Study of the Reaction <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mi>n</mi><mo>→</mo><mi>p</mi><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math></span> at 2.1 GeV/<i>c</i>

K. J. Braun; D. B. Cline

doi:10.1103/PhysRevD.8.3794

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Study of the Reaction $π^{+} n \to p π^{0} π^{0}$ at 2.1 GeV/c

K. J. Braun^* and D. B. Cline

University of Wisconsin, Madison, Wisconsin 53706

^*Division of Physical Oceanography RSMAS, University of Miami, 10 Rickenbacker Causeway, Miami, Florida 33149.

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Phys. Rev. D 8, 3794 – Published 1 December, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.3794

Abstract

Using the reaction $π^{+} d \to p p (MM)$ at 2.13 GeV/c with photons from the final-state $π^{0}' s$ detected by tantalum plates in the 30-in. ANL bubble chamber, a $2 π^{0}$ mass spectrum has been obtained in several ways. This spectrum is found to be in good agreement with phase-space expectations and presents no evidence for the production of a "narrow" $ε$ ( $Γ < 200$ MeV). The $2 π^{0}$ cross section for $Δ^{2} < 15 μ^{2}$ is 386 ± 80 μb. $π π$ production and scattering angular distributions are presented. Good agreement with the one-pion-exchange model is noted. Assuming that the ratios of peripheral pion-production cross sections are equal to their pole values, a new method for extracting $π π$ scattering parameters is discussed. Using this method the $I = 0$ $s$ -wave phase shift is uniquely determined from threshold to 1 GeV/ $c^{2}$ and found to be similar to the so-called UP-DOWN solutions of $s - p$ wave interference analyses. In addition, the ratios of $I = 0$ to $I = 2$ $s$ -wave scattering phase shifts and scattering lengths are found to be equal to -( ${3.2}_{- 1.0}^{+ 1.5}$ ) near $π π$ threshold. Using a dispersion sum rule, the $π π$ scattering lengths are found to be $a_{0} = + (0.15 \pm 0.08) μ^{- 1}$ and $a_{2} = - (0.05 \pm 0.01) μ^{- 1}$ .

References (38)

