Decay Spectra of Particles and Resonances Produced in a Central Plateau

R. Michael Barnett; D. Silverman

doi:10.1103/PhysRevD.8.4151

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Decay Spectra of Particles and Resonances Produced in a Central Plateau

R. Michael Barnett and D. Silverman^*

University of California, Irvine, Irvine, California 92664

^*Work supported in part by the National Science Foundation.

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Phys. Rev. D 8, 4151 – Published 1 December, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.4151

Abstract

We consider the two-body decay of the spinless resonance or particle produced in a central plateau, with an arbitrary transverse-momentum spectrum. The spectrum of the decay products is calculated exactly as an integral over the spectrum of the centrally produced resonance or particle. Special forms applicable to large and small momentum transfer are presented along with an accurate inversion formula. We show how the large-transverse-momentum behavior of the resonance production is replicated in the decay products. The decay $π^{0} \to γ + γ$ is considered in detail.

References (14)

J. Sens, in Proceedings of the Fourth International Conference on High Energy Collisions, Oxford, 1972, edited by J. R. Smith (Rutherford High Energy Laboratory, Chilton, Didcot, Berkshire, England, 1972), p. 177
R. M. Barnett and D. Silverman, Phys. Lett. 44B, 281 (1973)
R. M. Barnett and D. Silverman, Phys. Rev. D 8, 2108 (1973)
D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962)
R. M. Sternheimer, Phys. Rev. 99, 277 (1955)
B. Webber, Phys. Rev. Lett. 27, 448 (1971)
R. N. Cahn, Phys. Rev. D 7, 247 (1973) Phys. Rev. Lett. 29, 1481 (1972)
G. I. Kopylov, Nucl. Phys. B52, 126 (1973)
R. G. Glasser, Phys. Rev. D 6, 1993 (1972)
S. S. Pinsky and P. R. Stevens, Phys. Rev. D (to be published)
J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), p. 285
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), Eqs. 3.147.3, 8.112.1, and 8.113.1
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Eq. 15. Eq. 15.3.13
[8]

[c1] J. Sens, in Proceedings of the Fourth International Conference on High Energy Collisions, Oxford, 1972, edited by J. R. Smith (Rutherford High Energy Laboratory, Chilton, Didcot, Berkshire, England, 1972), p. 177

[c2] R. M. Barnett and D. Silverman, Phys. Lett. 44B, 281 (1973)

[c3] R. M. Barnett and D. Silverman, Phys. Rev. D 8, 2108 (1973)

[c4] D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962)

[c5] R. M. Sternheimer, Phys. Rev. 99, 277 (1955)

[c6] B. Webber, Phys. Rev. Lett. 27, 448 (1971)

[c7] R. N. Cahn, Phys. Rev. D 7, 247 (1973) Phys. Rev. Lett. 29, 1481 (1972)

[c8] G. I. Kopylov, Nucl. Phys. B52, 126 (1973)

[c9] R. G. Glasser, Phys. Rev. D 6, 1993 (1972)

[c10] S. S. Pinsky and P. R. Stevens, Phys. Rev. D (to be published)

[c11] J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), p. 285

[c12] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), Eqs. 3.147.3, 8.112.1, and 8.113.1

[c13] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Eq. 15. Eq. 15.3.13

[c14] [8]

Physical Review D

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Decay Spectra of Particles and Resonances Produced in a Central Plateau

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