Heavy baryon spectra from QCD sum rules

1. Heavy baryon spectra from QCD sum rules Jian-Rong Zhang National University of Defense Technology, China In collaboration withMing-Qiu Huang April 19-22 @ Beijing NSTAR 2009

2. 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. ZhangandM. Q. Huang, PRD 77, 094002 (2008); D 78, 094007 (2008); D 78, 094015 (2008); PLB 674, 28 (2009).

3. 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);

4. ★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) ……

5. QCD sum rules M. A. Shifman,A. I. Vainshtein,andV. I. Zakharov seminal papers: NPB147, 385 (1979); B147, 448 (1979) B. L. Ioffebaryon E. V. Shuryakheavy 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

6. 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

7. 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.

8. For doubly heavy baryon, e.g. For triply heavy baryon, e.g.

9. 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

10. 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,

11. 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

12. 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.

13. A. P. Martynenko potential model J. M. Richard etc. potential model J. D. Bjorken potential model Y. Jia Varitional method 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.

14. 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 forsinglyheavy 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.

15. Outlook ◆In experiment 1) quantum numbers 2) More data on singly bottom baryons, doubly heavy baryons evidence on triply heavy baryons LHC startup ◆ InQCDSR 1) take into account the QCD corrections 2) triply lattice QCD

16. Thank you!