From gluons to hybrids : Coulomb From gluons to hybrids : Coulomb gauge perspective gauge perspective

Adam Szczepaniak IU

Adam Szczepaniak IU

Gluons and glueballs in Coulomb gauge

Gluons and glueballs in Coulomb gauge

Gluelumps and HybridsGluelumps and Hybrids

Spectrum of gluonic excitations in presence of static sources : level ordering

Spectrum of gluonic excitations in presence of static sources : level ordering

Pawel Krupinski, Peng Guo Pawel Krupinski, Peng Guo

Constituent gluons vs strings

Coulomb gauge QCDCoulomb gauge QCDCoulomb gauge QCDCoulomb gauge QCD

QCD Quasi-particles:

QCD Quasi-particles:

Choose a physical gauge, e.g. Coulomb

gauge

Choose a physical gauge, e.g. Coulomb

gauge

Compute the QCD HamiltonianCompute the QCD Hamiltonian

Diagonalize in a quasi-particle Fock space

Diagonalize in a quasi-particle Fock space

QCD Coulomb interaction leads to confinement(Zwanziger,Greensite,Szczepaniak,SwansonReinhardt, Feuchter)

QCD Coulomb interaction leads to confinement(Zwanziger,Greensite,Szczepaniak,SwansonReinhardt, Feuchter)

for high momentum transverse gluons

for high momentum transverse gluons

for low momentum transverse gluons

for low momentum transverse gluons

space

time

space

time

<H> ( pQCD O(α2) )<H> ( pQCD O(α2) )

Debye screening

real (quasi) particles propagating expected to be suppresses

real (quasi) particles propagating expected to be suppresses

QCDQCD

<H> enhanced in the IR from modes near horizon

<H> enhanced in the IR from modes near horizon

E(R) = E(R) =

12 comes from the Coulomb

potential

12 comes from the Coulomb

potential

For other choices see Zwanziger hep-ph/0312254,

Phys.Rev.Lett.78:3814,1997C. Feuchter, H. Reinhardt

hep-th/0402106

For other choices see Zwanziger hep-ph/0312254,

Phys.Rev.Lett.78:3814,1997C. Feuchter, H. Reinhardt

hep-th/0402106

Self-consistent mean field Self-consistent mean field Self-consistent mean field Self-consistent mean field

Summation of all planar Summation of all planar diagrams can be expressed indiagrams can be expressed in terms of two Dyson equationterms of two Dyson equation

Summation of all planar Summation of all planar diagrams can be expressed indiagrams can be expressed in terms of two Dyson equationterms of two Dyson equation

ωωk -> k -> ωΛ

ωΛ

Not to be confused with a one-gluon energy which is IR unstable

Not to be confused with a one-gluon energy which is IR unstable

sum is IR finite (for color singlet)sum is IR finite (for color singlet)

plays the role of average one-gluon kinetic energy in a color singlet state

plays the role of average one-gluon kinetic energy in a color singlet state

Quasi-gluons and glueballs

Quasi-gluons and glueballs

lattice

SpinPC

Coulomb

Glueball Spectrum Szczepaniak,Swanson

RPA correctionsCompleted for 0++

D.Whittington,APS

Gluonic excitations in Gluonic excitations in presence of static presence of static

sourcessources

Gluon degrees of freedom Alternatives to lattice

Gluon degrees of freedom Alternatives to lattice

Bag Model

Bag Model

Quasi-particles

Quasi-particles

Flux tube model

Flux tube model

Juge, Kuti, Morningstar

Juge, Kuti, Morningstar

deformed bagsdeformed bags

gluons in the baggluons in the bagTE TM

Single gluon hybrids (with static Single gluon hybrids (with static sources)sources)

Single gluon hybrids (with static Single gluon hybrids (with static sources)sources)

one-body Schrodinger eq.one-body Schrodinger eq.one-body Schrodinger eq.one-body Schrodinger eq.

one-body one-body potentialpotential

one-body one-body potentialpotential

two-body two-body potentialpotential

two-body two-body potentialpotential

Szczepaniak, Swanson

Coulomb energy vs “True” (Wilson) energy

Coulomb energy vs “True” (Wilson) energy

Zwanziger Zwanziger

“No confinement without Coulomb confinement” “No confinement without Coulomb confinement”

Greensite and OlejnikGreensite and Olejnik

Here |0> is the lattice vacuum state

Here |0> is the lattice vacuum state

Lattice(Morningstar et al.)

