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, 045201 (2005) Osaka, April 8th, 2005

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 N* N p e + D Corresponding to "s meson"

+ = Calculation of Invariant Mass Distributions p E. Hernandez et al. PRC 66 (2002) 065201 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" )

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.

「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.

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 )

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.

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

+ + + 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!!

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.

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 .

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 ) -1.22 ( 1.97 ) The closed diagram does not play an essential role in the phenomenological understanding of .

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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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

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/0412281 ) The requirements from the "broken" chiral symmetry are included.

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)