Analysis of the Low-Energy π±p Elastic-Scattering Data
Affiliation(s)
Centre for Applied Mathematics and Physics, Zurich University of Applied Sciences, Winterthur, Switzerland. Institut fur Theoretische Physik der Universitat, Zurich, Switzerland.
Centre for Applied Mathematics and Physics, Zurich University of Applied Sciences, Winterthur, Switzerland. Institut fur Theoretische Physik der Universitat, Zurich, Switzerland.
ABSTRACT
We report the results of a phase-shift analysis (PSA) of the low-energy π±p elastic-scattering data. Following the method which we had set forth in our previous PSA [1], we first investigate the self-consistency of the low-energy π±p elastic-scattering databases, via two separate analyses of (first) the π+p and (subsequently) the π-p elastic-scattering data. There are two main differences to our previous PSA: 1) we now perform only one test for the acceptance of each data set (based on its contribution to the overall
2) and 2) we adopt a more stringent acceptance criterion in the statistical tests. We show that it is possible to obtain self-consistent databases after removing a very small amount of the data (4.57% of the initial database). We subsequently fit the ETH model [38] to the truncatedπ±p elastic-scattering databases. The model-parameter values show reasonable stability when subjected to different criteria for the rejection of single data points and entire data sets. Our result for the pseudovector πNN coupling constant is 0.0726±0.0014. We extract the scattering lengths and volumes, as well as the s- and p-wave hadronic phase shifts up to T = 100 MeV. Large differences in the s-wave part of the interaction can be seen when comparing our hadronic phase shifts with the current SAID solution (WI08); there is general agreement in the p waves, save for the 
~1/21- hadronic phase shift.
We report the results of a phase-shift analysis (PSA) of the low-energy π±p elastic-scattering data. Following the method which we had set forth in our previous PSA [1], we first investigate the self-consistency of the low-energy π±p elastic-scattering databases, via two separate analyses of (first) the π+p and (subsequently) the π-p elastic-scattering data. There are two main differences to our previous PSA: 1) we now perform only one test for the acceptance of each data set (based on its contribution to the overall
KEYWORDS
πN Elastic Scattering; πN Hadronic Phase Shifts;πN Coupling Constants; πN Threshold Constants
πN Elastic Scattering; πN Hadronic Phase Shifts;πN Coupling Constants; πN Threshold Constants
Cite this paper
E. Matsinos and G. Rasche, "Analysis of the Low-Energy π±p Elastic-Scattering Data," Journal of Modern Physics, Vol. 3 No. 10, 2012, pp. 1369-1387. doi: 10.4236/jmp.2012.310174.
E. Matsinos and G. Rasche, "Analysis of the Low-Energy π±p Elastic-Scattering Data," Journal of Modern Physics, Vol. 3 No. 10, 2012, pp. 1369-1387. doi: 10.4236/jmp.2012.310174.
