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

QCD and the Hadrons Parameters:,

QCD and the Hadrons Structure

QCD and the Hadrons Dynamics Bali et al. 95

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:

how is this?

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

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

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. Quarkonium at the beginning

Progress based on New data New Theory

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

QQ: a multiscale System and

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

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.

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

EFTs for Quarkonium

Poincare invariance of the EFT

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

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 The bottleneck are nonperturbative contributions: but they are suppressed ---> precision calculations are possible perturbative singlet potential singlet octet low energy gluon Dealing with the QCD perturbative series:

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

The Gluelump Spectrum

QQ Static spectrum with gluons Juge Kuti Mornigstar hybrid LatticeLattice

Gluelumps and hybrids in pNRQCD latticelattice Juge Kuti Morningstar Brambilla Pineda Soto Vairo 00 for small r pNRQCD applies

Gluelumps and hybrids in pNRQCD: more symmetry! latticelattice Juge Kuti Morningstar Brambilla Pineda Soto Vairo 00

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

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

Gluelumps Masses

Inclusive decays

Inclusive decays: perturbation and singlet model

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

Inclusive Inclusive decaysdecays pNRQCD factorization nonperturbative effects in condensates

large systems

Brambilla Pineda Soto Vairo 00 A potential (quark model like) description emerges from the EFT 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 , Dosch, Simonov: Baker et al Big systems: strongly coupled pNRQCD The QCD potential contains a hard and a soft part (in terms of Wilson loops)

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

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

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

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

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

QCD Spin independent potentials

QQq and QQQ baryons

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

QQq systems Notice that diquark approximation not valid

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

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

Good testing bed for QCD vacuum models

OPEN CHALLENGES

Quarkonium Production at Tevatron and LHC Polarization at tevatron CFD 06 The polarization problem A solution may come from an EFT with different power counting

Most of the new states are close to threshold It is most important to construct and EFT close to threshold (talk Weise)

Quarkonium at finite T & Heavy Ion collisions Spectral density above and below Tc QQbar singlet Free energy at finite T EFT approach for the scale T, gT, g^2 T

Direct formulation on the lattice:pNRQCD on the lattice Quarkonium Van Der Waals Interaction and Quarkonium on nuclei

Search for Physics BSM Dark matter: run at Belle at Y(3S) Light Higgs in eta_b search: breakdown of lepton universality in Y decays LFV processes and CPV processes in J/psi decays at BESIII

Outlook Effective field theories provide a systematic tool to investigate a wide range of heavy quark observables inside QCD They need to be complemented by lattice calculations These theory tools can match some of the intense experimental progress of the last few years and of the near future, but more has to be done: Heavy quark bound states are a unique lab for the study of the strong interactions from the high energy scales where precision studies can be made to the low energy region: use all the present and future data to test/develop our theory tools on the way to the hadron structure and dynamics Some Perturbative calculations at higher order Lattice calculations of condensates/wilson loops Models for the QCD vacuum New EFTs close to threshold