ANTICHARMED PENTAQUARK WITHIN THE QCD SUM RULES

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ANTICHARMED PENTAQUARK WITHIN THE QCD SUM RULES

• Yasemin Saraç
• Collaborators H. Kim, S. H. Lee

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• 1. INTRODUCTION
• 2. QCD SUM RULES FOR THE ANTICHARMED PENTAQUARK
• 2.1 Interpolating Field For ?c
• 2.2 Dispersion Relation
• 2.3 Phenomenological Side
• 2.3.1 ?c1 and ?cs1
• 2.3.2 ?c2 and ?cs2
• 2.3.3 Final Form of the Phenomenological Side
• 2.4 OPE Side
• 3.4.1 The OPE For ?c1
• 3.4.2 The OPE For ?c2
• 3.4.3 The OPE For ?cs1
• 3.4.4 The OPE For ?cs2
• 3. QCD SUM RULES AND ANALYSIS
• 3.1 The Couplings to the DN Continuum, ?DN
• 3.2 Parity
• 3.3 Mass

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1. Introduction

• The observation of ? by LEPS collaboration
• The latest experiments at JLAB No signal from
  the photoproduction process on a deuteron or on a
  proton target.
• H1 collaboration at HERA Observation of
  antic-harmed pentaquark state ?c(3099) from Dp
  invariant mass spectrum.
• In this work we applied QCD sum rules calculation
  to investigate the anti-charmed pentaquark state
  with and without strangeness using two different
  current for each case. We refined the convergent
  sum rule by explicitly including the DN-two
  particle irreducible contribution.

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2. QCD Sum Rules for the Anticharmed Pentaquark
2.1 Interpolating Fields for ?c

• 
  (2.1)
• 
  
  
• 
  (2.2)
• 
  

(2.3)
(2.4)
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2.2 Dispersion Relation
(2.6) (2.7) (2.8)

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In the zero-width resonance approximation, the
imaginary part in the rest frame is
written as
(2.9) (2.10) (2.11) (2.12) (2.13) (
2.14)
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2.3 Phenomenological Side2.3.1 ?c1 and ?cs1

• For ?c1 current, the interpolating field couples
  to a positive parity state as
  
• and to a negative parity state as

(2.15)
(2.16)
(2.17)
(2.18)
(2.19)
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(2.20)
(2.21)
The corresponding spectral density for the pole
and DN contributions
(2.22)
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2.3.2 ?c2 and ?cs2

• ?c2 transforms differently compared to ?c1 under
  parity. Thus, the couplings to the interpolating
  field are

(2.23)
(2.24)
(2.25)
(2.26)
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2.3.3 Final Form of the Phenomenological side
(2.27)
The spectral density for the two-particle
irreducible part is
(2.28)
(2.29)
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2.4 OPE Side2.4.1 The OPE for ?c1
Our OPE is given by
(2.30)
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The imaginary part of each diagram
(2.31)
?mc2/q2
L(u)q2u(1-u)-mc2u
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(2.32)
We use the following QCD parameters in our sum
rules
ms0.12 GeV , mc1.26 GeV
(2.33)
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S0(3.3 GeV)2
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3.4.2 The OPE for ?c2
The OPE for this current is given as follows
(2.34)
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2.4.3 The OPE for ?cs1

The OPE for this current is given as follows
(2.35)
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The OPE for ?cs2
The OPE for this current is given as follows
(2.36)
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3. QCD Sum Rules Analysis3.1 The Couplings to
the DN Continuum, ?DN

• As discussed before, it is important to subtract
  out the contribution from the DN continuum. For
  that, one needs to know the coupling strength
  ?DN.
• we determine the coupling strength directly from
  the sum rule method. To do that, we eliminate the
  contribution from the low-lying pole by
  introducing the additional weight
• W(q2)q2-m?2
• Then, substituting the corresponding imaginary
  parts, we obtain

(3.1)
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• The Plot of ?DN2

We will choose the following range for ??DN?2
values
(3.2)
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3.2 Parity

• Using the dispersion relation (Eq. 2.14) and
  the equation for spectral density (Eq. 2.27) one
  finds the following sum rule,

(3.3)
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3.3 Mass

• The sum rule for ?c mass is obtained by
  taking the derivative of previous equation (Eq.
  (3.2)) with respect to 1/M2 . The solid and
  dashed lines in figure represents the mass for
  two different ?DN values

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4. Conclusions

• OPE is convergent only for the non strange
  pentaquark with diquark structure.
• The OPE for this structure is dominated by gluon
  condensate coming from diquark.
• The heavy pentaquark without strangeness have
  positive parity and its mass lies below 3 GeV,
  when the DN irreducible contribution is
  explicitly included in the phenomenological side
  of the sum rule.