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Successes and problems of chiral soliton approach to exotic baryons

Micha ł Praszałowicz - Jagellonian University Kraków , Poland. Successes and problems of chiral soliton approach to exotic baryons. Cracow Epiphany Conference on Hadron Spectroscopy January 6-8, 2005. Early predictions: quark models: Gell-Mann mentioned 10 *

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Successes and problems of chiral soliton approach to exotic baryons

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  1. Michał Praszałowicz - Jagellonian University Kraków, Poland Successes and problems of chiral soliton approach to exotic baryons Cracow Epiphany Conference on Hadron Spectroscopy January 6-8, 2005

  2. M. Praszałowicz (Kraków)

  3. Early predictions: quark models: Gell-Mann mentioned 10* but Z+ was expected to be negative parity heavy (> 1700 MeV) and wide soliton models: positive parity Biedenharn, Dothan (1984): 10-8 ~ 600 MeV from Skyrme model MP (1987): M= 1535 MeV from Skyrme model in model independent approach, second order Diakonov, Petrov, Polyakov (1997): QM- model independent approach, 1/Nc corrections M= 1530 MeV, < 15 MeV

  4. Spectrum of the Dirac operator M. Praszałowicz (Kraków)

  5. Spectrum of the Dirac operator M. Praszałowicz (Kraków)

  6. Spontaneously broken chiral symmetry constituent quark mass: How does a low-momentum chirally invariant Lagrangian with massive quarks look like?

  7. Spontaneously broken chiral symmetry constituent quark mass: How does a low-momentum chirally invariant Lagrangian with massive quarks look like? is invariant, because one can absorb chiral rotation into the redefined pseudoscalar meson fieldsA Note that = f (q, q)  quarks do interact Chiral symmetry is spontaneously broken: < A > = 0 Goldstone bosons are massless

  8. Baryons M. Praszałowicz (Kraków)

  9. Baryons M. Praszałowicz (Kraków)

  10. Baryons valence level: energy decreases sea levels: energy increases This is Soliton system stabilzes M. Praszałowicz (Kraków)

  11. Chiral Quark Model constituent quark mass ~ 350 MeV pions fermions integrate out quarks "Skyrme" Model only massless pion fields, kinetic term + interaction terms M. Praszałowicz (Kraków)

  12. Chiral Quark Model constituent quark mass ~ 350 MeV pions fermions integrate out quarks Skyrme Model only massless pion fields, kinetic term + interaction terms Soliton in the Skyrme model is stabilizes by the Sk. term M. Praszałowicz (Kraków)

  13. Quantizing SU(3) Skyrmion and QM time-dependent rotation angular velocities: analogy with symmetric top M. Praszałowicz (Kraków)

  14. Wave functions and allowed states B S I3 Y M. Praszałowicz (Kraków)

  15. Mass formula O(1) corrections to Mcl do not allow for absolute mass predictions octet-decuplet splitting exotic-nonexotic splittings known ? first order perturbation in the strange quark mass and in Nc: x M. Praszałowicz (Kraków)

  16. Mass formula octet-decuplet splitting exotic-nonexotic splittings known ? first order perturbation in the strange quark mass and in Nc: x E. Guadagnini Nucl.Phys.B236 (1984) 35 M. Praszałowicz (Kraków)

  17. Skyrme model spectrum symmetry breaking Hamiltonian is too primitive: richer structure is needed M. Praszałowicz (Kraków)

  18. go to higher orders in ms go to higher orders in Nc M. Praszałowicz (Kraków)

  19. Yabu-Ando: higher orders in ms H. Yabu, K. Ando, Nucl.Phys.B301 (1988) 601 second order: M.P., Phys. Lett. B575 (2003) 234 talk at the Cracow Workshop on Skyrmions and Anomalies, Mogilany, Poland, 1987, World Scientific 1987, p.112. first order in  Constraints: M. Praszałowicz (Kraków)

  20. Numerical values for all masses Talk at the Cracow Workshop on Skyrmions and Anomalies, Mogilany, Poland, Feb 20-24, 1987, World Scientific 1987, p.112. M. Praszałowicz (Kraków)

  21. go to higher orders in ms go to higher orders in Nc M. Praszałowicz (Kraków)

