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E.M. Tursunov, INP, Tashkent with S. Krewald, FZ, Juelich

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Presentation on theme: "E.M. Tursunov, INP, Tashkent with S. Krewald, FZ, Juelich"— Presentation transcript:

1 Spectrum of the excited Nucleon and Delta baryons in a relativistic chiral quark model
E.M. Tursunov, INP, Tashkent with S. Krewald, FZ, Juelich J. Phys. G:Nucl. Part. Phys., 31 (2005) J. Phys. G:Nucl. Part. Phys., 36 (2009) J. Phys. G: Nuc. Part . Phys., 37(2010) arXiv (hep-ph): (2011) arXiv (hep-ph): (2012)

2 Outline Motivation Chiral quark potential model (ChQPM)
Selection rules for quantum numbers: connection with the strong decay of excited baryons with orbital structure (1S)2(nlj) Center of mass correction for the zero-order energy values of the N and Delta states Numerical estimation of the ground and excited Nucleon and Delta mass spectrum within ChQPM Conclusions

3 Motivation Ciral Quark Models have been extensively used to study the structure of the ground state N(939) S. Theberge, A.W. Thomas and G.A. Miller, Phys. Rev. D22, 2838 (1980); A.W. Thomas, S. Theberge and G.A. Miller, Phys. Rev. D24, 216 (1981). K. Saito, Prog. Theor. Phys. V71, 775 (1984). E. Oset, R. Tegen, W. Weise Nucl. Phys. A426, 456 (1984) Th. Gutsche & D. Robson . Phys.Lett. B229, 333 (1989) A.W. Thomas, Prog.Part.Nucl.Phys. 61, 219 (2008); F. Myhrer and A.W. Thomas, Phys.Lett. B663, 302 (2008).

4 Excited baryon spectroscopy: problems within Constituent Quark Models
relativistic effects v ≈ c; the “missing resonances” problem a number of fitting parameters (5-10) what is the most important exchange mechanism between quarks: one gluon exchange ? (Isgur & Karl, Phys. Let. B72, 109 (1977); Phys. Rev. D21, 779(1980) π, K, η exchange?(Glozman & Riska. Phys. Rep. 268 (1996) 263) OR g (mq= MeV) π, K, η N* (∆*) N* (∆*)

5 Spectrum of N* in the CQM (2000 г.) (PPNP, 45, 241)

6 Spectrum of ∆* in the CQM (2000 ) (PPNP, 45, 241)

7 Chiral quark potential model
Effective chiral Lagrangian (based on the linearized σ-model) E. Oset, R. Tegen, W. Weise Nucl. Phys. A426, 456 (1984) Th. Gutsche & D. Robson Phys.Lett. B229, 333 (1989) N* (∆*)

8 The confinement and Coulomb potentials
The Dirac equation (variational method on a harmonic oscillator basis)

9 Field operators for the quark

10 Field operators for the pion

11 Propagators (Green functions)

12 Estimation of the energy spectrum
At zeroth order: Higher orders (Gell-Mann & Low ):

13 Contribution of the self-energy diagramms ( π )

14 2-nd order Feynman diagrams of the self energy term due-to pion field

15 Final expression for the contribution of the 2-nd order self-energy diagrams due-to pion fields

16 Contribution of the 2-nd order self-energy diagrams due-to gluon fields

17 2-nd order self-energy Feynman diagrams due-to gluon fields

18 Final expression for the contribution of the 2-nd order self-energy diagrams due-to gluon to the energy spectrum of baryons

19

20 Contribution of the exchange diagrams (pion)
Wave functions of the SU(2) baryons Contribution of the exchange diagrams (pion)

21 Feynman pion exchange diagrams

22 Pion exchange operators
π ( ) ( ) ℓβ ℓβ± ℓα ℓα±

23 One-gluon exchange operators

24 Feynman gluon-exchange diagrams

25 -the orbital configuration of the SU(2) baryon
Selection rules for quantum numbers: connection with the strong decay of an excited baryons N* (J,T) and ∆*(J,T) -the orbital configuration of the SU(2) baryon 1S π ℓ± ( 1 ) ( ) π (nlj) N* (∆*) (J,T) Chiral constraints: π Ng.s.(1/2+)

