1. Status of two pion production in πN IntroductionIntroduction Summary of ππN dataSummary of ππN data Isobar-model formalismIsobar-model formalism Parametrization of PW amplitudesParametrization of PW amplitudes New resultsNew results SummarySummary PWA Workshop Bad Honnef, Germany March 2, 2009

2. πN→ππN charge channels There are 5 measurable channels: π - p→π + π - n π - p→π 0 π 0 n π - p→π - π 0 p π + p→π + π 0 p π + p→π + π + n

3. Why study πN→ππN? At c.m. energies below 2 GeV, this is the dominant inelastic reaction in πN scattering Drawbacks – analysis of 3-body final states is complicated (many partial waves are involved) There remains a strong need for detailed new measurements in all charge channels!

4. 10 major papers Partial wave analysis of the reaction πN→Nππ below 1 GeV (I) π - p inelastic interactions, M. DeBeer et al., Nucl. Phys. B12, 599 (1969). [Saclay] Partial wave analysis of the reaction πN→Nππ below 1 GeV (II) π + p inelastic interactions, M. DeBeer et al., Nucl. Phys. B12, 617 (1969). [Saclay] A partial-wave analysis of three body π + proton interactions at low energy, P. Chavanon, J. Dolbeau, and G. Smadja, Nucl. Phys. B76, 157 (1974). [Saclay] Partial-wave analysis of the reaction πN→ππN in the c.m. energy range 1300-2000 MeV, D. J. Herndon et al., Phys. Rev. D 11, 3183 (1975). [LBL-SLAC] A partial-wave analysis of πN→ππN at center-of-mass energies below 2000 MeV, A. H. Rosenfeld et al., Phys. Lett. 55B, 486 (1975). [LBL-SLAC]

5. 10 major papers (cont’d) Energy-independent partial-wave analysis of the reactions π ± p→Nππ in the c.m. energy range 1.36-1.76 GeV, J. Dolbeau, F.A. Triantis, M. Neveu, and F. Cadiet, Nucl. Phys. B108, 365 (1976). [Saclay] Partial-wave analysis including π exchange for πN→Nππ in the c.m. energy range 1.65-1.97 GeV, D. E. Novoseller, Nucl. Phys. B137, 445 (1978). [CalTech] An isobar model partial-wave analysis of three-body final states in π + p interactions from threshold to 1700 MeV c.m. energy, K.W.J. Barnham et al., Nucl. Phys. B168 243, (1980). [Imperial College] Isobar-model partial-wave analysis of πN→ππN in the c.m. energy range 1320-1930 MeV, D.M. Manley, R.A. Arndt, Y. Goradia, and V.L. Teplitz, Phys. Rev. D 30, 904 (1984). [VATech] Dynamical coupled-channels study of πN→ππN reactions, H. Kamano et al., nucl-th/0807.2273v2. [EBAC]

6. Tabular Summary of πN→ππN data

7. Graphical Summary of πN→ππN data

8. Isobar Model for πN→ππN The total amplitude for a given charge channel can be written as a coherent sum over all isobars and partial waves: where the subscripts represent the collection of quantum numbers that describe the partial waves associated with a given isobar.

9. Multichannel fits New fits include πN, ππN, and γN channels Working to add ηN and KΛ channels Fits determine BW masses and widths, pole positions, partial widths, decay amplitudes, and helicity amplitudes S 11, P 11, P 13, D 13, F 15 – 10 channels D 15 – 8 channels P 33, D 33 – 7 channels S 31, F 35 – 6 channels D 35 – 5 channels P 31, F 37 – 4 channels G 17 – 3 channels else – 2 channels

10. Parametrization of amplitudes My parametrization of PW amplitudes satisfies unitarity and time-reversal invariance. The total partial-wave S-matrix has the form where the background matrix B is unitary but not generally symmetric: The matrix R is both unitary and symmetric. It is a generalization of the multichannel BW form to include multiple resonances. It is con- structed from a K- matrix:

11. Parametrization of amplitudes (cont’d) For N resonances, K has the form Elements of the matrices factorizable, where summing over all decay channels gives were assumed to be

12. Parametrization of amplitudes (cont’d) For the special case of two resonances, we have and the corresponding T-matrix has the form where the coefficients can be calculated analytically. For further details, see Baryon partial-wave analysis, D.M. Manley, Int. J. Modern Phys. A 18, 441 (2003).

13. F 15 amplitudes

16. F 15 amplitudes: γp→πN

17. F 15 amplitudes: γn→πN

18. F 15 amplitudes (summary) first resonance Mass = 1687 ± 2 MeV Width = 131 ± 4 MeV x = 63.3 ± 1.1 % A 1/2 (γp) = –0.017(2) A 3/2 (γp) = +0.135(3) A 1/2 (γn) = +0.040(7) A 3/2 (γn) = –0.067(7) second resonance Mass = 1900 ± 27 MeV Width = 300 ± 84 MeV x = 12.5 ± 1.5 % A 1/2 (γp) = –0.023(10) A 3/2 (γp) = +0.035(13) Note: Helicity amplitudes in GeV -1/2

19. S 31 amplitudes

22. S 31 amplitudes (summary) first resonance Mass = 1600 ± 4 MeV Width = 112 ± 8 MeV x = 33.0 ± 4.9 % A 1/2 (γN) = –0.003(11) second resonance Mass = 1868 ± 26 MeV Width = 234 ± 82 MeV x = 8.4 ± 4.1 % A 1/2 (γN) = –0.082(29) Note: Helicity amplitudes in GeV -1/2

23. Preliminary results for π - p→ηn

24. Preliminary results for π - p→KΛ

25. Dynamical coupled-channels study of πN→ππN reactions H. Kamano, B. Juliá-Díaz, T.-S. H. Lee, A. Matsuyama, and T. Sato, nucl-th/0807.2273v2. [EBAC]

26. Dynamical coupled-channels study of πN→ππN reactions (cont’d)

27. Summary Few measurements (old or new) exist for πN→ππN channels Original bubble-chamber database has been preserved on SAID 1984 solution for partial-wave amplitudes exists as a data file and has been provided to many different groups Further progress is likely to rely on incorporating ππN amplitudes into various multichannel schemes, particularly those involving meson photoproduction Funding for this work was provided in part by U.S. DOE Grant DE-FG02-01ER41194