(a) K. J. Braun, D. B. Cline and V. Scherer, Phys. Rev. Lett. 21, 1275 (1968) (b) D. B. Cline, K. J. Braun and V. Scherer, in Proceedings of the Conference on $π π$ and $K π$ Interactions, Argonne National Laboratory, 1969, edited by F. Loeffler and E. D. Malamud (Argonne National Laboratory, Argonne, Ill., 1969), p. 179 (c) D. Cline, K. J. Braun, and V. Scherer, Nucl. Phys. B18, 77 (1970) (d) K. J. Braun, Ph.D. thesis, University of Wisconsin, Madison, 1972 (unpublished)
(a) C. Goebel, Phys. Rev. Lett. 1, 337 (1958) (b) G. F. Chew and F. E. Low, Phys. Rev. 113, 1640 (1959)
R. J. Miller, S. Lichtman, and R. B. Willmann, Purdue University Report No. C00-1428-93 (unpublished)
C. Moore, Ph.D. thesis, University of Wisconsin, 1970 (unpublished)
V. Scherer, private communication
M. A. Abolins, O. I. Dahl, J. S. Danburg, D. Davies, P. Hoch, J. Kirz, D. H. Miller, and R. Rader, paper submitted to Heidelberg International Conference on Elementary Particles, Heidelberg, Germany, 1967 (unpublished)
(a) diana, written by R. W. Hartung, was combined with R. H. Marchhash, written by , into a reconstruction-fitting program (b) O. I. Dahl, T. B. Day, and F. T. Solmitz, Alvarez Group Programming Note No. P-126, 1965 (unpublished)
(a) R. M. Morse, Ph.D. thesis, University of Wisconsin, Madison, 1969 (unpublished) (b) T. Carroll, Ph.D. thesis, University of Wisconsin, Madison, 1971 (unpublished)
(a) Program fake was written by G. Lynch, LBL Report No. UCRL-10335 (unpublished) (b) D. Dekkers et al., Phys. Lett. 11, 161 (1964)
J. Danburg, M. A. Abolins, O. I. Dahl, D. W. Davies, P. L. Hoch, J. Kirz, D. H. Miller, and R. K. Rader, Lawrence Berkeley Laboratory Report No. UCRL-19272, 1970 (unpublished)
A. S. Carroll, I. F. Corbett, C. J. S. Damerell, N. Middlemas, D. Newton, A. B. Clegg, and W. S. C. Williams, Phys. Rev. Lett. 16, 288 (1966)
D. F. Crawford and H. Messel, Phys. Rev. 128, 2352 (1962)
A. S. Carroll, I. F. Corbett, C. J. S. Damerell, N. Middlemas, D. Newton, A. B. Clegg, and W. S. C. Williams, Phys. Rev. 177, 2047 (1969)
(a) V. V. Barmin, A. G. Dolgolenko, A. G. Meshkovsky, and V. A. Shebanov, Phys. Lett. 24B, 249 (1967) (b) J. Alitti et al., 21, 354 (1966)
(a) H. R. Crouch et al., Phys. Rev. Lett. 21, 845 (1968) (b) , 21, 849 (1968)
G. C. Benson, Ph.D. thesis, University of Michigan, Ann Arbor, 1966 (unpublished)
R. J. Manning, Ph.D. thesis, University of California, Berkeley, LBL Report No. UCRL-19339, 1969 (unpublished)
(a) J. R. Bensinger, Ph.D. thesis, University of Wisconsin, Madison, 1970 (unpublished) (b) J. R. Bensinger, A. R. Erwin, M. A. Thompson, and W. D. Walker, Phys. Lett. 36B, 134 (1971)
R. K. Rader, Ph.D. thesis, University of California, Berkeley, LBL Report No. UCRL-1943, 1969 (unpublished)
Omitted endnote
J. H. Boyd, A. R. Erwin, W. D. Walker, and E. West, Phys. Rev. 166, 1458 (1968)
T. C. Bacon, W. J. Fickinger, D. G. Hill, H. W. K. Hopkins, D. K. Robinson, and E. O. Salant, Phys. Rev. 157, 1263 (1967)
Particle Data Group, Rev. Mod. Phys. 43, S1 (1971)
E. West, J. H. Boyd, A. R. Erwin, and W. D. Walker, Phys. Rev. 149, 1089 (1966)
B. G. Reynolds, J. R. Albright, R. H. Bradley, E. B. Brucher, B. C. Harms, W. C. Harrison, J. D. Kimel, J. E. Lannutti, W. H. Sims, and R. P. Wieckowicz, Phys. Rev. 184, 1424 (1969)
L. D. Jacobs, Ph.D. thesis, University of California, Berkeley, LBL Report No. UCRL-16877, 1966 (unpublished)
(a) F. E. James and H. L. Kraybill, Phys. Rev. 142, 896 (1966) (b) A. Benvenuti, Ph.D. thesis, University of Minnesota, Minneapolis, 1969 (unpublished)
I. F. Corbett et al., Phys. Rev. 156, 1451 (1967) [13]
P. Sonderegger and P. Bonamy, paper submitted to the Fifth International Conference on High Energy Physics, Lund, Sweden, 1969 (unpublished)
J. L. Petersen, Phys. Rep. 2C, 155 (1971)
(a) P. E. Schlein, Phys. Rev. Lett. 19, 1052 (1967) (b) E. Malamud and P. Schlein, 19, 1056 (1967)
W. Deinet, A. Menzione, H. Müller, H. M. Staudenmaier, S. Buniatov, and D. Schmitt, paper submitted to the Fifth International Conference on High Energy Physics, Lund, Sweden, 1969 (unpublished) W. Deinet et al., Phys. Lett. 30B, 359 (1969)
L. J. Gutay, Purdue University Report No. COD-1428-126, 1969 (unpublished) in Proceedings of the Conference on $π π$ and $K π$ Interactions, Argonne National Laboratory, 1969, edited by F. Loeffler and E. D. Malamud ([1]), p. 241
M. Bander, G. L. Shaw, and J. R. Fulco, Phys. Rev. 168, 1679 (1968)
M. R. Pennington and S. D. Protopescu, Phys. Rev. D 7, 1429 (1973)
M. G. Olsson, Wisconsin report, 1969 (unpublished)
T. Maung, G. E. Masek, E. Miller, H. Ruderman, W. Vernon, K. M. Crowe, and N. T. Dairiki, Phys. Lett. 33B, 521 (1970)
A. Mann, private communication

