Doubly Heavy Baryons

1. Doubly Heavy Baryons Likhoded A.K. IHEP, Protvino, Russia

2. Contents • Introduction • Mass spectrum • Decays • Production • Conclusion

3. Double-heavy Baryons The only experimental information about DHB gives SELEX collaboration: There are several questions to SELEX results: 1) Lifetime 2) Cross sections

4. Theoretical information about DHB: 1) Mass spectrum • Potential Models (two step calculation) • QCD Sum Rules • QCD Effective field theory • Lattice QCD 2) Life time and leading decay modes • OPE • Exclusive decays in NRQCD sum rules 3) Cross section • Perturbative QCD + nonrelativistc ME

5. Mass spectrum

6. Potential models Diquark approximation Heavy Quark Symmetry Heavy Quark-Diquark Symmetry Simplification in (QQ’q) dnamics in Born-Oppenheimer or adiabatic approximations: VQ,VQ’<< Vq Two step calculation in Potential Model

7. Potential models Three-body problem

8. Ground states mass predictions [20] [20]

9. PM predictions for ground state cc-diquark 3c are [V. Kiselev, A.Onishchenko, A.L.] Metastable state (2P1S) ½-(3702) have L=1, S=0 for diquark. Transitions to the ground state (L=0, S=1) requires simultaneous change of orbital momentum and spin. PM predictions

10. SR and Lattice QCD • NRQCD Sum Rules M(cc)=3.470.05 GeV M(bc)=6.800.05 GeV M(bb)=10.070.09 GeV • Lattice QCD M(cc)=3.600.02 GeV [V. Kiselev, A.Onishchenko, A.L.] [R.Lewis et al]

11. Spin-dependent corrections For heavy diquark:

12. Spin-dependent corrections Taking into account interaction with the light quark gives (S=Sd+Sl )

13. cc spectrum

14. bb spectrum

15. Hyperfine mass splittings [20] Hyperfine splitting for cc: • PM:  =(130±30) MeV • QCDEFT =(120±40) MeV • Lat.QCD =76.6 MeV [V. Kiselev, A.Onishchenko, A.L.] [N.Brambilla et al] [R.Lewis et al]

16. Summary • Ground state mass predictions depend on the model (~200 MeV) • Uncertainties in PM are mainly connected with different value of heavy quark masses. • The lightest S- and P-wave exitations of the diquark are quasistationar.

17. Lifetimes

18. OPE Where is standard hamiltonian of weak c-quark transitions

19. OPE In decays of heavy quarks released energy is significant, so it is possible to expand Heff in the series of local operators suppressed by inverse powers of heavy quark mass spectator Pauli interference EW scattering

20. OPE For example, for semileptonic decay mode where In numerical estimates we have used following parameter values: mc=1.6 GeV ms=0.45 GeV mq=0.3 GeV M(++cc)=M(+cc)=3.56 GeV MHF=0.1 GeV |diq(0)| = 0.17 GeV3/2

21. OPE

22. OPE

23. Exclusive decays in NRQCD sum rules • Semileptonic DHB decays Heavy Quark Spin Symmetry makes possible to describe semileptonic decays close to zero-recoil point HQSS put constraints on SL FF

24. Exclusive decays in NRQCD sum rules Quark loop for 3-point correlator in the baryon decay For 1/21/2 transition there are 6 form-factors:

26. Exclusive decays in NRQCD sum rules These 6 FF are independent. However, in NRQCD in LO for small recoil it is possible to obtain following relations: Only 2 FF are not suppressed by heavy quark mass: Vector current conversation requires

27. NRQCD Sum Rules In the case of zero recoil IW(1) is determined from Borell transfromation For calculation of exclusive widths one can adopt pole model

28. NRQCD Sum Rules

29. Production of cc-baryons

30. In all papers it was assumed, that This is quite reasonable assumption in the framework of NRQCD, where, for example, octet states transforms to heavy quarkonium. Analogously, we have to assume, that dissociation of (cc)3 into DD is small.

31. Similar to quarkonium production cross sections factorizes into hard (pertubative) and soft (non-pertubative) parts. In both cases second part is described by wave function of bound state at origin. That’s why it is reasonable to compare, for example, J/cc and cc final states. In this case only one uncertainty remains – the of squared wave functions at origin.

32. Fragmentation mechanism e.g.

33. In e+e-, where FM dominates, expected cross sections at is At SuperB, where expected luminocity is L=1036 cm-2 s-1

34. Hadronic production

35. 4c sector LO calculations for (4c) at gives at mc=1.25 GeV s=0.24 It should be compared with This gives At Z-pole Main uncertainties come from errors in mc and s

36. Violation of factorization in hadroproduction at low pT cc total cross sections: Tevatron: (cc)=12 nb LHC : (cc)=122 nb

37. Conclusion • Double heavy quark pair production is a new battle field (see, e.g. B-factories) • Test of fragmentation approximation in production • NRQCD factorization • Properties of weak decays

38. Backup slides

39. X cc final state 1) Fragmetation mechanism M2/s corrections are neglected (M2/s <<1)

40. X cc final state 2) Complete calculations (with M2/s corrections) (c) = 40 (49) fb, (J/) = 104 (148) fb, ( c0) = (48.8) fb ( c1) = (13.5) fb ( c2) = (6.3) fb [A.Berezhnoi, A.L.] [K.Y. Liu, Z.G. He, K.T. Chao] Complete calculations deviate from fragmetation calculations at M2/s terms are important

41. X cc final state 3) Quark-Hadron duality It should be compared with total sum of complete calculations. Q-H duality does not contradict Color Singlet model within uncertainties in mcs and 

42. X cc final state a) fragmentation approach S=1 Dccc(z) similar to DcJ/(z) Difference in wave functions |J/ (0)|2 and |cc(0)|2 Again, similar to J/ case, at complete calculations for vector (cc)3 -diquark are needed

43. X cc final state b) Quark-Hadron duality One inclusive cross section for vector 3c in S=1 Uncertainties are caused by errors in s and  This value is close to results of complete calculations with cc(0) taken from PM.

44. Conclusion 1) at ( at LHC ) 2) For lumonocity L=1034 cm-2 s-1 it gives ~104cc-baryons per year 3) Taking into account Br ~10-1 in exclusive modes we expect 103 cc events per year