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Glueballs, Constituent Gluons and Instantons

Edward Shuryak, Ismail Zahed

Abstract

We present a constituent two-gluon description of the lowest-lying glueball states in pure Yang--Mills theory, calibrated against quenched lattice results. The framework incorporates an instanton-induced dynamical gluon mass, Casimir-scaled adjoint confinement, the short-distance adjoint Coulomb interaction, and instanton-induced central and tensor forces. The scalar $0^{++}$ glueball is found to be exceptionally compact, with a radius of order the instanton size, $ρ\sim \frac 13\,\mathrm{fm}$, consistent with lattice indications. By contrast, the tensor $2^{++}$ state remains spatially extended due to the centrifugal barrier. We also discuss the role of $S$-$D$ mixing. A semiclassical analysis further supports Regge behavior for excited states, in agreement with lattice results.

Glueballs, Constituent Gluons and Instantons

Abstract

We present a constituent two-gluon description of the lowest-lying glueball states in pure Yang--Mills theory, calibrated against quenched lattice results. The framework incorporates an instanton-induced dynamical gluon mass, Casimir-scaled adjoint confinement, the short-distance adjoint Coulomb interaction, and instanton-induced central and tensor forces. The scalar glueball is found to be exceptionally compact, with a radius of order the instanton size, , consistent with lattice indications. By contrast, the tensor state remains spatially extended due to the centrifugal barrier. We also discuss the role of - mixing. A semiclassical analysis further supports Regge behavior for excited states, in agreement with lattice results.

Paper Structure

This paper contains 43 sections, 179 equations, 9 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Historic remarks
  3. Outline of this work
  4. The Hamiltonian
  5. Adjoint Coulomb
  6. Adjoint confining potential
  7. The short-distance nonperturbative interactions
  8. Glueball spectra from the Schrödinger equation
  9. The $S=0,\,J=L$ sector
  10. The lowest $0^{++}$ scalar glueball
  11. Pseudoscalar $0^{-+}$ glueballs
  12. WKB baseline for the $0^{-+}$ channel
  13. Quantum numbers of other glueballs
  14. Relativistic treatment of short-distance dynamics
  15. Emergent 4-gluon interaction
  16. ...and 28 more sections

Figures (9)

  • Figure 1: Repulsive, neutral and attractive channels induced by instanton-induced effects in Euclidean correlation functions, for mesons and glueballs.
  • Figure 2: Scalar $G^2$ and pseudoscalar $G\tilde{G}$ gluonic correlation functions normalized to the corresponding free correlators as functions of the Euclidean time separation, taken from Schafer:1994fd. Results in the random, quenched, and full ensembles are denoted by stars, open triangles, and solid squares, respectively. The solid lines show the parametrization described in the text, the dashed line the dilute instanton gas approximation, and the dotted line the QCD sum-rule calculation. The horizontal line in the second panel is added to guide the eye.
  • Figure 3: Lattice data for glueball masses, normalized to lowest scalar, triangles from Meyer et al and circles from Morningstar et al.
  • Figure 4: Central potential $V_{conf}(r)\, (\rm GeV)$ used versus $r \,(\rm GeV^{-1})$
  • Figure 5: The colored points show the calculated energies $E_0,E_1,E_2,E_3$ (GeV) of the four lowest states with $L=0,2,4,6$. Small points with error bars are H.Meyer's lattice simulations in pure SU(3) gauge theory Meyer:2004gx. We used $J^{PC}$ lattice states $0^{++}$, $2^{++}$, $4^{++}$, and $6^{++}$ (from bottom to top) as a function of the principal quantum number $n$.
  • ...and 4 more figures