[c1] (a) K. J. Braun, D. B. Cline and V. Scherer, Phys. Rev. Lett. 21, 1275 (1968) (b) D. B. Cline, K. J. Braun and V. Scherer, in Proceedings of the Conference on $π π$ and $K π$ Interactions, Argonne National Laboratory, 1969, edited by F. Loeffler and E. D. Malamud (Argonne National Laboratory, Argonne, Ill., 1969), p. 179 (c) D. Cline, K. J. Braun, and V. Scherer, Nucl. Phys. B18, 77 (1970) (d) K. J. Braun, Ph.D. thesis, University of Wisconsin, Madison, 1972 (unpublished)

[c2] (a) C. Goebel, Phys. Rev. Lett. 1, 337 (1958) (b) G. F. Chew and F. E. Low, Phys. Rev. 113, 1640 (1959)

[c3] R. J. Miller, S. Lichtman, and R. B. Willmann, Purdue University Report No. C00-1428-93 (unpublished)

[c4] C. Moore, Ph.D. thesis, University of Wisconsin, 1970 (unpublished)

[c5] V. Scherer, private communication

[c6] M. A. Abolins, O. I. Dahl, J. S. Danburg, D. Davies, P. Hoch, J. Kirz, D. H. Miller, and R. Rader, paper submitted to Heidelberg International Conference on Elementary Particles, Heidelberg, Germany, 1967 (unpublished)

[c7] (a) diana, written by R. W. Hartung, was combined with R. H. Marchhash, written by , into a reconstruction-fitting program (b) O. I. Dahl, T. B. Day, and F. T. Solmitz, Alvarez Group Programming Note No. P-126, 1965 (unpublished)

[c8] (a) R. M. Morse, Ph.D. thesis, University of Wisconsin, Madison, 1969 (unpublished) (b) T. Carroll, Ph.D. thesis, University of Wisconsin, Madison, 1971 (unpublished)

[c9] (a) Program fake was written by G. Lynch, LBL Report No. UCRL-10335 (unpublished) (b) D. Dekkers et al., Phys. Lett. 11, 161 (1964)

[c10] J. Danburg, M. A. Abolins, O. I. Dahl, D. W. Davies, P. L. Hoch, J. Kirz, D. H. Miller, and R. K. Rader, Lawrence Berkeley Laboratory Report No. UCRL-19272, 1970 (unpublished)

[c11] A. S. Carroll, I. F. Corbett, C. J. S. Damerell, N. Middlemas, D. Newton, A. B. Clegg, and W. S. C. Williams, Phys. Rev. Lett. 16, 288 (1966)

[c12] D. F. Crawford and H. Messel, Phys. Rev. 128, 2352 (1962)

[c13] A. S. Carroll, I. F. Corbett, C. J. S. Damerell, N. Middlemas, D. Newton, A. B. Clegg, and W. S. C. Williams, Phys. Rev. 177, 2047 (1969)

[c14] (a) V. V. Barmin, A. G. Dolgolenko, A. G. Meshkovsky, and V. A. Shebanov, Phys. Lett. 24B, 249 (1967) (b) J. Alitti et al., 21, 354 (1966)

[c15] (a) H. R. Crouch et al., Phys. Rev. Lett. 21, 845 (1968) (b) , 21, 849 (1968)