  22. QM breaking hamiltonian E. Guadagnini Nucl.Phys.B236 (1984) 35 calculate next-to-leading contributions to H' equivalent to Guadagnini mass formula: O(Nc)+O(1) O(1) O(1) all O(ms) M. Praszałowicz (Kraków)

  23. QM breaking hamiltonian calculate next-to-leading contributions to H' O(Nc)+O(1) O(1) O(1) all O(ms) Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 richer H': * no handle on I2 * only 2 linear combinations of parameters ',  and  enter nonexotic splittings splittings in 10  10 M. Praszałowicz (Kraków)

  24. QM breaking hamiltonian calculate next-to-leading contributions to H' O(Nc)+O(1) O(1) O(1) all O(ms) Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 richer H': * no handle on I2 * only 2 linear combinations of parameters ',  and  enter nonexotic splittings splittings in 10  10 models give I2 ~ 0.5 fm ~ 400 MeV -1 M10 ~ 1750 MeV M ~ 1450 MeV M. Praszałowicz (Kraków)

  25. Antidecuplet in QM richer H': splittings in 10  10 , still no handle on I2 fixes I2 Diakonov, Petrov Polyakov Z.Phys A359 (97) fixed by N  M10

  26. Freedom in QM M.Diakonov, V.Petrov, M.Polyakov, Z.Phys. A359 (1997) 305 NA49 27 -plet M.M.Pavan, I.I.Strakovsky, R.L.Workman, R.A.Arndt,PiN Newslett.16 (2002) 110 T.Inoue, V.E.Lyubovitskij, T.Gutsche, A.Faessler,arXiv:hep-ph/0311275 M. Praszałowicz (Kraków)

  27. Width G.S. Adkins, C.R. Nappi, E. Witten, Nucl. Phys. B228 (1983) 552 operator V has the same structure as axial current Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 Weigel, Eur.Phys.J.A2 (98) 391, hep-ph/0006619 M. Praszałowicz (Kraków)

  28. Width in the soliton model SU(3) relations   Decuplet decay: Antidecuplet decay: In NRQM limit: M. Praszałowicz (Kraków)

  29. Small Soliton Limit Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 MP, A.Blotz K.Goeke, Phys.Lett.B354:415-422,1995 energy is calculated with respect to the vacuum: in the small soliton limit only valence level contributes M. Praszałowicz (Kraków)

  30. Width Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 Decuplet decay: Antidecuplet decay: In small soliton limit: In reality: < 15 MeV M. Praszałowicz (Kraków)

  31. Mass formula O(Nc) O(Nc,ms) unknown corrections O(1) O(1) O(Nc) O(1/Nc) O(Nc,ms) + O(1,ms) M. Praszałowicz (Kraków)

  32. Width chiral limit: nonzero meson masses: M. Praszałowicz (Kraków)

  33. Matching with the bound state approach Callan, Klebanov Nucl.Phys.B262:365,1985 Nadeau, Nowak, Rho, VentoPhys.Rev.Lett.57:2127-2130,1986 Callan, Klebanov , Hornbostel, Phys.Lett.B202:269,1988 Itzhaki, Klebanov, Quyang, Rastelli, Nucl.Phys.B684:264-280,2004 K- is bound K+ is not bound and has no smooth limit to rigid rotator K WZ M. Praszałowicz (Kraków)

  34. Applications of Chiral Quark Models • Spectra: Diakonov, Petrov, Polyakov , Z.Phys A359 (97) • M.P., Phys. Lett. B575 (2003) 234 • 2. Nucleon quark distribution functions: • D.Diakonov, V.Petrov, P.Pobylitsa, • M.V.Polyakov C.Weiss, • Nucl. Phys.B480, 341 (1996) M. Praszałowicz (Kraków)

  35. Applications of Chiral Quark Models • Spectra: Diakonov, Petrov, Polyakov , Z.Phys A359 (97) • M.P., Phys. Lett. B575 (2003) 234 • 2. Nucleon distribution functions: • D.Diakonov, V.Petrov, P.Pobylitsa, • M.V.Polyakov C.Weiss, • Nucl. Phys.B480, 341 (1996) • 3. Skewed parton distributions: • V.Y.Petrov, P.V.Pobylitsa, M.V.Polyakov, • I.Bornig, K.Goeke and C.Weiss,Phys. • Rev. D574325 (1998) M. Praszałowicz (Kraków)

