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Pentaquark decay width in QCD sum rules
F.S. Navarra , M. Nielsen and R.R da Silva
University of São Paulo, USP
Brazil
Introduction
Pentaquark mass
? decay width
Conclusions
LC 2005 CAIRNS
(? mass) Phys. Lett. B578 (2004) 323
(? mass) Phys. Lett. B602 (2004) 185
(? decay width) hep-ph/0503193
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Introduction
Something new in Hadron Physics
? (1540 MeV)
july/2003
?-- (1860 MeV)
september/2003
?c (3099 MeV)
april/2004
Exotic baryons can not be three-quark states
contain an antiquark !
vanishing...
may/2005

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? decay width
Resonance in the s channel ? peak in the cross
section
K d scattering Sibirtsev et al., PLB 599
(2004) 230
No peak !
MeV
Extremely narrow !
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Pentaquark structure
Meson-baryon molecules?
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QCD Sum Rules
Method for calculations in the non - perturbative
regime of QCD
Identities between correlation functions written
with hadron and quark gluon degrees of freedom
Two - point function hadron masses
Three - point function form factors and decay
width
Results are functions of the quark masses and
vacuum expectation values of QCD operators
condensates
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? mass
hadronic fields
?
composite quark fields
How to combine quark fields in a DDA arrange ?
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Matheus, Navarra, Nielsen, Rodrigues da Silva,
PLB 578 (2004) 323
2 scalar diquarks
2 pseudoscalar diquarks
Sugiyama, Doi, Oka PLB 581 (2004) 167
pseudoscalar diquark
scalar diquark
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Current contains contribution from the pole
(particle) and from the continuum
(resonances)
S0 continuum threshold parameter
Im ? ? spectral density
Combination of ?1 and ?2
Insert ? in the correlation function
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Operator product expansion (OPE)
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Numerical inputs (standard)
Parameters
s0
ms
t
What is good sum rule?
Borel stability
Good OPE convergence
Dominance of the pole contribution
Reasonable value of S0
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M?
ms0.1 GeV
t1
?s02.3 GeV
m?1.87 0.22 GeV
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OPE
perturbative
dimension 4
dimension 6
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continuum
pole
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? decay width
Extremely narrow width lt 10 MeV or even lt 1 MeV
Mass excess of 100 MeV (no problem with phase
space)
Possible reasons for a narrow width
Spatial configuration
Color configuration
Non-trivial string rearrangement
Destructive interference between almost
degenerate states
Chiral symmetry
. . .
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? decay in QCDSR
n
(p)
T
(p)
Three-point function
(q)
K
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Phenomenological side
L
(negative parity)
(positive parity)
L
(positive parity)
(negative parity)
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(positive parity)
(negative parity)
from QCD sum rules
continuum
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Theoretical side (OPE side)
currents
correlator
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OPE
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color disconnected
color connected
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Continuum and pole-continuum transitions
continuum
pole
pole
continuum
continuum
pole
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Continuum and pole-continuum transitions
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Continuum and pole-continuum transitions
(quark-hadron duality)
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A
B
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Borel transform schemes
I)
II)
III)
(unstable sum rule)
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Sum rules
I A
I B
II A
II B
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Numerical evaluation of the sum rules
From each sum rule and its derivative determine G
and A
? s are known from the mass sum rules G ?
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Sum rules with color connected diagrams
?N 0.4 GeV
I A
?N 0.5 GeV
?N 0.6 GeV
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?N 0.4 GeV
II A
?N 0.5 GeV
?N 0.6 GeV
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?N 0.4 GeV
?N 0.5 GeV
?N 0.6 GeV
I B
M 1.0 GeV
M 1.5 GeV
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?N 0.4 GeV
?N 0.5 GeV
?N 0.6 GeV
II B
M 1.0 GeV
M 1.5 GeV
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Results
(negative parity)
all diagrams
color connected
IA
0.7
2.6
IIA
0.8
3.6
IB
0.8
3.2
IIB
1.0
4.5
?? 8.6 MeV implies that g?nK 0.4
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Decay width
?? 650 MeV
All diagrams
Negative parity
Color connected
?? 37 MeV
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Conclusions
We have used QCDSR to study pentaquark properties
QCDSR for pentaquarks are not as satisfying as
for other hadrons
It is possible to obtain reasonable values for
the ? and ? masses
However the continuum contribution is large !
the OPE has irregular behavior !
The ? narrow width is more difficult to
understand
With all diagrams we can not obtain a narrow
width!
With only the color connected diagrams we obtain
a smaller width
Negative parity ? strongly disfavored
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Pentaquarks properties
? mass
?mq 340 510 860 MeV
Adition of two quarks
One unit of angular momentum
Non-trivial atraction mechanism