Lattice(Morningstar et al.)

Excited states without 3-body interactions

Excited states without 3-body interactions

Szczepaniak, Swanson

Szczepaniak,Krupinski

QED Coulomb Energy

QCD Coulomb Energy

In the quasi-particle representation generates a

3-body force

Krupinski,Szczepaniak

@ R =0

With 3-body interactions

With 3-body interactions

Glue-lumps : (“R=0” static Glue-lumps : (“R=0” static hybrids)hybrids)

Glue-lumps : (“R=0” static Glue-lumps : (“R=0” static hybrids)hybrids)

Glue-lumps : (“R=0” static Glue-lumps : (“R=0” static hybrids)hybrids)

Real Heavy Hybrids via Foldy -Real Heavy Hybrids via Foldy -Wouthuysen HamiltonianWouthuysen Hamiltonian

expected degeneraciesexpected degeneraciesexpected degeneraciesexpected degeneracies

JPC glueJPC glue

JPC QQ_

J.Dudek, et al.

Morningstar et al.

2 fm

Szczepaniak, Krupinski

where is the where is the string limit ?string limit ?

(lattice :Morningstar et al.)(lattice :Morningstar et al.)

Szczepaniak,Krupinski

Szczepaniak,Krupinski

P-wave coupling : vanishes as

P-wave coupling : vanishes as

andand

Towards the gluons chain Towards the gluons chain (Thorn, Greensite)

~[fm]

Coulomb energy

Coulomb energy

True energyTrue energy

with up to 40 gluons with up to 40 gluons

SummarySummary

Coulomb gauge offers “natural” framework for studies of YM spectra

Coulomb gauge offers “natural” framework for studies of YM spectra

The non-abelian Coulomb potential is responsible for the nontrivial ordering of spin-parity states in seen on lattice in the gluelump and hybrid spectra and possibly for generation of the glue string.

The non-abelian Coulomb potential is responsible for the nontrivial ordering of spin-parity states in seen on lattice in the gluelump and hybrid spectra and possibly for generation of the glue string.

New states ?New states ? BaliMorningstar, et al.

BaliMorningstar, et al.

Constituent gluon models : low lying states should reproduce JPC = 1+- (Lg =1)not JPC=1-- (Lg=0) for the lowest

gluon state

Constituent gluon models : low lying states should reproduce JPC = 1+- (Lg =1)not JPC=1-- (Lg=0) for the lowest

gluon state

R/2

-R/2

z

x

y

+e

-e

(from dimensional anal.)

(Van der Waals)

R/2

-R/2

z

x

y

+e

-e

(from dimensional anal.)

(Van der Waals)

approximate analytical solution with UV suppressed

P.Bowman, Szczepaniak

Flux

tube

forms

between

qq

r

r0 = 0.5 fm

Adiabatic potential

Soft gluons lead to : Confinement Flux

tube

forms

between

qq

r

r0 = 0.5 fm

Adiabatic potential

Soft gluons lead to : Confinement

lattice : Langfeld and Moyaertslines : fit based on Coulomb gauge from Swanson and Szczepaniak

lattice : Langfeld and Moyaertslines : fit based on Coulomb gauge from Swanson and Szczepaniak

The IR fit completely The IR fit completely agrees with solutions agrees with solutions

of Dyson eqs.of Dyson eqs.