1. On a possibility of baryonic exotica
Michał Praszałowicz
in collaboration with
M.V. Polyakov (Bochum) H.-C. Kim (Incheon)

2. 2003
LEPS Collaboration

3. July 2003

4. exotic quantum numbers very small width: a few MeV
July 2003
exotic quantum numbers
small mass: 1.5 GeV
very small width: a few MeV

5. Michal Praszalowicz, Krakow
Quark Model
(uudds): 4 x ~ 1900 MeV
 ~ MeV
pentaquark: strangeness +1 +
(2s) - (s) = 150 MeV
spin 1/2
parity  
Michal Praszalowicz, Krakow

6. Michal Praszalowicz, Krakow
Chiral Soliton Models
Biedenharn, Dothan (1984):
10-8 ~ 600 MeV Skyrme model
MP (1987):
M= 1535 MeV Skyrme model
in model independent approach,
second order
Diakonov, Petrov, Polyakov (1997):
QM - model independent approach,
1/Nc corrections  M= 1530 MeV
small width < 15 MeV !
In Chiral Soliton Models quark-antiquark pairs are added as chiral
excitations of low mass (pion is massless!) rather than as two
constituent (i.e. heavy) quarks.
Michal Praszalowicz, Krakow

7. Michal Praszalowicz, Krakow
Soliton Quark Model
(uudds): 4 x ~ 1900 MeV MeV
 ~ 400 MeV a few MeV
pentaquark: strangeness +1 +
(2s) - (s) = 150 MeV 350
spin 1/2
parity + 
Michal Praszalowicz, Krakow

8. What is the experimental status of light pentaquarks today?+ 

9. LEPS
and various conference
proceedings
e.g. T. Nakano
MENU 2016

10. DIANA

11. dissidents from CLAS

12. disicalaimer from CLAS

13. What is the experimental status of light pentaquarks today?+ 

14. NA 49

15. What is the experimental status of light pentaquarks today?+ 

16. Pentanucleon? D. Werthmuller et al. [A2 Collaboration]
Phys. Rev. Lett. 111 (2013) 23,
Eur. Phys. J. A 49 (2013) 154
Phys. Rev. Rev. C 90 (2014)
Michał Praszałowicz

17. Pentanucleon?
M.V. Polyakov and A. Rathke,
On photoexcitation of baryon anti-decuplet
Eur. Phys. J. A 18 (2003) 691
natural (but not the only one) explanation if N* is a pentaquark

19. QCD: quarks and gluons many quark nonlocal interactions
integrate out gluons
many quark nonlocal interactions
Lagrangian chirally symmetric
approximation:
manyq, nonl q, local
Nambu Jona Lasinio model
spontaneous chiral symmetry breaking
semibosonization:
qqqq qq
Chiral Quark Model
M. Praszałowicz

20. Chiral Quark Soliton Model
QCD vacuum:

21. Chiral Quark Soliton Model
QCD vacuum:

22. Chiral Quark Soliton Model
chiral symmetry breaking:
chirally inv. manyquark int.

23. Chiral Quark Soliton Model
adding vlence quarks:
chirally inv. manyquark int.

24. Chiral Quark Soliton Model
“classical” baryon:
chirally inv. manyquark int.
soliton configuration
no quantum numbers except B

25. Chiral Quark Soliton Model
“classical” baryon:
= Nc ×
chiral symmetry breaking
chirally inv. manyquark int.
soliton configuration
no quantum numbers except B
color factorizes!

