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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