Valence quark spin distribution functions Page: 2 of 9
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I. INTRODUCTION
The quark model has enjoyed so much success as a qualitative guide to hadronic structure
that the discovery that only about 30% of the proton's spin could be attributed to quark
spin came as a surprise. Since the quark model remains unjustified within QCD, it is a
misnomer to call this "proton spin surprise" the "proton spin crisis". However, whatever we
call it, this result has generated much very productive experimental and theoretical activity.
While in general the spin of the proton could reside on any mixture of its quark and
gluon constituents or in their orbital angular momenta, a conservative interpretation [1] of
the current situation is that the valence quarks carry the spin expected by the quark model
but that the low x sea of qq pairs is negatively polarized. In this case E (defined to be twice
the expectation value of the quark plus antiquark spin along the spin direction of a polarized
proton, so that E = 1 would saturate the proton spin), when decomposed into its valence
and sea components, would beE = E, + A(q+ 4)..
(1)
where E, = f dxE,(x) is twice the spin on the valence quarks and Aq... = f dxAq,..(x)
and Aq.. = f dxAq,.(z) are, respectively, twice the spin on the sea quarks and antiquarks
of flavor q. If the valence quarks were in nonrelativistic S-waves as in the naive quark
model, then E. would be unity. However, as has been appreciated for nearly thirty years
[2], in realistic valence quark models lower components of quarks spinors convert about
25% of the quark spin into orbital angular momentum so that E. ~ 0.75. If in addition
each of the three light quark flavors carries A(q + q)... -0.15, a very modest per flavor
effect, E 0.30 would follow. Sea quark polarizations of just this sign and magnitude
have recently been obtained in a realistic model of qq pair creation [1]. (In a more general
context, such small A(q+q).. values are perfectly consistent with a 1/N, expansion of QCD
(where sea quarks appear at order 1/N. via quark-antiquark loops). Note that the condition
A(q + q).. 1, not how accurately E. approximates unity, determines the applicabilityof the 1/N. expansion: any nonzero A(q + q),.. would lead to a "spin crisis" as N1 (the
number of light flavors) tends to infinity. )
In the conservative scenario just described, both the 25% relativistic quenching of spin
from E, and the negative polarization of A(q + q).. are compensated by orbital angular
momentum. In general, however, we are only guaranteed that(2)
(where L, is the quark and antiquark orbital angular momentum and }E, is the total angu-
lar momentum residing in the gluonic fields), so major experimental efforts are planned to
measure the component parts of Eq. (2) in an effort to disentangle the "spin crisis". These
efforts begin with planned extensions of deep inelastic lepton scattering measurements of
the proton and neutron spin structure functions down to very small x to complete the inte-
grals required to calculate E, and studies of the Ql-dependence of spin structure functions
to make inferences about Ag(x), the gluon helicity contribution to E,(x). Major efforts
are also planned to directly measure Ag(x) based on helicity-dependent gluon-parton cross
sections. In addition to these classical inclusive measurements, flavor-tagging semi-inclusive
experiments are planned to measure separately As...(x), As..(z), Ai.n.(x), Ad..(x), and
also the quark contributions Au(x) _ Au,(x) + Au...(x) and Ad(x) Ad,(x) + Ad.. (x).
(Note that it is not possible to experimentally separate the quark contributions Au...(x)
and Ad,..(x) from Au,(x) and Ad.(x): this separation is conceptual only.) Additional
complementary information on the si content of the proton is expected from planned mea-
surements of the electric and magnetic form factors G& and G', of the kys current using
parity-violating electron-nucleon elastic scattering.
Given the substantial effort being devoted to this problem, it is surprising that we still do
not know whether our original simple picture of the spin structure of the valence quarks is
right! To some degree this is because this question is not well-defined: in contrast to other
methods (e.g., QCD sum rules [3]), the quark model is not normally embedded in a field-
theoretic framework. As a result, there are many difficulties in making comparisons between2
E, + EA(q+ q)..+ 2L,+ E, = 1
3
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Isgur, Nathan. Valence quark spin distribution functions, article, September 1, 1998; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc704129/m1/2/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.