The proton's spin: A quark model perspective Page: 7 of 14
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the valence-dominated region assumed that all Aq and q (valence) have the same x
dependence. Thus (see Refs. 3 and 4 for origins of these formulae)
An(x) = 4Ad + Au + 0,
(the zero following immediately from Eq. (9)' and
Ap(x) - (-Ad) + 3(gA4 v)
The prediction that Ap > 0 is non-trivial as a priori it could be anywhere in
the range -1 4 A < +1. The presence of a qq sea as x + 0 was expected to cause
A(x + 0) + 0. The other qualitative expectation26,27) was that A(x + 1) + 1 as
The valence picture above implicitly assumed that uv (x) - 2dv(x) for all x.
However, unpolarized data show this to be untrue in that it would require that
In practice, this ratio drops as x + 1, suggesting that the u(x + 1) >> d(x +
1), a phenomenon which follows from spin dependence via single gluon exchange.
Chromomagnetic hyperfine energy shifts split the a-N masses and elevate u(x + 1)
over d(x + 1). They also cause ut(x + 1) to dominate over u+(x + 1), which the
consequence that AP'n(x + 1) + 1. Thus, a qualitative expectation for AP
Ap(x + 0) + 0; Ap(x = 1/3) = 1/3 - ; Ap(x + 1) + 1.
These predictions turned out to be remarkably well verified and even agree with
the latest EMC data.
Recently Close and Thomas28) showed that, within the framework of the MIT
bag model, one could relate the x-dependent distortion of the valence distribu-
tions to the measured chromomagnetic energy shift in the A-N masses. All of
this suggests that the valence quark polarizations measured in polarized deep
inelastic scattering are similar to the polarizations of the constituent quarks
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Close, F. E. The proton's spin: A quark model perspective, article, January 1, 1989; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1059459/m1/7/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.