1. H. Kamano , M. Morishita , M. Arima ( Osaka City Univ. )
Chiral symmetry and
N*(1440) → Npp decay
H. Kamano , M. Morishita , M. Arima
( Osaka City Univ. )
Phys. Rev. C71, (2005)
Osaka, April 8th, 2005

2. N*(1440) → Npp Decay
Decay ratio is %.（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 , 1992
N*(1440) → Dp , Ne →　Npp N* N p e + D
Corresponding to "s meson"

3. + = Calculation of Invariant Mass Distributions p
E. Hernandez et al. PRC 66 (2002) N* N p +
I = 0
N, D, N*
open diagram
closed diagram =
The scalar-isoscalar correlation
is expressed by
the pp rescattering mechanism.
Hernandez et al. calculated
the pp and pN invariant
mass distributions
for N*(1440) → Npp decay.
This model well reproduces
the "experimental results"
( = "Manley's analysis" )

4. However ... Evaluation of the effective coupling constant of
phenomenological lagrangian for
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.

5. 「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.

6. This process is not considered in this work.
General Structure of Decay Amplitude N* N ×
Decay through the baryon propagation.
(N*(1440) → Dp etc.)
Also contributes to 　　 N* N ×
r - pole
Mainly express N*(1440) → Nr decay.
Two emitted pions are in the state of I = 1, P-wave.
This process is not considered in this work. N* N ×
Contributes to　　　　　　　　　　　　　　　　 only.
Due to the explicit breaking of chiral symmetry.
　 ( vanishes in the chiral limit mp → 0 )

7. Correspondence between General Structure and Model of Hernandez et al.
N, D, N*
open diagram N N* ×
Due to explicit breaking of chiral symmetry
in pp interaction. N N* ×
I = 0
N, D, N*
closed diagram N N* ×
The phenomenological amplitude of Hernandez et al. are consistent with
the general structure derived from the master formula.

8. Existence of Scalar-isoscalar Contact Interaction
The Ward identity derived from master formula suggests
the existence of scalar-isoscalar contact interaction.
spp = pp invariant
mass square
I = 0 N* N
This interaction consists of two contributions
arising from the different origin in the chiral structure
and having the different momentum dependence

9. + + + L FS , FAA Full Model of N*(1440) → Npp Decay p N N*
Cutoff to regularize
the loop integral
including baryon
FS , FAA
Due to explicit chiral symmetry breaking in
the contact interaction
open
diagram
closed
diagram
Hernandez's model
new!!

10. Full result (Hernandez)
Result 1 Full Calculation
p p pN
Full result　
Hernandez
Manley
( ="experiment" )
Mass distributions　(arb. unit)
pp invariant mass ( MeV )
pN invariant mass ( MeV )
We further obtain
parameters
L (MeV)
　　　　　 (MeV)
FAA (GeV-1)
Full result (Hernandez)
700 ( 700 )
157 ( － )
1.97 ( － )
Both the mass distributions and gRNpp can be reproduced
by considering our new contributions.

11. proportional to FS and FAA
Result 2
consist of two terms
proportional to FS and FAA
Which is necessary in our new contributions
for the simultaneous description of the mass distributions and gRNpp ?
p p pN
0 ( 1.97 )
FAA (GeV-1)
160 ( 157 )
　　　　　 (MeV)
460 ( 700 )
( Full result )
L (MeV)
parameters
pp invariant mass ( MeV )
pN invariant mass ( MeV )
Mass distributions　(arb. unit)
Full result
FAA = 0
In the case of FS = 0, we can not find parameter set
reproducing the mass distributions and gRNpp simultaneously.
The term proportional to FS which arises from the explicit
breaking of chiral symmetry is necessary for reproducing
both the mass distributions and gRNpp .

12. gRNpp is also reproduced.
Result 3
Phenomenological Meaning of Closed Diagram
p p
pp invariant mass ( MeV )
Full　result
No closed
diagrams pN
pN invariant mass ( MeV )
Mass distributions　(arb. unit)
gRNpp is also reproduced.
parameters
L (MeV)
　　　　　 (MeV)
FAA (GeV-1)
no closed diagram ( Full result )
－ ( 700 )
177 ( 157 )
( 1.97 )
The closed diagram does not play an essential role in the
phenomenological understanding of

13. 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 + +

14. back up

15. c-number external fields
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
Extended S-matrix
Currents and Density Operators, and T-products

16. The requirements from the "broken" chiral symmetry are included.
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/ )
The requirements from the "broken" chiral symmetry are included.

17. Chiral Reduction Formula
Scattering amplitudes including any number of on-shell pions
The scattering amplitudes are expressed by
the correlation functions
of the current and density operators (Ward identity)