Successes and problems of chiral soliton approach to exotic baryons Cracow Epiphany Conference on Hadron Spectroscopy January 6-8, 2005 Michał Praszałowicz - Jagellonian University Kraków, Poland
Jan 14, 2016
Successes and problems of chiral soliton approach
to exotic baryons
Cracow Epiphany Conferenceon Hadron Spectroscopy
January 6-8, 2005
Michał Praszałowicz - Jagellonian University
Kraków, Poland
Jan. 6, 2004 M. Praszałowicz (Kraków) 2
Jan. 6, 2004 3
Early predictions:
quark models: Gell-Mann mentioned 10*
but Z+ was expected to be negative parityheavy (> 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
Jan. 6, 2004 M. Praszałowicz (Kraków) 4
Spectrum of the Dirac operator
Jan. 6, 2004 M. Praszałowicz (Kraków) 5
Spectrum of the Dirac operator
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
Jan. 6, 2004 M. Praszałowicz (Kraków) 8
Baryons
Jan. 6, 2004 M. Praszałowicz (Kraków) 9
Baryons
Jan. 6, 2004 M. Praszałowicz (Kraków) 10
Baryons
sealevels:
energyincreases
valencelevel:
energydecreases
system stabilzes
This is
Jan. 6, 2004 M. Praszałowicz (Kraków) 11
Chiral Quark Model
fermionspions
integrate out quarks
"Skyrme" Model
only massless pion fields, kinetic term + interaction terms
constituent quarkmass ~ 350 MeV
Jan. 6, 2004 M. Praszałowicz (Kraków) 12
Chiral Quark Model
fermionspions
integrate out quarks
Skyrme Model
only massless pion fields, kinetic term + interaction terms
constituent quarkmass ~ 350 MeV
Soliton in the Skyrme model is stabilizes by the Sk. term
Jan. 6, 2004 M. Praszałowicz (Kraków) 13
time-dependent rotation
angular velocities:
Quantizing SU(3) Skyrmionand QM
analogy with symmetric top
Jan. 6, 2004 M. Praszałowicz (Kraków) 14
Wave functions and allowed states
B S
Y
I3
Jan. 6, 2004 M. Praszałowicz (Kraków) 15
Mass formula
x
first order perturbation in the strange quark massand in Nc:
octet-decupletsplitting
exotic-nonexotic splittingsknown ?
O(1) correctionsto Mcl do not allowfor absolute mass predictions
Jan. 6, 2004 M. Praszałowicz (Kraków) 16
Mass formula
x
first order perturbation in the strange quark massand in Nc:
octet-decupletsplitting
exotic-nonexotic splittingsknown ?
E. Guadagnini Nucl.Phys.B236 (1984) 35
Jan. 6, 2004 M. Praszałowicz (Kraków) 17
Skyrme model spectrum
symmetry breakingHamiltonian is tooprimitive: richerstructure is needed
Jan. 6, 2004 M. Praszałowicz (Kraków) 18
go to higher orders in ms go to higher orders in Nc
Jan. 6, 2004 M. Praszałowicz (Kraków) 19
Yabu-Ando: higher orders in ms
second order: H. Yabu, K. Ando, Nucl.Phys.B301 (1988) 601
Constraints:
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
Jan. 6, 2004 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.