References
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Woolcock, “Electromagnetic Corrections for the Analysis of Low Energy π ? p Scattering Data,” Nuclear Physics A, Vol. 686, No. 1-4, 2001, pp. 463-477. doi:10.1016/S0375-9474(00)00604-7 [6] K. Nakamura, et al. (Particle Data Group), “Review of Particle Physics,” Journal of Physics G, Vol. 37, No. 7A, 2010, Article ID: 075021. doi:10.1088/0954-3899/37/7A/075021 [7] W. R. Gibbs, L. Ai and W. B. Kaufmann, “Isospin Breaking in Low-Energy Pion-Nucleon Scattering,” Physical Review Letters, Vol. 74, No. 19, 1995, pp. 3740-3743. doi:10.1103/PhysRevLett.74.3740 [8] E. Matsinos, “Isospin Violation in the πN System at Low Energies,” Physical Review C, Vol. 56, No. 6, 1997, pp. 3014-3025. doi:10.1103/PhysRevC.56.3014 [9] R. A. Arndt and L. D. Roper, “The Use of Partial-Wave Representations in the Planning of Scattering Measurements. Application to 330 MeV np Scattering,” Nuclear Physics B, Vol. 50, No. 1, 1972, pp. 285-300. doi:10.1016/S0550-3213(72)80019-1 [10] E.G. Auld, et al., “π+ - p Elastic Scattering at 47.9 MeV,” Canadian Journal of Physics, Vol. 57, No. 1, 1979, pp. 73- 78. doi:10.1139/p79-008 [11] B. G. Ritchie, et al., “π+p Scattering at 65 to 140 MeV,” Physics Letters B, Vol. 125, No. 2-3, 1983, pp. 128-32. doi:10.1016/0370-2693(83)91251-0 [12] J. S. Frank, et al., “Measurement of Low-Energy Elastic π±p Differential cross Sections,” Physical Review D, Vol. 28, No. 7, 1983, pp. 1569-1585. doi:10.1103/PhysRevD.28.1569 [13] J. T. Brack, et al., “πp Elastic Scattering from 67 to 139 MeV,” Physical Review C, Vol. 34, No. 5, 1986, pp. 1771-1778. doi:10.1103/PhysRevC.34.1771 [14] J. T. Brack, et al., “Large-Angleπ±p Elastic Scattering at 66.8 MeV,” Physical Review C, Vol. 38, No. 5, 1988, pp. 2427-2429. doi:10.1103/PhysRevC.38.2427 [15] U. Wiedner, et al., “Hidden Strangeness in the Proton? Determination of the Real Part of the Isospin-Even Forward-Scattering Amplitude of Pion-Nucleon Scattering at 54.3 MeV,” Physical Review D, Vol. 40, No. 11, 1989, pp. 3568-3581. doi:10.1103/PhysRevD.40.3568 [16] J. T. Brack, et al., “Absolute Differential cross Sections forπ±p Elastic Scattering at 30 ≤ Tπ ≤ 67 MeV,” Physical Review C, Vol. 41, No. 5, 1990, pp. 2202-2214. doi:10.1103/PhysRevC.41.2202 [17] J. T. Brack, et al., “Forward Angleπ±p Elastic Scattering Differential cross Sections at Tπ = 87 to 139 MeV,” Physical Review C, Vol. 51, No. 2, 1995, pp. 929-936. doi:10.1103/PhysRevC.51.929 [18] Ch. Joram, et al., “Low-Energy Differential cross Sections of Pion-Proton (π±p) Scattering. I. The Isospin-Even forward Scattering Amplitude at Tπ = 32.2 and 44.6 MeV,” Physical Review C, Vol. 51, 1995, pp. 2144-2158. doi:10.1103/PhysRevC.51.2144; Ch. Joram, et al., “Low- Energy Differential cross Sections of Pion-Proton (π±p) Scattering. II. Phase Shifts at Tπ = 32.7, 45.1, and 68.6 MeV,” Physical Review C, Vol. 51, No. 4, 1995, pp. 2159-2165. doi:10.1103/Phys [19] M. E. Sevior, et al., “Analyzing Powers in Elastic Scattering from Tπ = 98 to 263 MeV,” Physical Review C, Vol. 40, No. 