Quarks and gluons in hadrons and nuclei Page: 6 of 31
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The color attractions among quarks and gluons lead to the prediction of glue-
balls and hybrid hadrons - the latter where gluons play a dynamical role, attrac-
ted to quarks to form hybrid mesons and baryons.
The problem in predicting the masses of these states is that we have to simu-
late the effects of confinement. Perhaps the simplest way of doing this is to
suppose that the constituent quarks or gluons are free until they hit an infi-
nitely high wall. This is the essence of cavity or bag models. Confine a mass-
less J=1/2 quark in a radius, R, and it gains an energy that scales as 1/R. This
energy becomes of the order of 350 MeV if R is of the order of the proton radius,
hence the proton mass may be modeled. For gluons, one solves the eigenvalue equa-
tions for J = 1 rather than J = 1/2 confined fields. There are electric or mag-
netic modes (actually TE and TM in the language of classical electrodynamics) with
different eigenvalues. If R is the same as for quark systems, the typical
confined-mass-scale is some 500 MeV per TE mode and 750 MeV per TM mode. Thus
follows the prediction that the lightest systems consisting of at least two con-
fined gluons weign in at 0(1 GeV) and that the lightest hybrid baryons weigh in at
0(1.5 GeV). A problem is that as soon as the hyperfine shifts in energy are taken
into account (this involves one first calculating the propagators of confined
quarks and gluons), the lowest spin-J systems are pulled down significantly in
mass. The lightest hybrid baryon might thus appear to have a mass near that of
the proton which suggests either a profound rethink of baryon spectroscopy or that
we have unearthed a naievity.
I suspect it is the latter. No one yet has convincingly set up a study of
loop effects with renormalization within a cavity. These loop diagrams enter at
the same order in perturbation theory to which the hyperfine shifts have been
calculated and may alter the naive "effective" energies per confined gluon. In
the case of quarks, their effects were subsumed in the MIT bag by an input mass
parameter for the quark; this mass fitted to the overall mass scale of the spec-
troscopy. In the gluonic sector we have no mass scale to set the scale, and until
we make sense of the (infinite!) self-energy diagrams, we cannot predict the abso-
lute scale. So the mass separations among the various states may be reliable, but
the absolute mass scale is beyond present analysis. To predict the masses of
glueballs and hybrid hadrons, we have to resort to computer simulations - lattice
QCD. This has proved to be a harder task than was originally thought.
The eventual discovery of the gluonic spectroscopy may give important in-
sights into the nature of confinement of gluons. If lattice calculations, includ-
ing quarks and gluons (to date, people work in the "quenched" approximation, which
roughly translated means "ignore the quarks") merely point out masses of states
that correspond to the particle data tables, we will confirm QCD but may still re-
quire much study to elucidate the analytic dynamics of confinement. The main
outcome of such a success may be the advances that will have come in the art of
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Close, F. E. Quarks and gluons in hadrons and nuclei, article, December 1, 1989; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1058782/m1/6/?rotate=180: accessed May 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.