The Structure and Dynamics

1. The Structure and Dynamics of Hadron Systems with two Heavy Quarks Nora Brambilla (U. Milano)

2. QCD and the Hadrons Parameters: ,

3. QCD and the Hadrons Structure

4. QCD and the Hadrons Dynamics Bali et al. 95

5. Systems made by two quarks are golden systems for strong interactions • Precision determinations of QCD parameters (of interest for SM and BSM physics) • information on QCD vacuum and low energy properties (of interest for theories beyond QCD) • information on the transition region from high energy to low energy (of interest for the behaviour of perturbative series) They can provide us with:

6. how is this?

7. Low energy (nonperturbative) factorized effects depend on the size of the physical system

8. Plan of the talk • Introduction • small systems,condensates,resummations and precise determinations • gluelumps, hybrids and condensates • inclusive decays, octets and factorization • Big systems,nonperturbative potentials and qcd vacuum models • “QQ” systems in baryons • challenges

9. Quarkonium at the beginning • With the November 1974 revolution also the traditional quarkonium spectroscopy started: • huge impact: • c quark discovery; • asymptotic freedom; • confinement. • few conventional charmonium states; • limited production mechanisms; • limited statistics; • potential model.

10. Progress based on New data New Theory

11. (perturbative scale!) quark pair creation relevant only for light quarks and at large distances one channel is dominant

12. QQ: a multiscale System and

13. Multiscale Non-relativistic bound states No correlation between the number of gluons and the importance of the amplitude due to multiple scales; gauge dependence. In the Bethe-Salpeter approach great difficulties

14. Nonrelativistic EFTs • Systematic expansion; • Model independent; Gauge invariant; • Factorization between high and low energy; • Only the relevant degrees of freedom remain dynamical (the rest integrated out in a controlled way); • All the relevant Fock components appear and with a power counting in v (e.g. octets) • Symmetries of the original theory constrain the c • Additional Symmetries of the system become manifest; • At the scale m the matching coeff. can be calculated in perturbation theory • Large logs can be resummed via RG.

15. Disentangling scales with EFTs Hard Soft (relative momentum) Ultrasoft (binding energy) In QCD another scale is relevant

16. EFTs for Quarkonium

17. Poincare invariance of the EFT

18. Constraints from Poincare Invariance Brambilla, Gromes, Vairo 03 In the same way one gets relations among the matching potentials V

19. Small systems: QQ energies at • Summing large beta0 (removing the renormalon of the series) Beneke et al., Hoang et al.,Brambilla et al, Pineda • Summing the logs: RG correlated scales Luke and Savage; Manohar and Stewart; Pineda Soto low energy gluon singlet octet singlet perturbative singlet potential Dealing with the QCD perturbative series: The bottleneck are nonperturbative contributions: but they are suppressed ---> precision calculations are possible

20. --Precise determinations of m_b and m_c --High order calculations of the static singlet QQbar potential (four loops NLL): full agreement with lattice --

22. The Gluelump Spectrum

23. QQ Static spectrum with gluons hybrid L a t t i c e Juge Kuti Mornigstar 98-06

24. Gluelumps and hybrids in pNRQCD l a t t i c e Juge Kuti Morningstar 00 03 for small r pNRQCD applies Brambilla Pineda Soto Vairo 00

25. Gluelumps and hybrids in pNRQCD: more symmetry! l a t t i c e Juge Kuti Morningstar 00 03 Brambilla Pineda Soto Vairo 00

26. Gluelumps Masses Magnetic gluelump mass Electric gluelump mass is the fundamental object in many models of QCD vacuum Stochastic Vacuum Model, Dosch et al Dual QCD Baker et al Brambilla et al 97, 98,00

27. Gluelumps Masses Magnetic gluelump mass Electric gluelump mass it gives also the leading nonperturbative correction to spectra and decay It needs better lattice calculation!

28. Gluelumps Masses

29. Inclusive decays

30. Inclusive decays: perturbation and singlet model

31. Inclusive decays: NRQCD Fock state content of QQbar in NRQCD:

32. I n c l u s i v e d e c a y s pNRQCD factorization nonperturbative effects in condensates

36. large systems

37. Big systems: strongly coupled pNRQCD Brambilla Pineda Soto Vairo 00 • A potential (quark model like) description emerges from the EFT The QCD potential contains a hard and a soft part (in terms of Wilson loops) • V soft may be calculated on the lattice or in QCD vacuum models Creutz et al 82, Campostrini 85, Michael 85, Born et al 94, Bali et al 97k, Koma, Koma Wittig 2006, Brambilla et al 90 93 95 97, Dosch, Simonov: Baker et al

38. Investigating the QCD vacuum All QQ dynamics is given in terms of Wilson loops and electric and magnetic insertion in the Wilson loop A QCD vacuum model is an assumption on the low energy behaviour of the Wilson loop (gauge invariant, all the rest follows)

39. Studies of Confinement on Wilson loops/V_0 Bali et al Boryakov et al. 04

40. QCD Spin dependent potentials -factorization; power counting; QM divergences absorbed by NRQCD matching coefficients

41. Spin dependent potentials Such data can distinguish different models for the dynamics of low energy QCD

42. Exact relations on the V’s from Poincare e. g. Gromes relation It is a check of the lattice calculation many other such relations in pNRQCD, Brambilla et al. 2003 Koma and Koma 2006

43. QCD Spin independent potentials

44. QQq and QQQ baryons

45. Doubly Charmed Baryons Selex 02,04,06 but no confirmation by Focus and babar

46. QQq systems Notice that diquark approximation not valid

47. Hyperfine separation pNRQCD result L a t t i c e Selex data,Fig. from T. Cohen et al. See the internal QQ excitations ? state 3780 l>0? problems with e.m. transitions

48. QQQ states The lowest QQQ states are few hundreds Mevs lower than Bjiorken’s Y. Jia 06

49. Good testing bed for QCD vacuum models