Quarks and gluons in hadrons and nuclei Page: 15 of 31
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3. THE PROTON'S SPIN: A QUARK MODEL PERSPECTIVE
Inelastic lepton scattering from nucleons at high momentum transfer measures
the number densities of charged constituents, q(x), q(x), as a function of the
Bjorken variable x (essentia'ly the ratio of the constituent and target longitudi-
nal momenta in an infinite momentum frame). There is a weak dependence of these
distributions on the momentum transfer, Q2, but I shall suppress this in much of
If the beam and target are polarized, one can extract the helicity-dependent
distributions for quarks or antiquarks polarized parallel (q+(x)) or antiparallel
(q+(x)) to the target polarization. I shall define eq(x) = q+(x) - q+(x); q(x) _
q+(x) + q+(x), and similarly for antiquarks, q.
Data are presented in two ways.1-3 One is in terms of the polarization asym-
A(x) = ei2 (eq (x) + aq(x))/E ei2 (qi(x) + qi(x)), (33)
(note that -1 < A < + 1). The other involves the polarized structure function
gl(x) = e 2 (eq (x) + eq (x)). (34)
9l(x) __ A(x) F1(x). (35)
In advance of the data, the expectations were that
(i) At x > 0.2 where valence quarks dominate, A(x) should be large and posi-
tive.3,4 This follows from intuition developed for constituent valence quarks in
baryon spectroscopy where the Pauli principle requires eu > 0, Ad < 0. As the
charge-squared weighting of &u is four times that of d in protons, so Ap(x > 0.2)
> 0. Data confirm this brilliantly. For a neutron target, it is Ad that is
weighted 4:1 relative to au, hence these tend to cancel and one predicts' a small
(zero?) asymmetry on the neutron.
(ii) Form gl(x), which directly shows the charge weighted helicity-dependent
distributions and integrate over all x.5,6 If it were not for the charge weight-
ings, this would measure the net eq + eq (eq fl dxAq(x) = net quark polariza-
tion). Explicitly, in the quark parton model
Ip f dx gi(x) = u + - (eu+ed+es) + (Aqi - tql). (36)
The surprise2 is that Ip(EMC) = 0.12 and is almost saturated by7 u(=0.75) leaving
n (e q + a)a 0, (37)
hence, the much-advertised claim that maybe "none of the Droton's s5in
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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/m1/15/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.