Heavy baryon spectra from QCD sum rules

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Heavy baryon spectra from QCD sum rules
Jian-Rong Zhang National University of Defense
Technology, China In collaboration with
Ming-Qiu Huang April 19-22 _at_ Beijing NSTAR 2009
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• Content
• 1. Introduction
• Experimental and theoretical overview
• 2. Heavy baryons in QCD sum rules
• Heavy baryon QCDSR
• Numerical results and discussions
• 3. Summary and outlook

Based on J. R. Zhang and M. Q. Huang, PRD 77,
094002 (2008) D 78, 094007 (2008) D 78, 094015
(2008) PLB 674, 28 (2009).
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1. Introduction
The heavy baryon is a field for testing Standard
Model and understanding the strong interaction
theory. ?Experiments CDF collaboration D0
collaboration BABAR collaboration Belle
collaboration SELEX collaboration
doubly heavy baryons However, BABAR
collaboration and Belle collaboration have not
observed doubly charmed baryon in
annihilations. ?
triply heavy baryons
CDF Collaboration, PRL 96, 202001 (2006) BABAR
Collaboration, PRL 97, 232001 (2006) D0
Collaboration, PRL 99, 052001 (2007) CDF
Collaboration, PRL 99, 052002 (2007) BABAR
Collaboration, PRL 99, 062001 (2007) CDF
Collaboration, PRL 99, 202001 (2007) BABAR
Collaboration, PRD 77, 012002 (2008) D0
Collaboration, PRL 101, 232002 (2008) Belle
Collaboration, PLB 672, 1 (2009) .
singly heavy baryons
SELEX Collaboration, PRL 89, 112001 (2002) SELEX
Collaboration, PLB 628, 18 (2005)
Belle Collaboration, PRL 97, 162001 (2006) BABAR
Collaboration, PRD 74, 011103 (R) (2006)
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?The feasibility studied at the
LHC ?Theoretically quark models mass
formulas lattice QCD stimulations MIT bag
model variational method
J. P. Ma et al., PLB 568, 135 (2003) M. A. Gomshi
Nobary et al., NPB741, 34 (2006) C. H. Chang et
al., CPC 177, 467 (2007) M. A. Gomshi Nobary et
al., PRD 76, 114006 (2007)
P. Hasenfratz et al., PLB 94, 401 (1980) J. D.
Bjorken, Preprint FERMILAB-Conf-85-069 S.
Capstick et al., PRD 34, 2809 (1986) D. Ebert et
al., PRD 72, 034026 (2005) D. Ebert et al., PLB
659, 612 (2008) R. Roncaglia et al., PRD 52, 1722
(1995) T. W. Chiu et al., NPA 755, 471c (2005) D.
H. He et al., PRD 70, 094004 (2004) Y. Jia, JHEP
0610, 073 (2006)
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QCD sum rules M. A. Shifman, A. I. Vainshtein,
and V. I. Zakharov seminal papers NPB147, 385
(1979) B147, 448 (1979) B. L. Ioffe
baryon E. V. Shuryak heavy baryon A.
G. Grozin, Y. B. Dai, S. Groote etc.
HQET E. Bagan, V. V. Kiselev, T. M. Aliev, M.
Nielsen etc. full theory our studies
on singly, doubly, and triply heavy baryon spectra
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2. Heavy baryons in QCD sum rules
basic point interpolating current diquark-quark
picture, namely (qq)-Q for the singly heavy baryon
Singlet state
Doublet states
(QQ)-q for doubly, (QQ)-Q for triply heavy
baryon
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For singly heavy baryon, e.g.
Here the index T means matrix transposition, C is
the charge conjugation matrix, a, b, and c are
color indices, Q denotes the heavy quark, and q
is u or d.
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For doubly heavy baryon, e.g.
For triply heavy baryon, e.g.
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QCDSR basic idea 1) a phenomenological
description of the correlator 2) a theoretical
description of the same correlator via an OPE 3)
a procedure for matching these two descriptions
and extracting the parameters that characterize
the hadronic state of interest. The accuracy is
limited by a very complicated hadronic dispersion
integrals and by the approximations in the OPE
of the correlator. Mass sum rules for the singly
heavy baryon the starting point
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In the phenomenology side, the correlator can be
expressed as
In the OPE side, the correlator can be written as
After equating the two sides, assuming
quark-hadron duality, making a Borel transform,
and eliminating the baryon coupling constant,
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D. Ebert etc. Quark model
R. Roncaglia etc. Mass formulas
N. Mathur etc. Lattice results
S. L. Zhu etc. HQET SR
uncertainty in our results are merely due to the
sum rule windows
Note that the QCD corrections are not
covered
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D. H. He etc. MIT bag model
V. V. Kiselev etc. NRQCDSR
R. Roncaglia etc. Mass formulas
D. Ebert etc. Quark model
E. Bagan etc. QCDSR
the absolute discrepancies are not small,
whereas, the relative ones are in the tolerable
ranges of the sum rule accuracy.
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J. M. Richard etc. potential model
Y. Jia Varitional method
J. D. Bjorken potential model
A. P. Martynenko potential model
T. W. Chiu etc. Lattice result
agree well
our central values are lower than potential model
predictions, in particular, for , slightly
more than 1 GeV, whereas the relative discrepancy
approximates to 10, which is still acceptable.
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3. Summary

• We have studied the mass spectra of singly,
  doubly, and triply heavy baryons in the framework
  of full QCD sum rules.
• Our results for singly heavy baryons are well
  compatible with the experimental data.
• The mass values for doubly heavy baryons are in
  reasonable accord with other predictions.
• The numerical results for triply heavy baryons
  are lower than the predictions from potential
  models, nevertheless, the one for is in
  good agreement with the lattice study.

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Outlook

• ?In experiment
• 1) quantum numbers
• 2) More data on singly bottom baryons, doubly
  heavy baryons
• evidence on triply heavy baryons
• LHC startup
• ? In QCDSR
• 1) take into account the QCD
  corrections
• 2) triply lattice QCD

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Thank you!