[c16] G. C. Benson, Ph.D. thesis, University of Michigan, Ann Arbor, 1966 (unpublished)

[c17] R. J. Manning, Ph.D. thesis, University of California, Berkeley, LBL Report No. UCRL-19339, 1969 (unpublished)

[c18] (a) J. R. Bensinger, Ph.D. thesis, University of Wisconsin, Madison, 1970 (unpublished) (b) J. R. Bensinger, A. R. Erwin, M. A. Thompson, and W. D. Walker, Phys. Lett. 36B, 134 (1971)

[c19] R. K. Rader, Ph.D. thesis, University of California, Berkeley, LBL Report No. UCRL-1943, 1969 (unpublished)

[c20] Omitted endnote

[c21] J. H. Boyd, A. R. Erwin, W. D. Walker, and E. West, Phys. Rev. 166, 1458 (1968)

[c22] T. C. Bacon, W. J. Fickinger, D. G. Hill, H. W. K. Hopkins, D. K. Robinson, and E. O. Salant, Phys. Rev. 157, 1263 (1967)

[c23] Particle Data Group, Rev. Mod. Phys. 43, S1 (1971)

[c24] E. West, J. H. Boyd, A. R. Erwin, and W. D. Walker, Phys. Rev. 149, 1089 (1966)

[c25] B. G. Reynolds, J. R. Albright, R. H. Bradley, E. B. Brucher, B. C. Harms, W. C. Harrison, J. D. Kimel, J. E. Lannutti, W. H. Sims, and R. P. Wieckowicz, Phys. Rev. 184, 1424 (1969)

[c26] L. D. Jacobs, Ph.D. thesis, University of California, Berkeley, LBL Report No. UCRL-16877, 1966 (unpublished)

[c27] (a) F. E. James and H. L. Kraybill, Phys. Rev. 142, 896 (1966) (b) A. Benvenuti, Ph.D. thesis, University of Minnesota, Minneapolis, 1969 (unpublished)

[c28] I. F. Corbett et al., Phys. Rev. 156, 1451 (1967) [13]

[c29] P. Sonderegger and P. Bonamy, paper submitted to the Fifth International Conference on High Energy Physics, Lund, Sweden, 1969 (unpublished)

[c30] J. L. Petersen, Phys. Rep. 2C, 155 (1971)

[c31] (a) P. E. Schlein, Phys. Rev. Lett. 19, 1052 (1967) (b) E. Malamud and P. Schlein, 19, 1056 (1967)

[c32] W. Deinet, A. Menzione, H. Müller, H. M. Staudenmaier, S. Buniatov, and D. Schmitt, paper submitted to the Fifth International Conference on High Energy Physics, Lund, Sweden, 1969 (unpublished) W. Deinet et al., Phys. Lett. 30B, 359 (1969)

[c33] L. J. Gutay, Purdue University Report No. COD-1428-126, 1969 (unpublished) in Proceedings of the Conference on $π π$ and $K π$ Interactions, Argonne National Laboratory, 1969, edited by F. Loeffler and E. D. Malamud ([1]), p. 241

[c34] M. Bander, G. L. Shaw, and J. R. Fulco, Phys. Rev. 168, 1679 (1968)

[c35] M. R. Pennington and S. D. Protopescu, Phys. Rev. D 7, 1429 (1973)

[c36] M. G. Olsson, Wisconsin report, 1969 (unpublished)

[c37] T. Maung, G. E. Masek, E. Miller, H. Ruderman, W. Vernon, K. M. Crowe, and N. T. Dairiki, Phys. Lett. 33B, 521 (1970)

[c38] A. Mann, private communication

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Study of the Reaction $π^{+} n \to p π^{0} π^{0}$ at 2.1 GeV/c

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References (38)

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Study of the Reaction π+n→pπ0π0 at 2.1 GeV/c

Abstract

References (38)

Study of the Reaction $π^{+} n \to p π^{0} π^{0}$ at 2.1 GeV/c