H' Kamano , M' Morishita , M' Arima

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Chiral symmetry and N(1440) ? Npp decay

• H. Kamano , M. Morishita , M. Arima
• ( Osaka City Univ. )

Phys. Rev. C71, 045201 (2005)
Osaka, April 8th, 2005
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N(1440) ? Npp Decay

• Decay ratio is 30-40 .(PDG 2004)
• In particular,
  channel
• considerably influence the two-pion
  production reactions
• pN?ppN, gN?ppN, NN?NNpp.

Analyses of pN ? pN ppN reaction by Manley et
al.
D.M.Manley et al. 1984, 1992
N(1440) ? Dp , Ne ? Npp
Corresponding to "s meson"
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Calculation of Invariant Mass Distributions
E. Hernandez et al. PRC 66 (2002) 065201
This model well reproduces the "experimental
results" ( "Manley's analysis" )
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However ...
Hernandez's model gives much smaller value of the
coupling constant than the empirical value,
What is necessary for solving this problem ?
We try to discuss N(1440) ? Npp decay from the
general point of view based on chiral symmetry.
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• ?Master Formula for Chiral Symmetry Breaking?
• H.Yamagishi, I.Zahed Ann.Phys.247
  (1996) 292
• It expresses the invariance of the S-matrix
  with respect to
• the chiral transformation.
• It derives the Ward identities satisfied by
  the amplitudes of
• pion-induced reactions.
• The explicit breaking of chiral symmetry is
  naturally contained
• by imposing the asymptotic condition on the
  axial current
• ( PCAC condition )

We can discuss the general framework of
pion-induced reactions separately from the
detail of specific models.
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General Structure of Decay Amplitude
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Correspondence between General Structure and
Model of Hernandez et al.
Due to explicit breaking of chiral symmetry in
pp interaction.
The phenomenological amplitude of Hernandez et
al. are consistent with the general structure
derived from the master formula.
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Existence of Scalar-isoscalar Contact Interaction
The Ward identity derived from master formula
suggests the existence of scalar-isoscalar
contact interaction.
This interaction consists of two contributions
arising from the different origin in the chiral
structure and having the different momentum
dependence
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Full Model of N(1440) ? Npp Decay



open diagram
closed diagram
new!!
Hernandez's model
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Result 1 Full Calculation
Full result Hernandez Manley (
"experiment" )
Mass distributions (arb. unit)
pp invariant mass ( MeV )
pN invariant mass ( MeV )
We further obtain
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Result 2
consist of two terms proportional to FS and FAA
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Result 3 Phenomenological Meaning of Closed
Diagram
Mass distributions (arb. unit)
gRNpp is also reproduced.
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Summary

• We have calculated the pp and pN invariant mass
  distributions
• for the N(1440)?Npp decay, including new
  contributions from
• scalar-isoscalar contact interaction
  suggested by the master formula.
• The explicit breaking of chiral symmetry in the
  scalar-isoscalar
• contact interaction ( proportional to FS ) is
  necessary for
• the simultaneous description of the pp and pN
  invariant mass
• distributions and gRNpp.
• The contributions of the closed diagram are
  effectively
• substituted by our new diagrams around the
  energy region of
• the Roper resonance.

Minimal model for N(1440)?Npp decay

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back up
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Master Formula Notation
H.Yamagishi, I.Zahed Ann.Phys.247 (1996) 292
The key quantity in the master formula is the
extended S-matrix.
c-number external fields
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Commutation relations between creation
(annihilation) operators of the pion and the
extended S-matrix can be expressed by the
functional derivatives.
(H. Kamano hep-ph/0412281 )
The requirements from the "broken" chiral
symmetry are included.
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Chiral Reduction Formula
The scattering amplitudes are expressed by the
correlation functions of the current and density
operators (Ward identity)