6, 1989, pp. 2780-2788. doi:10.1103/PhysRevC.40.2780 [20] R. Wieser, et al., “Measurement of the π+→ pAnalyzing Power at 68.3 MeV,” Physical Review C, Vol. 54, No. 4, 1996, pp. 1930-1934. doi:10.1103/PhysRevC.54.1930 [21] B. J. Kriss, πN Newsletter, Vol. 12, 1997, pp. 20-25; B. J. Kriss, et al., “Pion-Proton Integral cross Sections at Tπ = 40 to 284 MeV,” Physical Review C, Vol. 59, No. 3, 1999, pp. 1480-1487. doi:10.1103/PhysRevC.59.1480 [22] E. Friedman, “Partial Total πN cross Sections,” πN Newsletter, Vol. 15, 1999, pp. 37-42. [23] A. A. Carter, J. R. Williams, D. V. Bugg, P. J. Bussey and D. R. Dance, “The Total cross Sections for Pion-Proton Scattering between 70 MeV and 290 MeV,” Nuclear Physics B, Vol. 26, No. 3, 1971, pp. 445-460. doi:10.1016/0550-3213(71)90188-X [24] E. Pedroni, et al., “A Study of Charge Independence and Symmetry fromπ+ andπ- Total cross Sections on Hydrogen and Deuterium near the 3,3 Resonance,” Nuclear Physics A, Vol. 300, No. 2, 1978, pp. 321-347. doi:10.1016/0375-9474(78)96136-5 [25] M. Janousch, et al., “Destructive Interference of s and p Waves in 180?C π-p Elastic Scattering,” Physics Letters B, Vol. 414, No. 3-4, 1997, pp. 237-241. doi:10.1016/S0370-2693(97)01169-6 [26] J. C. Alder, et al., “Measurement of the Asymmetry Parameter A inπ-p Elastic and Charge-Exchange Scattering at Pion Energies Tπ = 98, 238, 292, and 310 MeV,” Physical Review D, Vol. 27, No. 5, 1983, pp. 1040-1055. doi:10.1103/PhysRevD.27.1040 [27] G. J. Hofman, et al., “Analyzing Powers forπ-p → Elastic Scattering between 87 and 263 MeV,” Physical Review C, Vol. 58, No. 6, 1998, pp. 3484-3493. doi:10.1103/PhysRevC.58.3484 [28] J. D. Patterson, et al., “Analyzing Powers for πp Elastic Scattering between 57 and 139 MeV,” Physical Review C, Vol. 66, No. 2, 2002, Article ID: 025207. doi:10.1103/PhysRevC.66.025207 [29] P. Y. Bertin, et al., “π+p Scattering below 100 MeV,” Nuclear Physics B, Vol. 106, 1976, pp. 341-354. doi:10.1016/0550-3213(76)90383-7 [30] P. J. Bussey, et al., “πp Elastic Scattering from 88 to 292 MeV,” Nuclear Physics B, Vol. 58, No. 2, 1973, pp. 363-377. doi:10.1016/0550-3213(73)90589-0 [31] R. Meier, et al., “Low Energy Analyzing Powers in Pion-Proton Elastic Scattering,” Physics Letters B, Vol. 588, No. 3-4, 2004, pp. 155-162. doi:10.1016/j.physletb.2004.02.071 [32] H.-Ch. Schr?der, et al., “The Pion-Nucleon Scattering Lengths from Pionic Hydrogen and Deuterium,” European Physical Journal C, Vol. 21, No. 3, 2001, pp. 473- 488. doi:10.1007/s100520100754 [33] G. C. Oades, G. Rasche, W. S. Woolcock, E. Matsinos and A. Gashi, “Determination of the s-Wave Pion-Nucleon Threshold Scattering Parameters from the Results of Experiments on Pionic Hydrogen,” Nuclear Physics A, Vol. 794, No. 1-2, 2007, pp. 73-86. doi:10.1016/j.nuclphysa.2007.07.007 [34] R. A. Arndt, W. J. Briscoe, I. I. Strakovsky and R. L. Workman, “Extended Partial-Wave Analysis of πN Scattering Data,” Physical Review C, Vol. 74, No. 4, 2006, Article ID: 045205. doi:10.1103/PhysRevC.74.045205 [35] F. James, “MINUIT—Function Minimization and Error