From gluons to hybrids : Coulomb gauge perspective Adam Szczepaniak IU Gluons and glueballs in Coulomb gauge Gluelumps and Hybrids Spectrum of gluonic excitations in presence of static sources : level ordering Pawel Krupinski, Peng Guo Constituent gluons vs strings

Coulomb gauge QCD

QCD Quasi-particles: Choose a physical gauge, e.g. Coulomb gauge Compute the QCD Hamiltonian Diagonalize in a quasi- particle Fock space QCD Coulomb interaction leads to confinement (Zwanziger,Greensit e,Szczepaniak,Swan son Reinhardt, Feuchter) QCD Coulomb interaction leads to confinement (Zwanziger,Greensit e,Szczepaniak,Swan son Reinhardt, Feuchter) for high momentum transverse gluons for high momentum transverse gluons for low momentum transverse gluons for low momentum transverse gluons

( pQCD O(α 2 ) ) Debye screening real (quasi) particles propagating expected to be suppresses real (quasi) particles propagating expected to be suppresses QCD enhanced in the IR from modes near horizon enhanced in the IR from modes near horizon E(R) = 12 comes from the Coulomb potential 12 comes from the Coulomb potential

For other choices see Zwanziger hep-ph/ , Phys.Rev.Lett.78:3814,1997 C. Feuchter, H. Reinhardt hep- th/ For other choices see Zwanziger hep-ph/ , Phys.Rev.Lett.78:3814,1997 C. Feuchter, H. Reinhardt hep- th/ Self-consistent mean field Summation of all planar diagrams can be expressed in terms of two Dyson equation terms of two Dyson equation Summation of all planar diagrams can be expressed in terms of two Dyson equation terms of two Dyson equation  k ->  Λ 

Not to be confused with a one-gluon energy which is IR unstable sum is IR finite (for color singlet) plays the role of average one-gluon kinetic energy in a color singlet state Quasi-gluons and glueballs

Gluonic excitations in presence of static sources

Gluon degrees of freedom Alternatives to lattice Gluon degrees of freedom Alternatives to lattice Bag Model Quasi- particles Flux tube model

Juge, Kuti, Morningstar Juge, Kuti, Morningstar deformed bags gluons in the bag TETM

Single gluon hybrids (with static sources) one-body Schrodinger eq. one-body potential two-body potential

Szczepaniak, Swanson

Coulomb energy vs “True” (Wilson) energy Zwanziger “No confinement without Coulomb confinement”

Greensite and Olejnik Here |0> is the lattice vacuum state

Lattice (Morningstar et al.) Lattice (Morningstar et al.) Excited states without 3-body interactions Szczepaniak, Swanson Szczepaniak,Krupins ki

QED Coulomb Energy QCD Coulomb Energy In the quasi-particle representation generates a 3- body force R =0

With 3-body interactions

Glue-lumps : (“R=0” static hybrids)

Real Heavy Hybrids via Foldy - Wouthuysen Hamiltonian

expected degeneracies J PC glue J PC QQ _ J.Dudek, et al.

Morningstar et al.2 fm Szczepaniak, Krupinski where is the string limit ?

(lattice :Morningstar et al.) Szczepaniak,Krupins ki P-wave coupling : vanishes as and

Towards the gluons chain (Thorn, Greensite)

~[fm] Coulomb energy True energy with up to 40 gluons

Summary 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.

New states ? Bali Morningstar, et al. Bali Morningstar, et al. Constituent gluon models : low lying states should reproduce JPC = 1+- (Lg =1)not JPC=1- - (Lg=0) for the lowest gluon state

approximate analytical solution with UV suppressed P.Bowman, Szczepaniak

lattice : Langfeld and Moyaerts lines : fit based on Coulomb gauge from Swanson and Szczepaniak lattice : Langfeld and Moyaerts lines : fit based on Coulomb gauge from Swanson and Szczepaniak The IR fit completely agrees with solutions of Dyson eqs.