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) factorizedeffects 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 wayone gets relationsamong 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 singletoctet

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 98-06

hybrid

Lattice

Gluelumps and hybrids in pNRQCD

lattice

Juge Kuti Morningstar 00 03

Brambilla Pineda Soto Vairo 00

for small r pNRQCD applies

Gluelumps and hybrids in pNRQCD:more symmetry!

lattice

Juge Kuti Morningstar 00 03

Brambilla Pineda Soto Vairo 00

Gluelumps Masses

Magnetic gluelump mass

Electric gluelump mass

is the fundamental object in many models of QCD vacuumStochastic Vacuum Model, Dosch et alDual QCD Baker et alBrambilla et al 97, 98,00

Gluelumps Masses

Magnetic gluelump mass

Electric gluelump mass

it 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

decays

pNRQCDfactorization

nonperturbativeeffects 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 modelsCreutz 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

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

Lattice

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’sY. Jia 06

Goodtestingbed for

QCD vacuummodels

OPEN CHALLENGES

Quarkonium Production at Tevatron and LHC

Polarization at tevatronCFD 06

The polarization problem

A solution may come froman 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

OutlookEffective 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 orderLattice calculations of condensates/wilson loopsModels for the QCD vacuumNew EFTs close to threshold