Analysis,” CERN Program Library Long Writeup D506. [36] N. Fettes and E. Matsinos, “Analysis of Recentπ+p Low-Energy Differential Cross-Section Measurements,” Physical Review C, Vol. 55, No. 1, 1997, pp. 464-473. doi:10.1103/PhysRevC.55.464 [37] T. E. O. Ericson and W. Weise, “Pions and Nuclei,” Clarendon Press, Oxford, 1988. [38] P. F. A. Goudsmit, H. J. Leisi, E. Matsinos, B. L. Birbrair and A. B. Gridnev, “The Extended Tree-Level Model for the Pion-Nucleon Interaction,” Nuclear Physics A, Vol. 575, No. 4, 1994, pp. 673-706. doi:10.1016/0375-9474(94)90162-7 [39] R. Koch and E. Pietarinen, “Low-Energy πN Partial Wave Analysis,” Nuclear Physics A, Vol. 336, No. 3, 1980, pp. 331-346. doi:10.1016/0375-9474(80)90214-6; R. Koch, “A Calculation of Low-Energy πN Partial Waves Based on Fixed-t Analyticity,” Nuclear Physics A, Vol. 448, No. 4, 1986, pp. 707-731. doi:10.1016/0375-9474(86)90438-0 [40] J. M. Alacrón, J. M. Camalich and J. A. Oller, “Chiral Representation of the πN Scattering Amplitude and the Pion-Nucleon Sigma Term,” Physical Review D, Vol. 85, No. 5, 2012, Article ID: 051503. doi:10.1103/PhysRevD.85.051503
[1] E. Matsinos, W. S. Woolcock, G. C. Oades, G. Rasche and A. Gashi, “Phase-Shift Analysis of Low-Energy Elastic-Scattering Data,” Nuclear Physics A, Vol. 778, No. 1-2, 2006, pp. 95-123. doi:10.1016/j.nuclphysa.2006.07.040 [2] E. Matsinos and G. Rasche, “Analysis of the Low-Energy π±p Elastic-Scattering Data of the CHAOS Collaboration,” 2012. http://arxiv.org/abs/1203.3635 [3] H. Denz, et al., “π±p Differential cross Sections at Low Energies,” Physics Letters B, Vol. 633, No. 2-3, 2006, pp. 209-113. doi:10.1016/j.physletb.2005.12.017 [4] E. Matsinos and G. Rasche, “Analysis of the Low-Energyπ-p Charge-Exchange Data,” 2012. http://arxiv.org/abs/1203.3856 [5] A. Gashi, E. Matsinos, G. C. Oades, G. Rasche and W. S. Woolcock, Nuclear Physics A, Vol. 686, No. 1-4, 2001, pp. 447-462. doi:10.1016/S0375-9474(00)00603-5; A. Gashi, E. Matsinos, G. C. Oades, G. Rasche and W. S. Woolcock, “Electromagnetic Corrections for the Analysis of Low Energy π ? p Scattering Data,” Nuclear Physics A, Vol. 686, No. 1-4, 2001, pp. 463-477. doi:10.1016/S0375-9474(00)00604-7 [6] K. Nakamura, et al. (Particle Data Group), “Review of Particle Physics,” Journal of Physics G, Vol. 37, No. 7A, 2010, Article ID: 075021. doi:10.1088/0954-3899/37/7A/075021 [7] W. R. Gibbs, L. Ai and W. B. Kaufmann, “Isospin Breaking in Low-Energy Pion-Nucleon Scattering,” Physical Review Letters, Vol. 74, No. 19, 1995, pp. 3740-3743. doi:10.1103/PhysRevLett.74.3740 [8] E. Matsinos, “Isospin Violation in the πN System at Low Energies,” Physical Review C, Vol. 56, No. 6, 1997, pp. 3014-3025. doi:10.1103/PhysRevC.56.3014 [9] R. A. Arndt and L. D. Roper, “The Use of Partial-Wave Representations in the Planning of Scattering Measurements. Application to 330 MeV np Scattering,” Nuclear Physics B, Vol. 50, No. 1, 1972, pp. 285-300. doi:10.1016/S0550-3213(72)80019-1 [10] E.G. Auld, et al., “π+ - p Elastic Scattering at 47.9 MeV,” Canadian Journal of Physics, Vol. 57, No. 