Jan. 6, 2004 M. Praszałowicz (Kraków) 21
go to higher orders in ms go to higher orders in Nc
Jan. 6, 2004 M. Praszałowicz (Kraków) 22
QM breaking hamiltoniancalculate next-to-leading contributions to H'
O(Nc)+O(1) O(1) all O(ms)O(1)
equivalent to Guadagninimass formula:
E. Guadagnini Nucl.Phys.B236 (1984) 35
Jan. 6, 2004 M. Praszałowicz (Kraków) 23
QM breaking hamiltoniancalculate next-to-leading contributions to H'
O(Nc)+O(1) O(1) all O(ms)O(1)
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
Jan. 6, 2004 M. Praszałowicz (Kraków) 24
QM breaking hamiltoniancalculate next-to-leading contributions to H'
O(Nc)+O(1) O(1) all O(ms)O(1)
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
25
Antidecuplet in QMricher H': splittings in 10 10 , still no handle on I2
Diakonov, PetrovPolyakov Z.Phys A359 (97)
M10
fixes I2
fixed byN
Jan. 6, 2004 M. Praszałowicz (Kraków) 26
Freedom in QM
NA49
M.M.Pavan, I.I.Strakovsky, R.L.Workman, R.A.Arndt, PiN Newslett. 16 (2002) 110T.Inoue, V.E. Lyubovitskij, T.Gutsche, A.Faessler, arXiv:hep-ph/0311275
M.Diakonov, V.Petrov, M.Polyakov, Z.Phys. A359 (1997) 305
27 -plet
Jan. 6, 2004 M. Praszałowicz (Kraków) 27
Width
Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305
Weigel, Eur.Phys.J.A2 (98) 391, hep-ph/0006619
G.S. Adkins, C.R. Nappi, E. Witten, Nucl. Phys. B228 (1983) 552
operator V has the same structure as axial current
Jan. 6, 2004 M. Praszałowicz (Kraków) 28
Width in the soliton model
Decuplet decay:
Antidecuplet decay:
In NRQM limit:
SU(3)relations
Jan. 6, 2004 M. Praszałowicz (Kraków) 29
Small Soliton Limit
energy is calculated with respect to the vacuum:
in the small soliton limit only valence level contributes
Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305
MP, A.Blotz K.Goeke, Phys.Lett.B354:415-422,1995
Jan. 6, 2004 M. Praszałowicz (Kraków) 30
WidthDiakonov, Petrov, Polyakov, Z.Phys A359 (97)
305
Decuplet decay:
Antidecuplet decay:
In small soliton limit:In reality:
< 15 MeV
Jan. 6, 2004 M. Praszałowicz (Kraków) 31
Mass formula
O(Nc)
O(1/Nc)
O(Nc,ms)
O(Nc,ms)
unknown corrections O(1)
O(1) O(Nc)
+ O(1,ms)
Jan. 6, 2004 M. Praszałowicz (Kraków) 32
chiral limit:
nonzero meson masses:
Width
Jan. 6, 2004 M. Praszałowicz (Kraków) 33
Matching with the bound state approach
K
Callan, Klebanov Nucl.Phys.B262:365,1985Nadeau, Nowak, Rho, VentoPhys.Rev.Lett.57:2127-2130,1986 Callan, Klebanov , Hornbostel, Phys.Lett.B202:269,1988Itzhaki, Klebanov, Quyang, Rastelli, Nucl.Phys.B684:264-280,2004
K- is bound K+ is not bound and has no smooth limit to rigid rotator
WZ
Jan. 6, 2004 M. Praszałowicz (Kraków) 34
Applications of Chiral Quark Models1. 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)
Jan. 6, 2004 M. Praszałowicz (Kraków) 35
Applications of Chiral Quark Models1. 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. D57 4325 (1998)
Jan. 6, 2004 M. Praszałowicz (Kraków) 36
Applications of Chiral Quark Models1. 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. D57 4325 (1998)
4. Nucleon light-cone d.a.V.Y. Petrov, M.V. Polyakov, arXiv:hep-ph/0307077
Jan. 6, 2004 M. Praszałowicz (Kraków) 37
Applications of Chiral Quark Models1. 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. D57 4325 (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 0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6 (a)
(u)
M = 350 MeV, n = 3
u
nonlocal current local current asymptotic
Jan. 6, 2004 M. Praszałowicz (Kraków) 38
Applications of Chiral Quark Models1. 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. D57 4325 (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)
Jan. 6, 2004 M. Praszałowicz (Kraków) 39
SummarySoliton models are effective chiral descendants of QCDCollective quantization reproduces known multipletsExotics appears in a natural waySkyrme model indicates that exotics are lightQM 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 widthsreason: phase spacesplittings are O(1)
Is rigid rotator valid in this case?No exotics in bound state approach