Schwinger Terms, Hard Pions, and the Structure of the Deuteron

H. J. Weber

doi:10.1103/PhysRevD.2.407

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Schwinger Terms, Hard Pions, and the Structure of the Deuteron

H. J. Weber^*

Department of Physics, University of Virginia, Charlottesville, Virginia 22903

^*Supported in part by a University of Virginia NSF Institutional Grant.

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Phys. Rev. D 2, 407 – Published 15 July, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.407

Abstract

The $npd$ vertex, Ward and Jacobi identities are used to evaluate the equal-time commutator (ETC) of the deuteron axial vector with the nucleon field. Schwinger terms are shown to be related to the deuteron wave function. They are important for nuclear short-range correlations. Ward identities yield the pole-term amplitudes for $pp \to d π^{+}$ and $pn \to d γ$ at threshold. Pion-induced nucleon-nucleon scattering is traced to the deuteron ETC with the weak axial-vector current. The Bjorken limit with respect to the deuteron yields the nonrelativistic limit of the reaction amplitudes.

Original Article

Failure of Soft-Pion Techniques for the Reaction $pp \to d π^{+}$ at Threshold

M. E. Schillaci and R. R. Silbar

Phys. Rev. 185, 1830 (1969)

References (17)

M. E. Schillaci and R. R. Silbar, Phys. Rev. 185, 1830 (1969)
S. L. Adler and R. Dashen, Current Algebras (Benjamin, New York, 1968)
K. A. Brueckner, R. Serber, and K. M. Watson, Phys. Rev. 84, 258 (1951)
H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967) I. Gerstein and H. J. Schnitzer, ibid. 170, 1638 (1968) D. A. Wray, Ann. Phys. (N.Y.) 51, 162 (1969)
H. Pietschmann, L. P. Fulcher, and J. M. Eisenberg, Phys. Rev. Letters 19, 1259 (1967) M. Ericson and A. Figureau, Nucl. Phys. B3, 609 (1967)
M. Gell-Mann, Physics 1, 63 (1964) Phys. Rev. 125, 1067 (1962)
B. Sakita, Phys. Rev. 127, 1800 (1962)
J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)
S. Ciccariello et al., Nuovo Cimento 63A, 846 (1969) H. Leutwyler, Acta Phys. Austriaca Suppl. V, 320 (1968)
R. Blankenbecler et al., Nucl. Phys. 12, 629 (1959)
M. Gourdin et al., Nuovo Cimento 37, 524 (1965)
Omitted endnote
J. D. Bjorken, Phys. Rev. 148, 1467 (1966)
R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1768 (1967) G. Veneziano, Nuovo Cimento 57A, 190 (1968)
A. E. Woodruff, Phys. Rev. 117, 1113 (1960) D. S. Koltun and A. Reitan, ibid. 141, 1413 (1966)
S. L. Adler and Y. Dothan, Phys. Rev. 151, 1267 (1966) F. E. Low, ibid. 96, 1428 (1954)
H. J. Weber, Phys. Rev. Letters 23, 178 (1969) Ann. Phys. (N.Y.) 53, 98 (1969) ibid.57, 322 (1970)

[c1] M. E. Schillaci and R. R. Silbar, Phys. Rev. 185, 1830 (1969)

[c2] S. L. Adler and R. Dashen, Current Algebras (Benjamin, New York, 1968)

[c3] K. A. Brueckner, R. Serber, and K. M. Watson, Phys. Rev. 84, 258 (1951)

[c4] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967) I. Gerstein and H. J. Schnitzer, ibid. 170, 1638 (1968) D. A. Wray, Ann. Phys. (N.Y.) 51, 162 (1969)

[c5] H. Pietschmann, L. P. Fulcher, and J. M. Eisenberg, Phys. Rev. Letters 19, 1259 (1967) M. Ericson and A. Figureau, Nucl. Phys. B3, 609 (1967)

[c6] M. Gell-Mann, Physics 1, 63 (1964) Phys. Rev. 125, 1067 (1962)

[c7] B. Sakita, Phys. Rev. 127, 1800 (1962)

[c8] J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)

[c9] S. Ciccariello et al., Nuovo Cimento 63A, 846 (1969) H. Leutwyler, Acta Phys. Austriaca Suppl. V, 320 (1968)

[c10] R. Blankenbecler et al., Nucl. Phys. 12, 629 (1959)

[c11] M. Gourdin et al., Nuovo Cimento 37, 524 (1965)

[c12] Omitted endnote

[c13] J. D. Bjorken, Phys. Rev. 148, 1467 (1966)

[c14] R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1768 (1967) G. Veneziano, Nuovo Cimento 57A, 190 (1968)

[c15] A. E. Woodruff, Phys. Rev. 117, 1113 (1960) D. S. Koltun and A. Reitan, ibid. 141, 1413 (1966)

[c16] S. L. Adler and Y. Dothan, Phys. Rev. 151, 1267 (1966) F. E. Low, ibid. 96, 1428 (1954)

[c17] H. J. Weber, Phys. Rev. Letters 23, 178 (1969) Ann. Phys. (N.Y.) 53, 98 (1969) ibid.57, 322 (1970)

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Schwinger Terms, Hard Pions, and the Structure of the Deuteron

Abstract

Original Article

Failure of Soft-Pion Techniques for the Reaction $pp \to d π^{+}$ at Threshold

References (17)

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Schwinger Terms, Hard Pions, and the Structure of the Deuteron

Abstract

Original Article

Failure of Soft-Pion Techniques for the Reaction pp→dπ+ at Threshold

References (17)

Failure of Soft-Pion Techniques for the Reaction $pp \to d π^{+}$ at Threshold