  36. Applications of Chiral Quark Models • Spectra: Diakonov, Petrov, Polyakov , Z.Phys A359 (97) • M.P., Phys. Lett. B575 (2003) 234 • 2. Nucleon distribution functions: • D.Diakonov, V.Petrov, P.Pobylitsa, • M.V.Polyakov C.Weiss, • Nucl. Phys.B480, 341 (1996) • 3. Skewed parton distributions: • V.Y.Petrov, P.V.Pobylitsa, M.V.Polyakov, • I.Bornig, K.Goeke and C.Weiss,Phys. • Rev. D574325 (1998) • 4.Nucleon light-cone d.a. • V.Y.Petrov, M.V.Polyakov, arXiv:hep-ph/0307077 M. Praszałowicz (Kraków)

  37. Applications of Chiral Quark Models • Spectra: Diakonov, Petrov, Polyakov , Z.Phys A359 (97) • M.P., Phys. Lett. B575 (2003) 234 • 2. Nucleon distribution functions: • D.Diakonov, V.Petrov, P.Pobylitsa, • M.V.Polyakov C.Weiss, • Nucl. Phys.B480, 341 (1996) • 3. Skewed parton distributions: • V.Y.Petrov, P.V.Pobylitsa, M.V.Polyakov, • I.Bornig, K.Goeke and C.Weiss,Phys. • Rev. D574325 (1998) • 4.Nucleon light-cone d.a. • V.Y.Petrov, M.V.Polyakov, arXiv:hep-ph/0307077 • 5. Pion light-cone d.a. • M.P., A.Rostworowski: Phys. Rev. D64 (2001) 074003 Phys.Rev.D66 (2002) 054002, M.P., A. Bzdak Acta. Phys. • Pol. B34 (2003) 3401, V.Yu. Petrov and P.V. Pobylitsa, • hep-ph/9712203, V.Yu. Petrov, M.V. Polyakov, R. Ruskov, • C. Weiss and K. Goeke, Phys. Rev. D59 (1999)114018 M. Praszałowicz (Kraków)

  38. Applications of Chiral Quark Models • Spectra: Diakonov, Petrov, Polyakov , Z.Phys A359 (97) • M.P., Phys. Lett. B575 (2003) 234 • 2. Nucleon distribution functions: • D.Diakonov, V.Petrov, P.Pobylitsa, • M.V.Polyakov C.Weiss, • Nucl. Phys.B480, 341 (1996) • 3. Skewed parton distributions: • V.Y.Petrov, P.V.Pobylitsa, M.V.Polyakov, • I.Bornig, K.Goeke and C.Weiss,Phys. • Rev. D574325 (1998) • 4.Nucleon light-cone w.f. • V.Y.Petrov, M.V.Polyakov, arXiv:hep-ph/0307077 • 5. Pion light-cone w.f. • M.P., A.Rostworowski: Phys. Rev. D64 (2001) 074003 Phys.Rev.D66 (2002) 054002, M.P., A. Bzdak Acta. Phys. • Pol. B34 (2003) 3401, V.Yu. Petrov and P.V. Pobylitsa, • hep-ph/9712203, V.Yu. Petrov, M.V. Polyakov, R. Ruskov, • C. Weiss and K. Goeke, Phys. Rev. D59 (1999)114018 • 6. Two pion DA, pion skewed and off-forward distributions and structure functions: M.P., A.Rostworowski, Acta Phys.Polon.B34, 2699 (2003) M. Praszałowicz (Kraków)

  39. Summary Soliton models are effective chiral descendants of QCD Collective quantization reproduces known multiplets Exotics appears in a natural way Skyrme model indicates that exotics are light QM has some freedom concerning spectrum, states are narrow, cancellation consistent with Nc QM is able to describe various properties of baryons Nc counting is wrong for the widths reason: phase space splittings are O(1) Is rigid rotator valid in this case? No exotics in bound state approach M. Praszałowicz (Kraków)

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