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