Study of the Decay <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo>→</mo><mi>π</mi><mi>π</mi><mi>γ</mi></math></span>

Naomi Levy; Paul Singer

doi:10.1103/PhysRevD.3.2134

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Study of the Decay $ω \to π π γ$

Naomi Levy^* and Paul Singer

Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel

^*Present address: Theoretical Group, DESY, 2 Hamburg 52, Germany.

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Phys. Rev. D 3, 2134 – Published 1 May, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.2134

Abstract

The effect of $π - π$ interaction in isospin-zero states on the characteristics of the $ω \to π π γ$ decay is investigated by means of partial-wave dispersion relations. With the $ρ$ -exchange contribution as the driving term and elastic unitarity for $π - π$ scattering on the right-hand cut, we arrive at integral equations whose solutions explicitly depend on the $π - π$ phase shift. Various scattering-length and resonance models are used to represent the $π - π$ phase shift. The high-energy contribution to the integral equation is treated in three ways: by subtraction, adding an effective pole on the left-hand cut, and normalizing the amplitude at the $f_{0}$ resonance to a Veneziano model for $ω \to π π γ$ . Numerical results for rate and spectrum are discussed in the light of the possibility of discriminating by experimental results among the various models for $π - π$ interaction.

References (26)

G. L. Kane, in Proceedings of the 1970 Conference on Meson Spectroscopy, Philadelphia, Pa. (unpublished) the Proceedings of the Conference on $π π$ and $K π$ Interactions, edited by F. Loeffler and E. Malamud, Argonne National Laboratory, 1969 (unpublished)
P. Singer, Phys. Rev. 128, 2789 (1962)
Particle Data Group, Phys. Letters 33B, 1 (1970)
J. Yellin, Phys. Rev. 147, 1080 (1966)
S. M. Renard, Nuovo Cimento 62A, 475 (1969)
R. Aviv and S. Nussinov, Phys. Rev. D 2, 209 (1970)
S. M. Flatté, D. O. Huwe, J. J. Murray, J. Button-Shafer, F. T. Solmitz, M. L. Stevenson, and C. Wohl, Phys. Rev. Letters 14, 1095 (1965) Phys. Rev. 145, 1050 (1966)
V. V. Barmin, A. G. Dolgolenko, Yu. S. Krestnikov, A. G. Meshkovskii, Yu. P. Nikitin, and V. A. Shebanov, Zh. Eksperim. i Teor. Fiz. 45, 1879 (1963) [Soviet Phys. JETP 18, 1289 (1964)]
Z. S. Strugalski, I. V. Chuvilo, I. A. Ivanovskaya, Z. Jablonski, T. Kanarek, L. S. Okhrimenko, E. Fenyves, T. Gemesy, S. Kranovsky, and G. Pinter, Phys. Letters 29B, 532 (1969)
W. Deinet, A. Menzione, H. Müller, H. M. Staudenmaier, S. Buniatov, and D. Schmitt, Phys. Letters 30B, 426 (1969) F. Jacquet, U. Nguyen-Khac, A. Haatuft, and A. Halstemslied, Nuovo Cimento 63A, 743 (1969)
([12])
C. Kacser, P. Singer, and T. N. Truong, Phys. Rev. 137, B1605 (1965) ibid.139, AB5 (1965)
N. Levy and P. Singer, Phys. Rev. D 3, 1028 (1971)
P. Singer, Phys. Rev. 130, 2441 (1963) ibid.161, 1694 (1967) R. N. Chaudhuri and R. Dutt, ibid. 177, 2337 (1969)
M. Sapir and P. Singer, Phys. Rev. 163, 1756 (1967)
Omitted endnote
A. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, New Jersey, 1957), p. 55
J. D. Jackson, in Dispersion Relations, edited by G. R. Screation (Oliver and Boyd, London 1960) p. 54
G. F. Chew and S. Mandelstam, Phys. Rev. 119, 467 (1960)
V. V. Serebryakov and D. V. Shirkov, Zh. Eksperim. i Teor. Fiz. 42, 610 (1962) [Soviet Phys. JETP 15, 425 (1962)]
Omitted endnote
[13]
Omitted endnote
C. Lovelace, Phys. Letters 28B, 264 (1968)
F. Berends and P. Singer, Phys. Letters 19, 249 (1965) ibid.19, 616(E), (1965)
S. C. C. Ting, in Proceedings of the Fourteenth International Conference on High Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968), p. 43

