Successes and problems of chiral soliton approach to exotic baryons

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Successes and problems of chiral soliton approach to exotic baryons 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

M. Praszałowicz (Kraków) What will happen to this entry in PDG? Oct. 25, 2004 M. Praszałowicz (Kraków)

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

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Antidecuplet Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) NA49 @ CERN Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Spectrum of the Dirac operator Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Spectrum of the Dirac operator Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Spectrum of the Dirac operator Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Spectrum of the Dirac operator valence level: energy decreases sea levels: energy increases system stabilzes Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) SU(3) soliton: static solution hedgehog Ansatz:  Oct. 25, 2004 M. Praszałowicz (Kraków)

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

M. Praszałowicz (Kraków) Chiral Quark Model constituent quark mass ~ 350 MeV pions fermions integrate out quarks "Skyrme" Model only pion fields, kinetic term + interaction terms Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

Quantizing SU(3) Skyrmion and QM time-dependent rotation angular velocities: Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Wave functions analogy with a symmetric top m - momentum projection on z k - momentum projection on z' z z' QM textbook Landau, Lipschitz: QM &103  ~ N D(J)*(',,) m,k - angular momentum projections 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

Quantizing SU(3) Skyrmion and QM add small moment of inertia  generalized "momenta": Hamiltonian: constraint for   0 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Wave functions and allowed states B S I3 Y Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Skyrme model spectrum symmetry breaking Hamiltonian is too primitive: richer structure is needed Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) go to higher orders in ms go to higher orders in Nc Oct. 25, 2004 M. Praszałowicz (Kraków)

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 I2 contributes to nonexotic splittings fix  and then minimize 2 with respect to the remaining parameters GMO YA GMO YA Oct. 25, 2004 M. Praszałowicz (Kraków)

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

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: Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) go to higher orders in ms go to higher orders in Nc Oct. 25, 2004 M. Praszałowicz (Kraków)

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)

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 Oct. 25, 2004 M. Praszałowicz (Kraków)

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 Oct. 25, 2004 M. Praszałowicz (Kraków)

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

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

Width operator V has the same structure as axial current 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

Width in the soliton model SU(3) relations   Decuplet decay: Antidecuplet decay: In NRQM limit: Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

Width < 15 MeV Decuplet decay: Antidecuplet decay: Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 Decuplet decay: Antidecuplet decay: In small soliton limit: In reality: < 15 MeV Oct. 25, 2004 M. Praszałowicz (Kraków)

Width  Nc Is this cancellation consistent with large Nc counting?  Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305  Nc  O(Nc) O(1) O(1) + 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: Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Three sources of Nc factors: quantum Y' = Nc/3 parametric M, I1,2 ~ Nc combinatorial SU(3) C-G's for arbitrary Nc Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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. Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Width MP Phys.Lett.B583:96-102,2004 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Mass formula O(Nc) O(Nc,ms) unknown corrections O(1) O(1) O(Nc) O(1/Nc) O(Nc,ms) + O(1,ms) Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Width 1/5 O(1/Nc2) O(1) O(Nc3) O(1/Nc2) O(1/Nc) O(Nc3) Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Width chiral limit: nonzero meson masses: Oct. 25, 2004 M. Praszałowicz (Kraków)

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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) 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 Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Comment on the width arithmetics Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 & Jaffe hep-ph/0401187 decreases width decreases In the paper: inverted Oct. 25, 2004 M. Praszałowicz (Kraków)

M. Praszałowicz (Kraków) Oct. 25, 2004 M. Praszałowicz (Kraków)