1, 1979, pp. 73- 78. doi:10.1139/p79-008 [11] B. G. Ritchie, et al., “π+p Scattering at 65 to 140 MeV,” Physics Letters B, Vol. 125, No. 2-3, 1983, pp. 128-32. doi:10.1016/0370-2693(83)91251-0 [12] J. S. Frank, et al., “Measurement of Low-Energy Elastic π±p Differential cross Sections,” Physical Review D, Vol. 28, No. 7, 1983, pp. 1569-1585. doi:10.1103/PhysRevD.28.1569 [13] J. T. Brack, et al., “πp Elastic Scattering from 67 to 139 MeV,” Physical Review C, Vol. 34, No. 5, 1986, pp. 1771-1778. doi:10.1103/PhysRevC.34.1771 [14] J. T. Brack, et al., “Large-Angleπ±p Elastic Scattering at 66.8 MeV,” Physical Review C, Vol. 38, No. 5, 1988, pp. 2427-2429. doi:10.1103/PhysRevC.38.2427 [15] U. Wiedner, et al., “Hidden Strangeness in the Proton? Determination of the Real Part of the Isospin-Even Forward-Scattering Amplitude of Pion-Nucleon Scattering at 54.3 MeV,” Physical Review D, Vol. 40, No. 11, 1989, pp. 3568-3581. doi:10.1103/PhysRevD.40.3568 [16] J. T. Brack, et al., “Absolute Differential cross Sections forπ±p Elastic Scattering at 30 ≤ Tπ ≤ 67 MeV,” Physical Review C, Vol. 41, No. 5, 1990, pp. 2202-2214. doi:10.1103/PhysRevC.41.2202 [17] J. T. Brack, et al., “Forward Angleπ±p Elastic Scattering Differential cross Sections at Tπ = 87 to 139 MeV,” Physical Review C, Vol. 51, No. 2, 1995, pp. 929-936. doi:10.1103/PhysRevC.51.929 [18] Ch. Joram, et al., “Low-Energy Differential cross Sections of Pion-Proton (π±p) Scattering. I. The Isospin-Even forward Scattering Amplitude at Tπ = 32.2 and 44.6 MeV,” Physical Review C, Vol. 51, 1995, pp. 2144-2158. doi:10.1103/PhysRevC.51.2144; Ch. Joram, et al., “Low- Energy Differential cross Sections of Pion-Proton (π±p) Scattering. II. Phase Shifts at Tπ = 32.7, 45.1, and 68.6 MeV,” Physical Review C, Vol. 51, No. 4, 1995, pp. 2159-2165. doi:10.1103/Phys [19] M. E. Sevior, et al., “Analyzing Powers in Elastic Scattering from Tπ = 98 to 263 MeV,” Physical Review C, Vol. 40, No. 6, 1989, pp. 2780-2788. doi:10.1103/PhysRevC.40.2780 [20] R. Wieser, et al., “Measurement of the π+→ pAnalyzing Power at 68.3 MeV,” Physical Review C, Vol. 54, No. 4, 1996, pp. 1930-1934. doi:10.1103/PhysRevC.54.1930 [21] B. J. Kriss, πN Newsletter, Vol. 12, 1997, pp. 20-25; B. J. Kriss, et al., “Pion-Proton Integral cross Sections at Tπ = 40 to 284 MeV,” Physical Review C, Vol. 59, No. 3, 1999, pp. 1480-1487. doi:10.1103/PhysRevC.59.1480 [22] E. Friedman, “Partial Total πN cross Sections,” πN Newsletter, Vol. 15, 1999, pp. 37-42. [23] A. A. Carter, J. R. Williams, D. V. Bugg, P. J. Bussey and D. R. Dance, “The Total cross Sections for Pion-Proton Scattering between 70 MeV and 290 MeV,” Nuclear Physics B, Vol. 26, No. 3, 1971, pp. 445-460. doi:10.1016/0550-3213(71)90188-X [24] E. Pedroni, et al., “A Study of Charge Independence and Symmetry fromπ+ andπ- Total cross Sections on Hydrogen and Deuterium near the 3,3 Resonance,” Nuclear Physics A, Vol. 300, No. 2, 1978, pp. 321-347. doi:10.1016/0375-9474(78)96136-5 [25] M. Janousch, et al., “Destructive Interference of s and p Waves in 180?C π-p Elastic Scattering,” Physics