[c1] G. L. Kane, in Proceedings of the 1970 Conference on Meson Spectroscopy, Philadelphia, Pa. (unpublished) the Proceedings of the Conference on $π π$ and $K π$ Interactions, edited by F. Loeffler and E. Malamud, Argonne National Laboratory, 1969 (unpublished)

[c2] P. Singer, Phys. Rev. 128, 2789 (1962)

[c3] Particle Data Group, Phys. Letters 33B, 1 (1970)

[c4] J. Yellin, Phys. Rev. 147, 1080 (1966)

[c5] S. M. Renard, Nuovo Cimento 62A, 475 (1969)

[c6] R. Aviv and S. Nussinov, Phys. Rev. D 2, 209 (1970)

[c7] S. M. Flatté, D. O. Huwe, J. J. Murray, J. Button-Shafer, F. T. Solmitz, M. L. Stevenson, and C. Wohl, Phys. Rev. Letters 14, 1095 (1965) Phys. Rev. 145, 1050 (1966)

[c8] V. V. Barmin, A. G. Dolgolenko, Yu. S. Krestnikov, A. G. Meshkovskii, Yu. P. Nikitin, and V. A. Shebanov, Zh. Eksperim. i Teor. Fiz. 45, 1879 (1963) [Soviet Phys. JETP 18, 1289 (1964)]

[c9] Z. S. Strugalski, I. V. Chuvilo, I. A. Ivanovskaya, Z. Jablonski, T. Kanarek, L. S. Okhrimenko, E. Fenyves, T. Gemesy, S. Kranovsky, and G. Pinter, Phys. Letters 29B, 532 (1969)

[c10] W. Deinet, A. Menzione, H. Müller, H. M. Staudenmaier, S. Buniatov, and D. Schmitt, Phys. Letters 30B, 426 (1969) F. Jacquet, U. Nguyen-Khac, A. Haatuft, and A. Halstemslied, Nuovo Cimento 63A, 743 (1969)

[c11] ([12])

[c12] C. Kacser, P. Singer, and T. N. Truong, Phys. Rev. 137, B1605 (1965) ibid.139, AB5 (1965)

[c13] N. Levy and P. Singer, Phys. Rev. D 3, 1028 (1971)

[c14] P. Singer, Phys. Rev. 130, 2441 (1963) ibid.161, 1694 (1967) R. N. Chaudhuri and R. Dutt, ibid. 177, 2337 (1969)

[c15] M. Sapir and P. Singer, Phys. Rev. 163, 1756 (1967)

[c16] Omitted endnote

[c17] A. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, New Jersey, 1957), p. 55

[c18] J. D. Jackson, in Dispersion Relations, edited by G. R. Screation (Oliver and Boyd, London 1960) p. 54

[c19] G. F. Chew and S. Mandelstam, Phys. Rev. 119, 467 (1960)

[c20] V. V. Serebryakov and D. V. Shirkov, Zh. Eksperim. i Teor. Fiz. 42, 610 (1962) [Soviet Phys. JETP 15, 425 (1962)]

[c21] Omitted endnote

[c22] [13]

[c23] Omitted endnote

[c24] C. Lovelace, Phys. Letters 28B, 264 (1968)

[c25] F. Berends and P. Singer, Phys. Letters 19, 249 (1965) ibid.19, 616(E), (1965)

[c26] S. C. C. Ting, in Proceedings of the Fourteenth International Conference on High Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968), p. 43

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Study of the Decay $ω \to π π γ$

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Study of the Decay ω→ππγ

Abstract

References (26)

Study of the Decay $ω \to π π γ$