Status of two pion production in pN

1
Status of two pion production in pN

• Introduction
• Summary of ppN data
• Isobar-model formalism
• Parametrization of PW amplitudes
• New results
• Summary

PWA Workshop Bad Honnef, Germany March 2, 2009
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pN?ppN charge channels

• There are 5 measurable channels

p-p?pp-n p-p?p0p0n p-p?p-p0p pp?pp0p pp?ppn
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Why study pN?ppN?

• At c.m. energies below 2 GeV, this is the
  dominant inelastic reaction in pN 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!

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10 major papers

• Partial wave analysis of the reaction pN?Npp
  below 1 GeV (I) p-p inelastic interactions,
  M. DeBeer et al., Nucl. Phys. B12, 599 (1969).
  Saclay
• Partial wave analysis of the reaction pN?Npp
  below 1 GeV (II) pp inelastic interactions, M.
  DeBeer et al., Nucl. Phys. B12, 617 (1969).
  Saclay
• A partial-wave analysis of three body p proton
  interactions at low energy, P. Chavanon, J.
  Dolbeau, and G. Smadja, Nucl. Phys. B76, 157
  (1974). Saclay
• Partial-wave analysis of the reaction pN?ppN 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 pN?ppN at
  center-of-mass energies below 2000 MeV, A. H.
  Rosenfeld et al., Phys. Lett. 55B, 486 (1975).
  LBL-SLAC

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10 major papers (contd)

• Energy-independent partial-wave analysis of the
  reactions pp?Npp 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 p exchange for
  pN?Npp 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 pp 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 pN?ppN 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 pN?ppN
  reactions, H. Kamano et al., nucl-th/0807.2273v2.
  EBAC

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Tabular Summary of pN?ppN data
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Graphical Summary of pN?ppN data
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Isobar Model for pN?ppN
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.
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Multichannel fits

• New fits include pN, ppN, and ?N channels
• Working to add ?N and K? 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

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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
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Parametrization of amplitudes (contd)

• For N resonances, K has the form

Elements of the matrices factorizable,
were assumed to be
where summing over all decay channels gives
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Parametrization of amplitudes (contd)

• 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).
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F15 amplitudes
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F15 amplitudes
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F15 amplitudes
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F15 amplitudes ?p?pN
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F15 amplitudes ?n?pN
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F15 amplitudes (summary)

• first resonance
• Mass 1687 2 MeV
• Width 131 4 MeV
• x 63.3 1.1
• A1/2(?p) 0.017(2)
• A3/2(?p) 0.135(3)
• A1/2(?n) 0.040(7)
• A3/2(?n) 0.067(7)

• second resonance
• Mass 1900 27 MeV
• Width 300 84 MeV
• x 12.5 1.5
• A1/2(?p) 0.023(10)
• A3/2(?p) 0.035(13)

Note Helicity amplitudes in GeV-1/2
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S31 amplitudes
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S31 amplitudes
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S31 amplitudes
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S31 amplitudes (summary)

• first resonance
• Mass 1600 4 MeV
• Width 112 8 MeV
• x 33.0 4.9
• A1/2(?N) 0.003(11)

• second resonance
• Mass 1868 26 MeV
• Width 234 82 MeV
• x 8.4 4.1
• A1/2(?N) 0.082(29)

Note Helicity amplitudes in GeV-1/2
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Preliminary results for p-p??n
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Preliminary results for p-p?K?
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Dynamical coupled-channels study of pN?ppN
reactions

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

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Dynamical coupled-channels study of pN?ppN
reactions (contd)
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Summary

• Few measurements (old or new) exist for pN?ppN
  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 ppN 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