Status of two pion production in Status of two pion production in ππNN

• IntroductionIntroduction• Summary of Summary of ππππN dataN data• Isobar-model formalismIsobar-model formalism• Parametrization of PW amplitudesParametrization of PW amplitudes• New resultsNew results• SummarySummary

PWA WorkshopPWA WorkshopBad Honnef, GermanyBad Honnef, Germany

March 2, 2009March 2, 2009

ππN→N→ππππN charge channelsN charge channels

• There are 5 measurable channels:

ππ--pp→π→π++ππ--nn

ππ--pp→π→π00ππ00nn

ππ--pp→π→π--ππ00pp

ππ++pp→π→π++ππ00ppππ++pp→π→π++ππ++nn

Why study Why study ππN→N→ππππN?N?

• 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!

10 major papers10 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]

10 major papers (cont’d)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]

Tabular Summary of Tabular Summary of ππN→N→ππππN dataN data

Graphical Summary of Graphical Summary of ππN→N→ππππN dataN data

Isobar Model for Isobar Model for ππN→N→ππππNNThe total amplitude for a givenThe total amplitude for a givencharge channel can be writtencharge channel can be writtenas a coherent sum over all isobarsas a coherent sum over all isobarsand partial waves:and partial waves:

where the subscripts represent thewhere the subscripts represent thecollection of quantum numbers thatcollection of quantum numbers thatdescribe the partial waves associated describe the partial waves associated with a given isobar.with a given isobar.

Multichannel fitsMultichannel 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

• 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

Parametrization of amplitudesParametrization 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 where the background matrix matrix BB is unitary but not is unitary but not generally symmetric:generally symmetric:

The matrix The matrix RR is both is both unitary and symmetric. unitary and symmetric. It is a generalization of It is a generalization of the multichannel BW the multichannel BW form to include multiple form to include multiple resonances. It is con-resonances. It is con-structed from a K-structed from a K-matrix:matrix:

Parametrization of amplitudes (cont’d)Parametrization of amplitudes (cont’d)

For N resonances, K has the form

Elements of the matrices Elements of the matrices factorizable,factorizable,

where summing over all decay channels giveswhere summing over all decay channels gives

were assumed to bewere assumed to be

Parametrization of amplitudes (cont’d)Parametrization of amplitudes (cont’d)

For the special case of two resonances, we have

and the corresponding T-matrix has the formand the corresponding T-matrix has the form

where the coefficients can be calculated analytically. where the coefficients can be calculated analytically.

For further details, see For further details, see Baryon partial-wave analysisBaryon partial-wave analysis,,D.M. Manley, Int. J. Modern Phys. A D.M. Manley, Int. J. Modern Phys. A 1818, 441 (2003)., 441 (2003).

FF1515 amplitudes amplitudes

FF1515 amplitudes amplitudes

FF1515 amplitudes amplitudes

FF1515 amplitudes: amplitudes: γγp→p→ππNN

FF1515 amplitudes: amplitudes: γγn→n→ππNN

FF1515 amplitudes (summary) amplitudes (summary)

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)

NoteNote: Helicity amplitudes in GeV: Helicity amplitudes in GeV-1/2-1/2

SS3131 amplitudes amplitudes

SS3131 amplitudes amplitudes

SS3131 amplitudes amplitudes

SS3131 amplitudes (summary) amplitudes (summary)

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)

NoteNote: Helicity amplitudes in GeV: Helicity amplitudes in GeV-1/2-1/2

Preliminary results forPreliminary results for ππ--p→p→ηηnn

Preliminary results forPreliminary results for ππ--p→Kp→KΛΛ

Dynamical coupled-channels study of Dynamical coupled-channels study of ππN→N→ππππN reactionsN reactions

H. Kamano, B. Juliá-Díaz, T.-S. H. Lee, A. Matsuyama, and T. Sato, nucl-th/0807.2273v2. [EBAC]

Dynamical coupled-channels study of Dynamical coupled-channels study of ππN→N→ππππN reactions (cont’d)N reactions (cont’d)

SummarySummary

• 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-FG02-01ER41194Funding for this work was provided in part by U.S. DOE Grant DE-FG02-01ER41194