Strangeness in the Nucleon or the quark model beyond the valence approximation Page: 4 of 20
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mesons and baryons, but not for glueballs or for the gluonic content of
mesons and baryons.
" In both pictures a propagating valence quark has contributions from not
only a positive energy quark propagator, but also from "Z-graphs". (A
"Z-graph" is a time-ordered graph in which the interactions first produce
a pair and then annihilate the antiparticle of the produced pair against
the original propagating particle). Cutting through a two-point function
at a fixed time therefore would in general reveal not only the valence
quarks but also a large qq sea. This does not seem to correspond to the
usual valence approximation. Consider, however, the Dirac equation for
a single light quark interacting with a static color source (or a single
light quark confined in a bag). This equation represents the sum of a set
of Feynman graphs which also include Z-graphs, but the effects of those
graphs is captured in the lower components of the single particle Dirac
spinor. Le., such Z-graphs correspond to relativistic corrections to the
quark model. That such corrections are important in the quark model
has been known for a long time. For us the important point is that while
they have quantitative effects on quark model predictions (e.g., they are
commonly held to be responsible for much of the required reduction of
the nonrelativistic quark model prediction that gA = 5/3 in neutron
beta decay), they do not qualitatively change the single-particle nature
of the spectrum of the quark of our example, nor would they qualitatively
change the spectrum of qq or qqq systems.
* Finally, we note that the large N, and quenched approximations are not
identical. For example, the NN interaction is a 1/N, effect, but it is not
apparently suppressed in the quenched approximation.
2.3 The Heavy Quark Limit
The third perspective from which there is support for the same picture is the
heavy quark limit 4. While this limit has the weakest theoretical connections to
the light quark world, it has powerful phenomenological connections: see Fig.
1. We see from this picture that in mesons containing a single heavy quark,
AEorbital (the gap between, for example, the JPC 1--- and 2++ states), is
approximately independent of mQ, as predicted in the heavy quark limit, while
AEhyperfine varies like mg as expected.
Recall that in the heavy quark limit a hadronic two-point function is domi-
nated by a single valence Q plus its associated "brown muck", with neither QQ
loops nor Q Z-graphs. The fact that heavy-quark-like behaviour persists all the
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Isgur, Nathan. Strangeness in the Nucleon or the quark model beyond the valence approximation, article, January 1, 1999; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc708714/m1/4/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.