Download - Heavy baryon spectra from QCD sum rules
National University of Defense Technology
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 @ 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 , PRD 7777, 094002 (2008); D , 094002 (2008); D 7878, 094007 (2008); D , 094007 (2008); D 7878, 094015 (2008); PLB , 094015 (2008); PLB 674674, 28 (2009), 28 (2009).
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1. IntroductionThe 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 baryonsHowever, BABAR collaboration and Belle collaboration have not observed doubly charmed baryon in annihilations.
? triply heavy baryons
singly 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).……
Belle Collaboration, PRL 97, 162001 (2006);BABAR Collaboration, PRD 74, 011103 (R)
(2006);
SELEX Collaboration, PRL 89, 112001 (2002);SELEX Collaboration, PLB 628, 18 (2005);
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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-85-069S. 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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basic point: interpolating current
diquark-quark picture, namely (qq)-Q for the singly heavy baryon
Doublet states
Singlet state
(QQ)-q for doubly, (QQ)-Q’ for triply heavy baryon
2. Heavy baryons in QCD sum rules
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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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After equating the two sides, assuming quark-hadron duality, making a Borel transform, and eliminating the baryon coupling constant,
In the OPE side, the correlator can be written as
In the phenomenology side, the correlator can be expressed as
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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 c
orrections are not covered
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D. Ebert etc.Quark model
R. Roncaglia etc.Mass formulas
D. H. He etc.MIT bag model
V. V. Kiselev etc.NRQCDSR
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. Bjorkenpotential model
A. P. Martynenko potential model
T. W. Chiu etc.Lattice result
agree wellour central values are lower than potential
model predictions, in particular, for , sli
ghtly more than 1 GeV, whereas the relati
ve discrepancy approximates to 10%, whic
h 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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