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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. KIAS-Hanyang Joint Workshop on Multifaceted Skyrmions and Effective Field Theory October 25 - 27, 2004. What will happen to this entry in PDG?.

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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 KIAS-Hanyang Joint Workshop on Multifaceted Skyrmions and Effective Field Theory October 25 - 27, 2004

  2. What will happen to this entry in PDG? M. Praszałowicz (Kraków)

  3. Experimental evidence forstrange baryon + Final state: K+ + n K0 + p K0 + p ? light + is predicted in chiral models typical QM value is 1700 - 1800 MeV

  4. Do we see + at all ? • Experiments that do not see +: • HERA-B, H1 • STAR & PHENIX (RHIC) - ? • Opal, Aleph, Delphi (LEP) • BES (Beijing) • CDF, Hyper-CP (Fermilab), E690 • BaBar • Phase shifts from old K-scattering exps. mostly high energy inclusive M. Praszałowicz (Kraków)

  5. Width • Most experiments give only upper limits: • CLAS ( p) < 23 MeV • DIANA (K+ Xe) < 9 MeV • However, some other experiments quote errors: • ZEUS (DIS) 6.1  1.6  MeV • COSY (p p) 18  4 MeV • HERMES (e p) 17  9  3 MeV • DUBNA (bubbl.ch.) 16  4 MeV • Phase shifts: < 2 MeV 2.0 1.6 M. Praszałowicz (Kraków)

  6. Spin and parity spin will be measured by CLAS later this year 1 2 Unknown, in most models S = parity: + - ChSM, correlated QM, QM with flavor dep.forces, 1  lattice parity: - - uncorrelated QM (but wider), lattice (if at all), SumRules M. Praszałowicz (Kraków)

  7. Antidecuplet M. Praszałowicz (Kraków)

  8. NA49 @ CERN M. Praszałowicz (Kraków)

  9. Spontaneously broken chiral symmetry constituent quark mass: How does a low-momentum chirally invariant Lagrangian look like? however, it is not invariant under chiral transformation M. Praszałowicz (Kraków)

  10. Spontaneously broken chiral symmetry Lagrangian is invariant, because one can absorb chiral rotation into the redefined pseudoscalar meson fieldsA Chiral symmetry is spontaneously broken Goldstone bosons are massless M. Praszałowicz (Kraków)

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

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

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

  14. Spectrum of the Dirac operator valence level: energy decreases sea levels: energy increases system stabilzes M. Praszałowicz (Kraków)

  15. SU(3) soliton: static solution hedgehog Ansatz:  M. Praszałowicz (Kraków)

  16. Soliton in the Chiral Quark Model from: D.I. Diakonov, hep-ph/0009006 sea levels valence level Skyrme limit QM limit true minimum

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

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

  19. Quantizing SU(3) Skyrmion and QM time-dependent rotation angular velocities: M. Praszałowicz (Kraków)

  20. Wave functions analogy with a symmetric top m - momentum projection on z k - momentum projection on z' z QM textbook Landau, Lipschitz: QM &103 ~ N D(J)*(',,) m,k - angular momentum projections z' mk y In SU(3) J R = (p,q), m,k (Y,I,I3) however, because of the constraint not all k's are allowed but only those which have k = (Y=1, I,I3) y' x' x M. Praszałowicz (Kraków)

  21. Quantizing SU(3) Skyrmion and QM add small moment of inertia  generalized "momenta": Hamiltonian: constraint for   0 M. Praszałowicz (Kraków)

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

  23. 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)

  24. 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)

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

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

  27. Yabu-Ando: higher orders in ms H. Yabu, K. Ando, Nucl.Phys.B301 (1988) 601 second order: sensitive to I2 4 free parameters: Msol, I1, I2 and , but now I2contributes to nonexotic splittings fix  and then minimize 2 with respect to the remaining parameters GMO YA GMO YA M. Praszałowicz (Kraków)

  28. M.P., Phys. Lett. B575 (2003) 234 and talk at the Cracow Workshop on Skyrmions and Anomalies, Mogilany, Poland, 1987, World Scientific 1987, p.112. threshold

  29. 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. Constraints: M. Praszałowicz (Kraków)

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

  31. 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)

  32. 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)

  33. 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)

  34. 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

  35. 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)

  36. 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)

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

  38. 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)

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

  40. Width Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 Nc O(1) O(1)  O(Nc) + O(1) Is this cancellation consistent with large Nc counting? MP Phys.Lett.B583:96-102,2004 In small soliton limit: Decuplet decay: Antidecuplet decay: M. Praszałowicz (Kraków)

  41. Three sources of Nc factors: • quantum Y' = Nc/3 • parametric M, I1,2 ~ Nc • combinatorial SU(3) C-G's for arbitrary Nc M. Praszałowicz (Kraków)

  42. Wave functions and allowed states G. Karl, J. Patera, S. Perantonis, Phys. Lett 172B (1986) 49, J. Bijnens, H. Sonoda, M. Wise, Can. J. Phys. 64 (1986) 1, Z. Duliński, M. Praszałowicz, Acta Phys.Pol. B18 (1988) 1157. M. Praszałowicz (Kraków)

  43. Width MP Phys.Lett.B583:96-102,2004 M. Praszałowicz (Kraków)

  44. Width MP Phys.Lett.B583:96-102,2004 MP, T. Watabe, K. Goeke Nucl.Phys.A647:49-71,1999 in small soliton limit cancellation takes place separately in each order in Nc M. Praszałowicz (Kraków)

  45. 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)

  46. Width 1/5 O(1/Nc2) O(1) O(Nc3) O(1/Nc2) O(1/Nc) O(Nc3) M. Praszałowicz (Kraków)

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

  48. 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)

  49. Summary 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 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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