarity equation is assumed to consist of $t$ -channel exchange of a $ρ$ meson. We also consider the case where the $π π$ interaction consists of $t$ -channel exchange of a scalar $σ$ meson. In both cases, continuum contributions to the pion radius were found to be small compared to the pole contribution.

References (6)

M. A. B. Bég, J. Bernstein, and M. Tausner, Phys. Rev. 173, 1523 (1968)
H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967)
S. D. Drell and D. J. Silverman, Phys. Rev. Letters 20, 1325 (1968)
M. A. B. Bég and A. Pais, Phys. Rev. Letters 14, 51 (1965) N. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967)
J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967), p. 180
W. D. Walker, J. Carroll, A. Garfinkel, and B. Y. Oh, Phys. Rev. Letters 18, 630 (1967)

[c1] M. A. B. Bég, J. Bernstein, and M. Tausner, Phys. Rev. 173, 1523 (1968)

[c2] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967)

[c3] S. D. Drell and D. J. Silverman, Phys. Rev. Letters 20, 1325 (1968)

[c4] M. A. B. Bég and A. Pais, Phys. Rev. Letters 14, 51 (1965) N. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967)

[c5] J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967), p. 180

[c6] W. D. Walker, J. Carroll, A. Garfinkel, and B. Y. Oh, Phys. Rev. Letters 18, 630 (1967)

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Continuum Contributions to the Pion Radius

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