Connection Between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>π</mi></mrow></msub></mrow><mn></mn><mo>(</mo><mi>t</mi><mo>)</mo><mn></mn></math> and the Amplitudes for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo>→</mo><mi>π</mi><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math>

D. A. Geffen

doi:10.1103/PhysRevLett.23.897

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Connection Between $F_{π} (t)$ and the Amplitudes for $π π \to π π$ and $π π \to π A_{1}$

D. A. Geffen

School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455

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Phys. Rev. Lett. 23, 897 – Published 13 October, 1969

DOI: https://doi.org/10.1103/PhysRevLett.23.897

Abstract

The current-algebra connection between the pion electromagnetic form factor $F_{π} (t)$ and the amplitudes for $π π \to π π$ and $π π \to π A_{1}$ is examined by explicitly extrapolating off the pion mass shell the matrix element $〈 π | A_{μ} | π π 〉$ which is taken to be dominated by $π$ and $A_{1}$ poles and possible subtractions. It is found that the connection is broken by the presence of an almost arbitrary subtraction function. In particular the $A ρ π$ interaction remains arbitrary as well as the form for $F_{π} (t)$ . The results are applied briefly to the Veneziano model.

References (6)

J. Schnitzer, Phys. Rev. Letters 22, 1154 (1969) R. Arnowitt, P. Nath, Y. Srivastava, and M. H. Friedman, 22, 1158 (1969)
G. Veneziano, Nuovo Cimento 57A, 190 (1968) J. Shapiro and J. Yellin, University of California Lawrence Radiation Laboratory Report No. UCRL-18500 (unpublished) J. A. Shapiro, Phys. Rev. 179, 1345 (1969) C. Lovelace, Phys. Letters 28B, 264 (1968) C. J. Goebel, M. L. Blackmon, and K. C. Wali, Phys. Rev. 182, 1487 (1969)
Y. Oyanagi, University of Tokyo Reports Nos. UT-16, 1969, and UT-19, 1969 (to be published)
J. L. Rosner and H. Suura, Phys. Rev. (to be published)
August 1969 preprint, P. Nath, R. Arnowitt, and M. H. Friedman
H. Suura, Phys. Rev. Letters 23, 551 (1969)

[c1] J. Schnitzer, Phys. Rev. Letters 22, 1154 (1969) R. Arnowitt, P. Nath, Y. Srivastava, and M. H. Friedman, 22, 1158 (1969)

[c2] G. Veneziano, Nuovo Cimento 57A, 190 (1968) J. Shapiro and J. Yellin, University of California Lawrence Radiation Laboratory Report No. UCRL-18500 (unpublished) J. A. Shapiro, Phys. Rev. 179, 1345 (1969) C. Lovelace, Phys. Letters 28B, 264 (1968) C. J. Goebel, M. L. Blackmon, and K. C. Wali, Phys. Rev. 182, 1487 (1969)

[c3] Y. Oyanagi, University of Tokyo Reports Nos. UT-16, 1969, and UT-19, 1969 (to be published)

[c4] J. L. Rosner and H. Suura, Phys. Rev. (to be published)

[c5] August 1969 preprint, P. Nath, R. Arnowitt, and M. H. Friedman

[c6] H. Suura, Phys. Rev. Letters 23, 551 (1969)

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Connection Between $F_{π} (t)$ and the Amplitudes for $π π \to π π$ and $π π \to π A_{1}$

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Connection Between Fπ(t) and the Amplitudes for ππ→ππ and ππ→πA1

Abstract

References (6)

Connection Between $F_{π} (t)$ and the Amplitudes for $π π \to π π$ and $π π \to π A_{1}$