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

Michał Praszałowicz - Jagellonian University

Kraków, Poland

Oct. 25, 2004 M. Praszałowicz (Kraków) 2

Wh

at

will

hap

pen

to t

his

en

try

in P

DG

?

3

Experimental evidence forstrange baryon +

Final state:

K0 + p

K+ + n

K0 + p ?

light + is predictedin chiral models

typical QM value is1700 - 1800 MeV

Oct. 25, 2004 M. Praszałowicz (Kraków) 4

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

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

2.01.6

Oct. 25, 2004 M. Praszałowicz (Kraków) 6

Spin and parity

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

12

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

Antidecuplet

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

NA49 @ CERN

Oct. 25, 2004 M. Praszałowicz (Kraków) 9

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

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

Spontaneously broken chiral symmetry

Oct. 25, 2004 M. Praszałowicz (Kraków) 11

Spectrum of the Dirac operator

Oct. 25, 2004 M. Praszałowicz (Kraków) 12

Spectrum of the Dirac operator

Oct. 25, 2004 M. Praszałowicz (Kraków) 13

Spectrum of the Dirac operator

Oct. 25, 2004 M. Praszałowicz (Kraków) 14

Spectrum of the Dirac operator

sealevels:

energyincreases

valencelevel:

energydecreases

system stabilzes

Oct. 25, 2004 M. Praszałowicz (Kraków) 15

SU(3) soliton: static solution

hedgehog Ansatz:

Soliton in the Chiral Quark Modelfrom: D.I. Diakonov, hep-ph/0009006

Skyrme limitQM limit true minimum

valence level

sea levels

Oct. 25, 2004 M. Praszałowicz (Kraków) 17

Chiral Quark Model

fermionspions

integrate out quarks

"Skyrme" Model

only pion fields, kinetic term + interaction terms

constituent quarkmass ~ 350 MeV

Oct. 25, 2004 M. Praszałowicz (Kraków) 18

Chiral Quark Model

fermionspions

integrate out quarks

Skyrme Model

only pion fields, kinetic term + interaction terms

constituent quarkmass ~ 350 MeV

Soliton in the Skyrme model is stabilizes by the Sk. term

Oct. 25, 2004 M. Praszałowicz (Kraków) 19

time-dependent rotation

angular velocities:

Quantizing SU(3) Skyrmionand QM

Oct. 25, 2004 M. Praszałowicz (Kraków) 20

x' y'

z'

k - momentum projection on z'

x

y

z

m - momentum projection on z

Wave functions analogy with a symmetric top

QM textbookLandau, Lipschitz: QM &103

~ N D(J)*(',,)

m,k - angular momentum projections

mk

In SU(3) J R = (p,q), m,k (Y,I,I3)however, because of the constraintnot all k's are allowed but onlythose which have k = (Y=1, I,I3)

Oct. 25, 2004 M. Praszałowicz (Kraków) 21

add small moment of inertia

generalized "momenta":

Hamiltonian:

constraint for 0

Quantizing SU(3) Skyrmion and QM

Oct. 25, 2004 M. Praszałowicz (Kraków) 22

Wave functions and allowed states

B S

Y

I3

Oct. 25, 2004 M. Praszałowicz (Kraków) 23

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 24

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

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

Skyrme model spectrum

symmetry breakingHamiltonian is tooprimitive: richerstructure is needed

Oct. 25, 2004 M. Praszałowicz (Kraków) 26

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

second order:

4 free parameters: Msol, I1, I2 and , but now I2 contributes to nonexotic splittings

fix and then minimize2 with respect to theremaining parameters

GMO YA

H. Yabu, K. Ando, Nucl.Phys.B301 (1988) 601

sensitive to I2

GMO YA

600 650 700 750 8001300

1400

1500

1600

1700

1800

1900(b)

_

3/2

10

N*

+

mas

s [M

eV]

[MeV]400 500 600 700 800 900

900

1000

1100

1200

1300

1400

1500

1600

1700(a)

+

*

*

N

mas

s [M

eV]

[MeV]

threshold

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.

Oct. 25, 2004 M. Praszałowicz (Kraków) 29

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.

Oct. 25, 2004 M. Praszałowicz (Kraków) 30

go to higher orders in ms go to higher orders in Nc

31

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 32

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 33

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

34

Antidecuplet in QMricher H': splittings in 10 10 , still no handle on I2

Diakonov, PetrovPolyakov Z.Phys A359 (97)

M10

fixes I2

fixed byN

Oct. 25, 2004 M. Praszałowicz (Kraków) 35

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

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

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 37

Width in the soliton model

Decuplet decay:

Antidecuplet decay:

In NRQM limit:

SU(3)relations

Oct. 25, 2004 M. Praszałowicz (Kraków) 38

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 39

WidthDiakonov, 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

WidthDiakonov, Petrov, Polyakov, Z.Phys A359 (97)

305

Decuplet decay:

Antidecuplet decay:

In small soliton limit:

O(Nc) O(1) O(1) Nc

+ O(1)Is this cancellationconsistent with large Nc counting?

MP Phys.Lett.B583:96-102,2004

Oct. 25, 2004 M. Praszałowicz (Kraków) 41

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

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

Width

MP Phys.Lett.B583:96-102,2004

Oct. 25, 2004 M. Praszałowicz (Kraków) 44

in small soliton limit cancellation takesplace separately in each order in Nc

Width

MP, T. Watabe, K. Goeke Nucl.Phys.A647:49-71,1999

MP Phys.Lett.B583:96-102,2004

Oct. 25, 2004 M. Praszałowicz (Kraków) 45

Mass formula

O(Nc)

O(1/Nc)

O(Nc,ms)

O(Nc,ms)

unknown corrections O(1)

O(1) O(Nc)

+ O(1,ms)

Oct. 25, 2004 M. Praszałowicz (Kraków) 46

O(1)

O(1/Nc)

O(Nc3)

O(Nc3)

O(1/Nc2)

O(1/Nc2)

Width1/5

Oct. 25, 2004 M. Praszałowicz (Kraków) 47

chiral limit:

nonzero meson masses:

Width

Oct. 25, 2004 M. Praszałowicz (Kraków) 48

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 49

Summary

Collective 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

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

Oct. 25, 2004 M. Praszałowicz (Kraków) 51

Comment on the width arithmeticsDiakonov, Petrov, Polyakov, Z.Phys A359 (97) 305 & Jaffe hep-ph/0401187

decreases

width decreasesIn the paper: inverted

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