26. Chiral Quark Soliton Model
baryon:
chirally inv. manyquark int.
soliton configuration
no quantum numbers except B
rotation generates flavor and spin

27. Mass formula first order perturbation in the strange quark mass
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
P.O. Mazur, M.A. Nowak, MP, Phys. Lett. 147B (1984) 137
E. Guadagnini, Nucl. Phys. B236 (1984) 35
S. Jain, S.R. Wadia, Nucl. Phys. B258 (1985) 713

28. Allowed states

29. Successful Phenomenology
Ch.V. Christov et al. Prog. Part. Nucl. Phys. 37 (1996) 91
Successful Phenomenology
In a ”model independent” approach
one can get both good fits to the existing data
(including very narrow light pentaquark Θ+)
one can fix all necessary model parameters:
M, I1, I2, α, β, γ

30. Successful Phenomenology
Ch.V. Christov et al. Prog. Part. Nucl. Phys. 37 (1996) 91
Successful Phenomenology
In a ”model independent” approach
one can get both good fits to the existing data
(including very narrow light pentaquark Θ+)
one can fix all necessary model parameters:
M, I1, I2, α, β, γ
but also one can recover the NRQM result
in a special limit
NRQM limit =
= squeezing the soliton to zero size
MP, A. Blotz, K. Goeke Phys. Lett. B354 (1995) 415

31. NRQM Limit energy is calculated with respect to the vacuum:
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:

32. NRQM Limit energy is calculated with respect to the vacuum:
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:

33. NRQM Limit energy is calculated with respect to the vacuum:
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 NRQM limit only valence level contributes

34. NRQM Limit energy is calculated with respect to the vacuum:
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 NRQM limit only valence level contributes

35. NRQM Limit pentaquark width = 0 ! energy is calculated
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:
pentaquark width = 0 !
in the NRQM limit only valence level contributes

36. Soliton with Nc− 1 quarks
if Nc is large, Nc- 1 is also large and one
can use the same mean field arguments
(Nc−1) ×
color factorizes!
plus one heavy quark
G.S. Yang, H.C. Kim, M.V. Polyakov, MP Phys. Rev. D94 (2016)

37. Allowed SU(3) irreps.
= (Nc−1)/3

38. Heavy Baryons: soliton + heavy Q

39. Splittings inside multiplets
= SL
one has to add
h.f. interaction

40. Splittings inside multiplets
Equal splittings within
multiplets follow from
Eckhart-Wigner theorem
(GMO relations)

41. Splittings inside multiplets
Equal splittings within
multiplets follow from
Eckhart-Wigner theorem
(GMO relations)
however the
relation between
the deltas does not follow from
Eckhart-Wigner theorem

42. Splittings inside multiplets
from the fits
to the light
sector we get:
(exp.: 178 MeV)
13%
(exp.: 121 MeV)

43. Splittings inside multiplets
Successful phenomenology
from the fits
to the light
sector we get:
G.S. Yang, H.C. Kim, M.V. Polyakov, MP Phys. Rev. D94 (2016)
(exp.: 178 MeV)
13%
(exp.: 121 MeV)

44. Rotational excitations: heavy pentaquarks
2/3
H.C. Kim, M.V. Plyakov, MP arXiv: [hep-ph]

45. Rotational excitations: heavy pentaquarks
soliton in 15 (quatroquark)
(spin 1 < spin 0)
+ heavy quark: 1/2 + 3/2
2/3
H.C. Kim, M.V. Plyakov, MP arXiv: [hep-ph]

46. Rotational excitations: heavy pentaquarks
soliton in 15 (quatroquark)
(spin 1 < spin 0)
+ heavy quark: 1/2 + 3/2
2/3
H.C. Kim, M.V. Plyakov, MP arXiv: [hep-ph]

47. Decay constants
H.C. Kim, M.V. Plyakov, MP arXiv: [hep-ph]

48. Decay constants Expectations: some decays will be suppressed
In NRQM limit:
Expectations:
some decays will be suppressed
H.C. Kim, M.V. Plyakov, MP arXiv: [hep-ph]

49. Quark excitations: non-exotic heavy baryons
V. Petrov, Acta Phys. Pol. B47 (2016) 59

50. Quark excitations: non-exotic heavy baryons
Rotations generate quantum numbers

51. One K=1 quark excited solitons

52. 3bar excited heavy baryons
add heavy quark
total spin 1/2 and 3/2

53. 3bar excited heavy baryons
experimentally:
add heavy quark
total spin 1/2 and 3/2
hyprfine
splitting
different
from the
ground
state

54. sextet excited baryons

55. sextet excited baryons
excited Omega_Q spectrum,
5 states

56. 5 states!

