1. 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 , 2004

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

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

4. 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)

5. 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)  1.6  MeV
COSY (p p)  4 MeV
HERMES (e p)  9  3 MeV
DUBNA (bubbl.ch.)  4 MeV
Phase shifts: < 2 MeV
2.0
1.6
Oct. 25, 2004
M. Praszałowicz (Kraków)

6. 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)

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

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

9. 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)

10. 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)

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

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

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

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

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

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

17. 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)

18. 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)

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

20. 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)

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

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

23. 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)

24. 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)

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

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

28. M.P., Phys. Lett. B575 (2003) 234 and talk at the Cracow Workshop
on Skyrmions and Anomalies, Mogilany, Poland, , 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:
Oct. 25, 2004
M. Praszałowicz (Kraków)

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

36. 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/
Oct. 25, 2004
M. Praszałowicz (Kraków)

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

38. M. Praszałowicz (Kraków)
Small Soliton Limit
Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305
MP, A.Blotz K.Goeke, Phys.Lett.B354: ,1995
energy is calculated
with respect to the vacuum:
in the small soliton limit only valence level contributes
Oct. 25, 2004
M. Praszałowicz (Kraków)

39. 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)

40. 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)

41. 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)

42. 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)

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

44. 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)

45. 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)

46. 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)

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

48. Matching with the bound state approach
Callan, Klebanov Nucl.Phys.B262:365,1985
Nadeau, Nowak, Rho, VentoPhys.Rev.Lett.57: ,1986
Callan, Klebanov , Hornbostel, Phys.Lett.B202:269,1988
Itzhaki, Klebanov, Quyang, Rastelli, Nucl.Phys.B684: ,2004
K- is bound
K+ is not bound and has
no smooth limit to rigid rotator K
WZ
Oct. 25, 2004
M. Praszałowicz (Kraków)

49. 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)

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

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