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Colour fields in gauge invariant quenched SU(3) Lattice QCD

This research study focuses on measuring the colour electric and magnetic fields in a gauge-invariant framework, using a Wilson loop and a plaquette. The goal is to understand quark and gluon confinement, compare it with confinement in superconductors, and provide a confining potential for constituent models of quarks and gluons. The study also explores Casimir scaling for SU(3) representations and investigates the dual gluon mass and correlation length.

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Colour fields in gauge invariant quenched SU(3) Lattice QCD

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  1. Colour fields in gauge invariant quenched SU(3) Lattice QCD Pedro Bicudo with Marco Cardoso, Nuno Cardoso CFTP, IST, Lisboa • Framework: a Wilson loop and a plaquette • Case study of the hybrid GQQ system • Casimir scaling for SU(3) representations • Dual gluon mass and correlation length Pedro Bicudo @ Lattice 10

  2. Motivation For ++ discussions, I also apply quark-gluon models and Lattice QCD to chiral symmetry, exotics and molecules, excited hadrons, finite T, and to surf tech Pedro Bicudo @ Lattice 10

  3. Motivation • Our goal is to measure in a gauge invariant framework, the components Ei of the colour electric field and Bi of the colour manetic field. • The colour fields Ei and Bi are relevant to • understand quantitatively the details of quark and gluon confinement, • compare QCD confinement with the confinement in superconductors, • provide the confining potentialfor constituent models of quarks and gluons, leading to model computations of the hadron spectrum and of the QCD Phase diagram. • Moreover the fields are relatively simple to compute, even in relatively small PC clusters. Pedro Bicudo @ Lattice 10

  4. Framework: Computing fields with a Wilson Loop and a plaquette Ei2 or Bi2 The Wilson loop for the gluon-quark-antiquark is given by: Using the Fiertz relation, We can prove that Pedro Bicudo @ Lattice 10

  5. Framework: Computing fields with a Wilson Loop and a plaquette • The plaquette produces the squared components of the fields, • In space: We use APE Smearing in the Wilson Loop. To increase the ground state overlap, the links are replaced by "fat links“, we use w = 0.2 and iterate this spatial procedure 25 times, • In Time: To achieve better accuracy in the flux tube, we apply the hypercubic blocking (HYP), [Hasenfratz and Knechtli, 2001]. The optimized parameters to reduce plaquette fluctuations are, Pedro Bicudo @ Lattice 10

  6. Case study of the fields in a static hybrid GQQ system 286 configurations with 243x48 and β=6.2 generated with the version 6 of the MILC code, via combination of Cabbibo-Mariani and overrelaxed updates; Results presented in lattice spacing units of a, with a=0.07261(85) fm or a -1=2718±32 MeV; Two geometries, U and L shape. Pedro Bicudo @ Lattice 10

  7. <E2> - <B2> -<B2> Case study of the fields in a static hybrid GQQ system Results with APE (space) Only : example of the L geometry L H Pedro Bicudo @ Lattice 10

  8. Case study of the fields in a static hybrid GQQ system Results with Hyp (time) + APE (space) : U gemometry <E2> - <B2> H L Pedro Bicudo @ Lattice 10

  9. Casimir Scaling: field ratio 8 / 3 representations of SU(3) Case study of the fields in a static hybrid GQQ system Pedro Bicudo @ Lattice 10

  10. U geometry: field profiles, perpendicular cut at y=4 and z=0 Case study of the fields in a static hybrid GQQ system Pedro Bicudo @ Lattice 10

  11. Casimir scaling in the fields of SU(3) Representations • We proceed with the study of the Casimir Scaling for sources of higher representations of SU(3): 3, 8, 6, 15a, 10, 24, 27, 15s. Casimir scaling was observed in Lattice Potentials by Bali and others. Semay has an interesting conjecture on bag model-like flux tube widths.Again, the Wilson loops can be decomposed in fundamental Wilson loops. Pedro Bicudo @ Lattice 10

  12. Casimir scaling in the fields of SU(3) Representations E(r) 2m In some representations, there is saturation atE ~2 m r • We place our sources at (0,-4,0) and (0,4,0), and utilize 287 configurations with 243x48 and β=6.2, with three levels HYP (time) + APE ( space) Notice that we can only reproduce the Casimir scaling at moderate distances, since the QCD flux tubes may break with gloun-gluon pair creation, according to the n-ealing rule. Pedro Bicudo @ Lattice 10

  13. Plane XY at z=0 Plane XZ at y=0 Casimir scaling in the fields of SU(3) Representations Electric field Ei Pedro Bicudo @ Lattice 10

  14. Plane XY at z=0 Plane XZ at y=0 Casimir scaling in the fields of SU(3) Representations Magnetic field Bi Pedro Bicudo @ Lattice 10

  15. Plane XY at z=0 Plane XZ at y=0 Casimir scaling in the fields of SU(3) Representations Action L Pedro Bicudo @ Lattice 10

  16. Plane XY at z=0 Plane XZ at y=0 Casimir scaling in the fields of SU(3) Representations Energy H Pedro Bicudo @ Lattice 10

  17. Casimir Scaling Plane XY at z=0 Plane XZ at y=0 Casimir scaling in the fields of SU(3) Representations Pedro Bicudo @ Lattice 10

  18. With 1 Hypercubic blocking in time and APE in space, we study the dual gluon mass, extracting it from the profile of the 3 and 8 flux tubes.We compare the profile with the solution of the Ginzburg-Landau and Ampère equations for the cooper pair field and the magnetic field in a superconductor. Ginsburg-Landau fit of the dual gluon mass and correlation length Pedro Bicudo @ Lattice 10

  19. Dual gluon mass Gluon mass Ginsburg-Landau fit of the dual gluon mass and correlation length Although gauge fields are usually massless, the superconductor (and other) examples, shows that gauge fields may acquire a mass. In the literature there are several studies of the dual gluon and of the gluon masses. Pedro Bicudo @ Lattice 10

  20. We fit our lattice SU(3) field profiles with parameters x, lof the solutions of Ginzburg-Landau and Ampère equations Ginsburg-Landau fit of the dual gluon mass and correlation length m =l-1 = 0.91 +- 0.16 GeV Pedro Bicudo @ Lattice 10

  21. Conclusion & Outlook on colour fields in gauge invariant Quenched SU(3) • We compute in a gauge invariant framework, i. e. with no gauge fixing, the electric Ei and magnetic Bi colour field components in quenched SU(3) Lattice gauge theory. We apply APE smearing 20 x in the spatial direction and Hypercubic blocking 0x to 3x in the temporal direction. • We find that the flux tubes, for separated charges separate in tubes with the flux of the fundamental 3 representation of SU(3). But when SU(3) charges are superposed in higher representations, 3, 8, 15a, 10, 27 …, we find that the superposition of the flux tubes verifiesCasimir scaling at moderate distances, as measured by Bali for the potentials. • We also compare the profiles of the flux tubes find with the Ginsburg-Landau model of superconductivity. The fit of our profiles produces the correlation lengthxand the penetration lengthlof the dual superconductor QCD model. We find it remarkable that a dual gluon mass, of m =l-1= 0.91 +- 0.16 GeV , possibly identical to the gluon mass, can be obtained gauge invariant framework. Pedro Bicudo @ Lattice 10

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