Status of two pion production in π N

1. Status of two pion production in πN • Introduction • Summary of ππN data • Isobar-model formalism • Parametrization of PW amplitudes • New results • Summary 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→π0π0n π-p→π-π0p π+p→π+π0p 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 reactionπN→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 ofπN→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 ofπN→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. 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 S11, P11, P13, D13, F15 – 10 channels D15 – 8 channels P33, D33 – 7 channels S31, F35 – 6 channels D35 – 5 channels P31, F37 – 4 channels G17 – 3 channels else – 2 channels Multichannel fits

10. Parametrization of amplitudes My parametrization of PW amplitudes satisfies unitarity and time-reversal invariance. The total partial-wave S-matrix has the form 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: where the background matrix B is unitary but not generally symmetric:

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

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. F15 amplitudes

14. F15 amplitudes

15. F15 amplitudes

16. F15 amplitudes: γp→πN

17. F15 amplitudes: γn→πN

18. first resonance Mass = 1687 ± 2 MeV Width = 131 ± 4 MeV x = 63.3 ± 1.1 % A1/2(γp) = –0.017(2) A3/2(γp) = +0.135(3) A1/2(γn) = +0.040(7) A3/2(γn) = –0.067(7) second resonance Mass = 1900 ± 27 MeV Width = 300 ± 84 MeV x = 12.5 ± 1.5 % A1/2(γp) = –0.023(10) A3/2(γp) = +0.035(13) F15 amplitudes (summary) Note: Helicity amplitudes in GeV-1/2

19. S31 amplitudes

20. S31 amplitudes

21. S31 amplitudes

22. first resonance Mass = 1600 ± 4 MeV Width = 112 ± 8 MeV x = 33.0 ± 4.9 % A1/2(γN) = –0.003(11) second resonance Mass = 1868 ± 26 MeV Width = 234 ± 82 MeV x = 8.4 ± 4.1 % A1/2(γN) = –0.082(29) S31 amplitudes (summary) Note: Helicity amplitudes in GeV-1/2

23. Preliminary results forπ-p→ηn

24. Preliminary results forπ-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