Successes%20and%20problems%20of%20chiral%20soliton%20approach%20to%20exotic%20baryons

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Successes and problems of chiral soliton
approach to exotic baryons
Michal Praszalowicz - Jagellonian
University Kraków, Poland

• KIAS-Hanyang Joint Workshop on
• Multifaceted Skyrmions and Effective Field Theory
  
• October 25 - 27, 2004

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What will happen to this entry in PDG?
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Experimental evidence forstrange baryon ?
Final state
K n
K0 p
K0 p ?
light ? is predicted in chiral models typical
QM value is 1700 - 1800 MeV
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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
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Width

• Most experiments give only upper limits
• CLAS (? p) lt 23 MeV
• DIANA (K Xe) lt 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 lt 2 MeV

2.0 1.6
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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
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Antidecuplet
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NA49 _at_ CERN
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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
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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
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Spectrum of the Dirac operator
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Spectrum of the Dirac operator
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Spectrum of the Dirac operator
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Spectrum of the Dirac operator
sea levels energy increases
valence level energy decreases
system stabilzes
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SU(3) soliton static solution
hedgehog Ansatz
?
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Soliton in the Chiral Quark Model
from D.I. Diakonov, hep-ph/0009006
sea levels
valence level
Skyrme limit
QM limit
true minimum
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Chiral Quark Model
constituent quark mass 350 MeV
pions
fermions
integrate out quarks
"Skyrme" Model
only pion fields, kinetic term interaction terms
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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
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Quantizing SU(3) Skyrmion and ?QM
time-dependent rotation
angular velocities
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Wave functions analogy with a symmetric top
m - momentum projection on z
k - momentum projection on z'
z
QM textbook Landau, Lipschitz QM 103 ? N
D(J)(?',?,?) m,k - angular momentum projections
z'
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
(Y1, I,I3)
y'
x'
x
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Quantizing SU(3) Skyrmion and ?QM
add small moment of inertia ?
generalized "momenta"
Hamiltonian
constraint for ? ? 0
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Wave functions and allowed states
B
S
I3
Y
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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
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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
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Skyrme model spectrum
symmetry breaking Hamiltonian is too primitive
richer structure is needed
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go to higher orders in ms
go to higher orders in Nc
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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
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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.
threshold
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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
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go to higher orders in ms
go to higher orders in Nc
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?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) all O(ms)
O(1)
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?QM breaking hamiltonian
calculate 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
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?QM breaking hamiltonian
calculate 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
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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
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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,
arXivhep-ph/0311275
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Width
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/0006619
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Width in the soliton model
SU(3) relations
? ?
Decuplet decay Antidecuplet decay
In NRQM limit
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Small Soliton Limit
Diakonov, Petrov, Polyakov, Z.Phys A359 (97)
305 MP, A.Blotz K.Goeke, Phys.Lett.B354415-422,19
95
energy is calculated with respect to the vacuum
in the small soliton limit only valence level
contributes
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Width
Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305
Decuplet decay Antidecuplet decay
In small soliton limit
In reality
lt 15 MeV
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Width
Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305
O(1)
O(1)
? Nc
O(Nc)
?
O(1)
Is this cancellation consistent with large Nc
counting? MP Phys.Lett.B58396-102,2004
In small soliton limit
Decuplet decay Antidecuplet decay
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• Three sources of Nc factors
• quantum Y' Nc/3
• parametric M, I1,2 Nc
• combinatorial SU(3) C-G's for arbitrary Nc

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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. Dulinski, M.
Praszalowicz, Acta Phys.Pol. B18 (1988) 1157.
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Width
MP Phys.Lett.B58396-102,2004
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Width
MP Phys.Lett.B58396-102,2004
MP, T. Watabe, K. Goeke Nucl.Phys.A64749-71,1999
in small soliton limit cancellation takes place
separately in each order in Nc
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Mass formula
O(Nc)
O(Nc,ms)
unknown corrections O(1)
O(1)
O(Nc)
O(1/Nc)
O(Nc,ms)
O(1,ms)
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Width
1/5
O(1/Nc2)
O(1)
O(Nc3)
O(1/Nc)
O(1/Nc2)
O(Nc3)
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Width
chiral limit
nonzero meson masses
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Matching with the bound state approach
Callan, Klebanov Nucl.Phys.B262365,1985 Nadeau,
Nowak, Rho, VentoPhys.Rev.Lett.572127-2130,1986
Callan, Klebanov , Hornbostel,
Phys.Lett.B202269,1988 Itzhaki, Klebanov,
Quyang, Rastelli, Nucl.Phys.B684264-280,2004
K- is bound K is not bound and has no
smooth limit to rigid rotator
K
?WZ
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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
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Comment on the width arithmetics
Diakonov, Petrov, Polyakov, Z.Phys A359 (97) 305
Jaffe hep-ph/0401187
decreases
width decreases
inverted
In the paper
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