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Structure of the nucleon and Roper Resonance with Diquark Correlations

Structure of the nucleon and Roper Resonance with Diquark Correlations. Keitaro Nagata, Chung-Yuan Christian University Atsushi Hosaka, RCNP, Osaka Univ. N and R in QD Model : K.N, A.H, J.Phys. G32,777 (‘06). EM structures : K.N, A.H, arXiv: 0708.3471.

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Structure of the nucleon and Roper Resonance with Diquark Correlations

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  1. Structure of the nucleon and Roper Resonance with Diquark Correlations Keitaro Nagata, Chung-Yuan Christian University Atsushi Hosaka, RCNP, Osaka Univ. N and R in QD Model : K.N, A.H, J.Phys. G32,777 (‘06). EM structures : K.N, A.H, arXiv: 0708.3471. Chiral 07 @ Osaka University, 13-16 November, 2007

  2. 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 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

  3. N and Roper in NRQM Wave-function of N ([S1+S2,S3]STotal) Quarks with (0s)3 config. Pauli principle In the non-relativistic description or the spin-flavor symmetry ofN, the E.E of Roper is about 1GeV (>> 0.5 GeV).

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

  5. Diquark correlation with D Jaffe, Phys. Rept. 409, 1(05) good diquark bad attraction repulsion spin-spin interaction If there is an interaction, (e.g., spin-spin), the two nucleon states have the mass diff. ~ MD-MN Recent lattice calculations: MA-MS ~100-400 MeV Babich et.al. PRD76,074021(‘07), Alexandrou,PRL97,222002(‘06), Orginos,hep-lat/0510082.

  6. Chiral quark-Diquark model • Mesons ~ q q-bar in NJL model • Two diquarks: DS [I(J)=0(0)], DA [I(J)=1(1)] • qD interaction ~ chiral invariant four point int. • Two nucleons:BS=qDS , BA= qDA • Non-linear realization of chiral sym. • Auxiliary field method : qD model -> chiralMB Lagrangian

  7. Chiral Q-D interaction (three types) Axial-vector channel q DS DA DA DS DA DS Mixing between two channels Scalar channel

  8. DA B2 B2 q Masses of two states [K.N, A.H, J. Phys. G32, 777 (2006)] DS B1,2 B1,2 B1 B1 B1 G q input scalardominance of N

  9. Scalar BS BS Axial-vector iso-doublet space BA BA

  10. Intrinsic diquark form factor (IDFF) point Weiss, et al,PLB312,6,(93) Scalar 0.5 fm in SD calculation Maris, nucl-th/0412059 Axial 0.6-0.9 -> 0.8 fm (Monopole and dipole shape from Kroll et al. PLB316,546('93))

  11. EM form factors of p, n, p*, n* BS BS BS BS BA BA BA BA Breit frame • Nucleon

  12. Electric form factors(with IDFF) Neutron Proton IDFF Neither Axial Scalar Both q2[GeV] q2[GeV] IDFF of scalar improve both GE of proton and neutron axial improve GE of proton but not of neutron.

  13. Electric form factor of Roper with IDFF Proton(p*) Neutron(n*) n n* p p* Q2[GeV] q2[GeV] q2[GeV] Charge radii of Roper resonance for proton : p* is slightly larger than p for neutron : n* is slightly smaller than n(~0)

  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. p u d, u p* BE =50MeV 0.8fm 0.8fm 0.6fm ud uu, ud Charge radii of N and R 0.8 0.8+0.1 0.8 0.6+0.1

  16. Discussion neutron component (R.M.S) size of Bs and BA are almost the same. n d d, u n* 0.8fm 0.8fm 0.6fm ud ud, dd Charge radii of N and R 0.8 0.8+0.1 0.8 0.6+0.1

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

  18. Assuming the non-relativistic description or the spin-flavor symmetryof thenucleon, the E.E of Roper is about 1GeV. Relativistic description of N Two types of wave-functions (r and l)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 -> Nucleon and Roper resonance What is the structure of the Roper ?

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