57. Five very narrow resonances, unknown quantum numbers

58. Scenario 1: all LHCb Omega’s are sextet states
violates constraints:

59. Scenario 1: all LHCb Omega’s are sextet states
violates constraints:
similar problem in the quark models

60. Scenario 2 force sextet constraints

61. heavy states above Ξ + D threshold, large p.s. also to Ωc+ π, can be
very
wide
=24

62. Two narrow heavy states states (1 MeV) above inerpreted as Ξ + D
pentaquarks
heavy
states
above
Ξ + D
threshold,
large p.s.
also to
Ωc+ π,
can be
very
wide
=24

63. Consequences Omega’s form isospin triplet,
easy to check experimentally

64. Consequences rich structure - many new states,
also in the case of b baryons
Omega’s form isospin triplet,
easy to check experimentally

65. Conclusions
naive QM admits heavy pentaquarks with naturally large width
soliton models ARE quark models
successful phenomenology in the light baryon sector
in soliton models pentaquarks are naturally light
in NR limit no decay of antidecuplet to ocet (!)
LEPS and DIANA results stand
null results put bounds on prod. mechanism rather than exclude 5q
narrow structure in eta photoproduction on n – signature of 5q?
confirmation or refutation of NA49 result needed
heavy baryons can be desribed in terms of Nc-1 quark soliton
two types of excitations:
rotations: 15-bar (exotic)
quark excitations (regular)
two of the LHCb Omega_c states may be interpreted as 5q

67. Backup slides

68. Prediction for Ω*b Ω*c = 2764.5 ± 3.1 MeV (2765.9 ± 2.0)
model – independent relation:
satisfied for charm:
Ω*c = ± 3.1 MeV ( ± 2.0)

69. Ω*b = 6079.8 ± 2.3 MeV (to be confirmed)
Prediction for Ω*b
model – independent relation:
satisfied for charm:
Ω*c = ± 3.1 MeV ( ± 2.0)
Ω*b = ± 2.3 MeV (to be confirmed)

70. How narrow they are?
Assume p-wave decay and extract coupling from Delta decay

71. ground state L = 0 spin 1/2 h.f. splitting 70 MeV spin 3/2 ss -diquark
heavy quark
h.f. splitting 70 MeV
ss -diquark
spin 3/2
heavy quark

72. spin 1/2, 3/2 spin 1/2, 3/2, 5/2 excited state L = 1 ss -diquark
heavy quark
ss -diquark
spin 1/2, 3/2, 5/2
heavy quark

73. FIVE STATES as in LHCb ! spin 1/2, 3/2 spin 1/2, 3/2, 5/2
excited state L = 1
ss -diquark
spin 1/2, 3/2
heavy quark
FIVE STATES as in LHCb !
ss -diquark
spin 1/2, 3/2, 5/2
heavy quark

74. Very narrow excited Ωc baryons
Marek Karliner, Jonathan L. Rosner, e-Print: arXiv:
take general spin potential, try sensible parameters, only 3 parameters: a2 + c, a1, b.
does not work
Six Ω0c states discovered by LHCb as new members of 1P and 2S charmed baryons
Bing Chen, Xiang Liu, e-Print: arXiv:
they have wave functions, so can calculate coefficients, calculate other known states.
different mass ordering than KR,
widths do not agree

75. Quantum numbers of recently discovered Ω0c baryons from lattice QCD
M. Padmanath, Nilmani Mathur, e-Print: arXiv:
h.f. splitting 70 MeV