Letters B, Vol. 414, No. 3-4, 1997, pp. 237-241. doi:10.1016/S0370-2693(97)01169-6 [26] J. C. Alder, et al., “Measurement of the Asymmetry Parameter A inπ-p Elastic and Charge-Exchange Scattering at Pion Energies Tπ = 98, 238, 292, and 310 MeV,” Physical Review D, Vol. 27, No. 5, 1983, pp. 1040-1055. doi:10.1103/PhysRevD.27.1040 [27] G. J. Hofman, et al., “Analyzing Powers forπ-p → Elastic Scattering between 87 and 263 MeV,” Physical Review C, Vol. 58, No. 6, 1998, pp. 3484-3493. doi:10.1103/PhysRevC.58.3484 [28] J. D. Patterson, et al., “Analyzing Powers for πp Elastic Scattering between 57 and 139 MeV,” Physical Review C, Vol. 66, No. 2, 2002, Article ID: 025207. doi:10.1103/PhysRevC.66.025207 [29] P. Y. Bertin, et al., “π+p Scattering below 100 MeV,” Nuclear Physics B, Vol. 106, 1976, pp. 341-354. doi:10.1016/0550-3213(76)90383-7 [30] P. J. Bussey, et al., “πp Elastic Scattering from 88 to 292 MeV,” Nuclear Physics B, Vol. 58, No. 2, 1973, pp. 363-377. doi:10.1016/0550-3213(73)90589-0 [31] R. Meier, et al., “Low Energy Analyzing Powers in Pion-Proton Elastic Scattering,” Physics Letters B, Vol. 588, No. 3-4, 2004, pp. 155-162. doi:10.1016/j.physletb.2004.02.071 [32] H.-Ch. Schr?der, et al., “The Pion-Nucleon Scattering Lengths from Pionic Hydrogen and Deuterium,” European Physical Journal C, Vol. 21, No. 3, 2001, pp. 473- 488. doi:10.1007/s100520100754 [33] G. C. Oades, G. Rasche, W. S. Woolcock, E. Matsinos and A. Gashi, “Determination of the s-Wave Pion-Nucleon Threshold Scattering Parameters from the Results of Experiments on Pionic Hydrogen,” Nuclear Physics A, Vol. 794, No. 1-2, 2007, pp. 73-86. doi:10.1016/j.nuclphysa.2007.07.007 [34] R. A. Arndt, W. J. Briscoe, I. I. Strakovsky and R. L. Workman, “Extended Partial-Wave Analysis of πN Scattering Data,” Physical Review C, Vol. 74, No. 4, 2006, Article ID: 045205. doi:10.1103/PhysRevC.74.045205 [35] F. James, “MINUIT—Function Minimization and Error Analysis,” CERN Program Library Long Writeup D506. [36] N. Fettes and E. Matsinos, “Analysis of Recentπ+p Low-Energy Differential Cross-Section Measurements,” Physical Review C, Vol. 55, No. 1, 1997, pp. 464-473. doi:10.1103/PhysRevC.55.464 [37] T. E. O. Ericson and W. Weise, “Pions and Nuclei,” Clarendon Press, Oxford, 1988. [38] P. F. A. Goudsmit, H. J. Leisi, E. Matsinos, B. L. Birbrair and A. B. Gridnev, “The Extended Tree-Level Model for the Pion-Nucleon Interaction,” Nuclear Physics A, Vol. 575, No. 4, 1994, pp. 673-706. doi:10.1016/0375-9474(94)90162-7 [39] R. Koch and E. Pietarinen, “Low-Energy πN Partial Wave Analysis,” Nuclear Physics A, Vol. 336, No. 3, 1980, pp. 331-346. doi:10.1016/0375-9474(80)90214-6; R. Koch, “A Calculation of Low-Energy πN Partial Waves Based on Fixed-t Analyticity,” Nuclear Physics A, Vol. 448, No. 4, 1986, pp. 707-731. doi:10.1016/0375-9474(86)90438-0 [40] J. M. Alacrón, J. M. Camalich and J. A. Oller, “Chiral Representation of the πN Scattering Amplitude and the Pion-Nucleon Sigma Term,” Physical Review D, Vol. 85, No. 5, 2012, Article ID: 051503. doi:10.1103/PhysRevD.85.051503