26 For the fixed orbital configuration (band)
Consequences of chiral constraints For the fixed orbital configuration (band) the number of N* and ∆* states decreases by 1 (lj)=P1/2 : l=1; Lπ=l’=0 S0=0 ; J=1/ (N*) S0=1 ; J=1/ (N*, ∆*) 2 (N*) + 1 (∆*) (lj)=P3/2 : l=1; Lπ = l’=2 S0=0: J=3/ (N*) S0=1: J=3/2, 5/2 (N*, ∆*) 3 (N*) + 2 (∆*) (lj) ≠ P1/2 : 3 (N*) + 2 (∆*)

27 Center of mass correction for the zero-order energy values of the g. s
Center of mass correction for the zero-order energy values of the g.s. N and Delta (Moshinsky transformation) K. Shimizu, et al. Phys. Rev. C60, (1999) [R=0 method] D. Lu, et al. Phys. Rev. C57, 2628 (1998) [P=0] R. Tegen, et al., Z. Phys. A307 (1982), 339 [LHO] L. Wilets “Non topological solitons”, World Scientific, Singapoure).1989 R=0: P=0: LHO: Normalization:

28 Center of mass correction for the zero-order energy values of the excited N* and Delta* states
Fixed orbital configuration: (degenerate at zero order) With spin coupling:

29 Scalar-vector oscillator potential
(exact separation in Jacobi coordinates) If S0=0

30 Simple solution of the two-body bound state Dirac equation

31 Test: Positronium 1S0 (singlet) (bound state of e+e-)
V(r)= α/r +2 βr me E(1S0 ) SchrÖdinger: eV Dirac: eV E(21S0 - 11S0 ) SchrÖdinger: 5.10 eV Dirac: 4.99 eV

32 Linear scalar and vector Coulomb potentials (in Jacobi coordinates)
Expansion over multipols: ( for ρ/3 < r/2)

33 First approximation (free diquark+ quark)

34 Numerical estimation of the ground and excited Nucleon and Delta mass spectrum within ChQPM (condition of the calculations) М.T. Kawanai & S. Sasaki, PPNP, 67(2012)130 МэВ Th. Gutsche, Ph.D. thesis M. Luescher, Nucl. Phys. B130 (1981) 317 αS=0.65

35 Self energy of the valence quark due-to pion fields as a function of the intermediate quark (antiquark) total momentum (convergence)

36 Self energy of the valence quark states due-to color-magnetic gluon fields (convergence)

37 Ground state nucleon N(939) energy values in MeV
CM correction : K. Shimizu, et al. Phys. Rev. C60, (1999) [100] D. Lu, et al. Phys. Rev. C57, 2628 (1998) [101] R. Tegen, et al., Z. Phys. A307 (1982), 339 [102] L. Wilets “Non topological solitons”, World Scientific, Singapoure).1989

38 Test of the CM correction for the g.s. N and Delta
First approximation (free scalar diquark+ quark) EQ=632 ( di-q)+419(q)=1051 MeV Modification (fit to g.s. N): EQ= =940 MeV

39 Spectrum of N* (our estimation)
Not presented in PDG2012 Exp. Data from: E. Klempt & J.M. Richard, Rev.Mod. Phys. 82 (2010) 1095

40

41 Spectrum of ∆* in our model
Exp. Data from: E. Klempt & J.M. Richard, Rev.Mod. Phys. 82 (2010) 1095

42

43 Conclusions For fixed orbital band of the SU(2) baryon states a)Chiral constraints (selection rules) b) Connection with the strong decay 2. A way to decrease the number of baryon resonances. Possible way to the solution of the “missing resonances” problem (!?) 3. a) Simple solution of the 2-body bound-state Dirac equation b) New method for the CM correction for E Q (N*; Δ*) 4. Without fitting parameters the spectrum of N* and ∆* are described at the CQM level !

44 THANKS !!!


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