# Presentation: 566153

## Heavy Quark Potentials

- Scales and Effective Field Theories:systematic approach
- pNRQCD: the QQbar and QQQ  potentials
- Applications of pNRQCD:  Potentials and Spectra, Decays, Transitions, SM parameters
- What at finite T?
- What’s more?

- at Zero Temperature

- Nora Brambilla (U. Milano)

## Bound states of two (or more)heavy quarks

## QQ: a multiscale System

## Non-relativistic bound states in QCD

- Difficult also
- for the lattice!

- The perturbative expansion breaks down when

## EFTs for Quarkonium

- Hard

- Soft
- (relative
- momentum)

- Ultrasoft
- (binding energy)

## EFTs for Quarkonium

## EFTs for Quarkonium

## EFTs for Quarkonium

- The matching procedure enforces the EFT to be equivalent to QCD

## EFTs for Quarkonium

## pNRQCD for Quarkonium with small radius

## pNRQCD for Quarkonium with small radius

## pNRQCD for Quarkonium with small radius

- Pineda, soto 97; Brambilla, Pineda, soto, Vairo 99-

## pNRQCD for Quarkonium with small radius

- Pineda, soto 97; Brambilla, Pineda, soto, Vairo 99-

## pNRQCD for Quarkonium with small radius

- Pineda, soto 97; Brambilla, Pineda, soto, Vairo 99-

## Static singlet QCD QQ potential 

- The potential is a Wilson coefficient of an EFT.
- In general, it  undergoes renormalization, develops scale
- dependence and satisfies renormalization
- group equations, which allow to resum large logarithms.

## Static singlet potential

- +

-  :calculated in the matching

- up to two loops:

## Static singlet potential at NNNNLO 

## Pert. Static Energy versus lattice  

- Perfect agreement up to more than 0.2 fm!

## Pert. Static Energy versus lattice  

- No signal of short range-linear nonperturbative effects

## Summing large beta0 (removing the renormalon of the series) Beneke et al., Hoang et al.,    
Summing the logs of v (coming from the ratio of scales:mv^2/mv, mv/m) RG correlated scales Luke and Savage; Manohar and Stewart; Pineda Soto
The  bottleneck  are nonperturbative contributions (condensates) but they are suppressed

- Summing large beta0 (removing the renormalon of the series) Beneke et al., Hoang et al.,
- Summing the logs of v (coming from the ratio of scales:mv^2/mv, mv/m) RG correlated scales Luke and Savage; Manohar and Stewart; Pineda Soto
- The  bottleneck  are nonperturbative contributions (condensates) but they are suppressed

- Precision calculations are possible

- perturbative singlet potential

- singlet

- singlet

- octet

- low energy gluon

-  Quarkonium  energies at

##  Quarkonium  energies at  

- b and c mass extraction from Y(1S) and J\psi

-  Quarkonium  energies at

##   mass  

- In CDF 05 the

- is found in

- Predictions of the

##  The missing mesons  

- Under  search at Fermilab and CLEO

##  Present Knowledge of the QQ Potentials  

- --Vs known  at four loops (no constants from 3 loop)

- --Vo known  at two loops

- --V Spin dependent potential known  one loop

- --V at order 1/m known   at two loops

- --At order 1/m^2  imaginary parts in the potentials appear-> describe inclusive decays at order m alpha_s^5

- The RG improvement is also known for several potentials

## QQQ states: pNRQCD for small radii

- Recent calculation of the potential at order g^4, three body contribution at order g^6  Brambilla, Ghiglieri, Vairo 08

## Tree level QQQ potential

## Tree level QQQ potential

- Octets mixing between symmetric and antysimmetric octets
- aaantysimmetricantisimmetrico

## One loop QQQ potential

- Esponentiation

- The potential is still two body

## One loop QQQ potential

- The first three body potential appears at g^6

## Strongly coupled pNRQCD

- (for systems with large radius)

## strong pNRQCD: Hitting 

- integrate out all scales above

- Bali et al. 98

- gluonic excitations develop a gap

- and  are integrated out

##  Strong coupled pNRQCD 

- Brambilla Pineda Soto Vairo 00

- A potential description emerges from the EFT

- The potentials

- from QCD in the matching

- V to 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 97, Brambilla et al 90 93 95 97, Koma et al. 06,07

## The nonperturbative QCD potential  

- The nonperturbative QCD potential

##  QCD potential  

- Koma, koma, wittig 07

##  QCD Spin dependent potentials  

-  -Factorization; Power counting; Quantum mechanical divergences absorbed by NRQCD matching coefficients

##  Spin dependent potentials  

- Differ from flux tube model prediction

- 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  

- Under calculation on the lattice Koma et al 07

## Good

- testing
- bed for
- QCD vacuum
- models

## Low energy (nonperturbative) QCD 

- Low energy (nonperturbative) QCD
- may be studied in a systematic way

- The potential is defined and calculated in all the regimes

## more scales

- ?

- see A. Vairo talk this afternoon!

## backup slides

## Lattice calculation of the QQQ potential