1 Keitaro Nagata, Chung-Yuan Christian University Atsushi Hosaka, RCNP, Osaka Univ. Structure of the nucleon and Roper Resonance with Diquark Correlations Chiral Osaka University, November, 2007 N and R in QD Model : K.N, A.H, J.Phys. G32,777 (‘06). EM structures : K.N, A.H, arXiv:

2 1. QD- Description of the Roper with (i) Relativistic description of the nucleon (ii) Diquark correlations (iii) Chiral symmetry 2. Electric properties of the Roper Roper Resonance: N(1440) I(J) P =1/2(1/2) + The mechanism of the E.E. of Roper and its structures are longstanding problem. Various descriptions have been investigated; unharmonicity in QM, collective excitation, deformation, Goldstone boson exchange, two-pole, gluonic-hybrid… Today, I want to talk about

3 Wave-function of N ( [S 1 +S 2,S 3 ] STotal ) Quarks with (0s) 3 config. N and Roper in NRQM In the non-relativistic description or the spin-flavor symmetry of N, the E.E of Roper is about 1GeV (>> 0.5 GeV). Pauli principle

Relativistic description (local interpolator) 4 a,b,c: color i,j,k: isospin (Ioffe, Z.Phys C18, 67 (83) ) forbidden in NRQM There are 5 possible operators for N, 2 among 5 are independent (Fierz transformation). NRLimit We choose the following operators (good NRLimit)

5 Diquark correlation with  spin-spin interaction attractionrepulsion If there is an interaction, (e.g., spin-spin), the two nucleon states have the mass diff. ~ M  -M N Recent lattice calculations: M A -M S ~ MeV Babich et.al. PRD76,074021(‘07), Alexandrou,PRL97,222002(‘06), Orginos,hep- lat/ good diquark bad Jaffe, Phys. Rept. 409, 1(05)

6 Chiral quark-Diquark model Mesons ~ q q-bar in NJL model Two diquarks : D S [I(J)=0(0)], D A [I(J)=1(1)] qD interaction ~ chiral invariant four point int. Two nucleons: B S =qD S, B A = qD A Non-linear realization of chiral sym. Auxiliary field method : qD model -> chiral MB Lagrangian

7 DSDS DSDS DADA DADA DADA DSDS q Chiral Q-D interaction (three types) Scalar channel Axial-vector channel Mixing between two channels

8 B1B1 q DSDS B1B1 B2B2 q DADA B2B2 B1B1 B 1,2 G Masses of two states [K.N, A.H, J. Phys. G32, 777 (2006)] scalardominance of N input

9 BSBS BSBS Scalar BABA BABA Axial-vector iso-doublet space

10 Intrinsic diquark form factor (IDFF) point Scalar (Monopole and dipole shape from Kroll et al. PLB316,546('93)) 0.5 fm > 0.8 fm Weiss, et al,PLB312,6,(93) Axial in SD calculation Maris, nucl-th/

11 EM form factors of p, n, p*, n* BSBS BSBS BSBS BSBS BABA BABA BABA BABA Nucleon Breit frame

12 Electric form factors(with IDFF) IDFF of scalar improve both G E of proton and neutron axial improve G E of proton but not of neutron. q 2 [GeV] Proton Neutron q 2 [GeV] IDFF Scalar Axial Both Neither

13 Electric form factor of Roper with IDFF Charge radii of Roper resonance for proton : p* is slightly larger than p for neutron : n* is slightly smaller than n (~0) Q 2 [GeV] q 2 [GeV] n* n p p* Proton(p*)Neutron(n*)

14 Summary and Conclusion QD picture for the nucleon and Roper resonance. In a relativistic framework, two kinds of the wave- functions are available for the the nucleon. With diquark correlations, the mass difference between the two states are about 500 MeV. The charge radii of the Roper are almost comparable to that of the nucleon. Future work : helicity amplitude (off-diagonal terms)

15 Discussion proton component (R.M.S) size of Bs and BA are almost the same. ud u BE =50MeV 0.6fm 0.8fm Charge radii of N and R uu, ud d, u 0.8fm pp*

16 Discussion neutron component (R.M.S) size of Bs and BA are almost the same. Charge radii of N and R ud d 0.6fm 0.8fm ud, dd d, u 0.8fm nn*

17 Roper-like excitation mode for octet, Not confirmed for decuplet. Roper in SU(3)

18 Assuming the non-relativistic description or the spin-flavor symmetry of thenucleon, the E.E of Roper is about 1GeV. Relativistic description of N Two types of wave-functions (  and  )is available. Each w.f. independently satisfies Pauli priciple. (spin flavor symmetry is not a good symmetry there) The second nucleon states (orthogonal to N(940)) ? (i) Relativistic descriptions of the nucleon (ii) Chiral symmetry (iii) Diquark correlations What is the structure of the Roper ? -> Nucleon and Roper resonance