Dynamic versus Static Hadronic Structure Functions Page: 2 of 6
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to an external field created by the virtual photon qq pair current [1,2], but such a gauge
link is process dependent , so the resulting augmented wavefunctions are not universal.
A remarkable feature of deep inelastic lepton-proton scattering at HERA is that ap-
proximately 10% events are diffractive [6,7]: the target proton remains intact, and there
is a large rapidity gap between the proton and the other hadrons in the final state. The
presence of a rapidity gap between the target and diffractive system requires that the
target remnant emerges in a color-singlet state; this is made possible in any gauge by soft
rescattering. The multiple scattering of the struck parton via instantaneous interactions
in the target generates dominantly imaginary diffractive amplitudes, giving rise to an
effective "hard pomeron" exchange. The resulting diffractive contributions leave the tar-
get intact and do not resolve its quark structure; thus there are contributions to the DIS
structure functions which cannot be interpreted as parton probabilities ; the leading-
twist contribution to DIS from rescattering of a quark in the target is thus a coherent
effect which is not included in the light-front wavefunctions computed in isolation.
The shadowing of nuclear structure functions arises from destructive interference be-
tween multi-nucleon amplitudes involving diffractive DIS and on-shell intermediate states
with a complex phase. The physics of rescattering and nuclear shadowing is not included
in the nuclear light-front wavefunctions, and a probabilistic interpretation of the nuclear
DIS cross section is precluded.
Antishadowing of nuclear structure functions is also observed in deep inelastic lepton-
nucleus scattering. Empirically, one finds RA(x, Q2) - (F2A(x, Q2)/(A/2)F(x, Q2)) > 1
in the domain 0.1 < x < 0.2; i.e., the measured nuclear structure function (referenced to
the deuteron) is larger than than the scattering on a set of A independent nucleons. Ivan
Schmidt, Jian-Jun Yang, and I  have extended the analysis of nuclear shadowing to
the shadowing and antishadowing of the electroweak structure functions. We note that
there are leading-twist diffractive contributions -*Nl -> (qq)N1 arising from Reggeon ex-
changes in the t-channel . For example, isospin non-singlet C + Reggeons contribute
to the difference of proton and neutron structure functions, giving the characteristic Kuti-
Weisskopf F2p - Fn ~ x1-c( A) x'5 behavior at small x. The x dependence of the
structure functions reflects the Regge behavior vaR() of the virtual Compton amplitude
at fixed Q2 and t 0. The phase of the diffractive amplitude is determined by ana-
lyticity and crossing to be proportional to -1 + i for aR 0.5, which together with
the phase from the Glauber cut, leads to constructive interference of the diffractive and
nondiffractive multi-step nuclear amplitudes. The nuclear structure function is predicted
to be enhanced precisely in the domain 0.1 < x < 0.2 where antishadowing is empirically
observed. The strength of the Reggeon amplitudes is fixed by the fits to the nucleon
structure functions, so there is little model dependence. Quarks of different flavors will
couple to different Reggeons; this leads to the remarkable prediction that nuclear an-
tishadowing is not universal; it depends on the quantum numbers of the struck quark.
This picture implies substantially different antishadowing for charged and neutral current
reactions, thus affecting the extraction of the weak-mixing angle Ow. We find that part
of the anomalous NuTeV result  for Ow could be due to the non-universality of nu-
clear antishadowing for charged and neutral currents. In fact, Schienbein et al.  have
recently given a comprehensive analysis of charged current deep inelastic neutrino-iron
scattering, finding significant differences with the nuclear corrections for electron-iron
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Brodsky, Stanley J. Dynamic versus Static Hadronic Structure Functions, article, January 9, 2009; United States. (https://digital.library.unt.edu/ark:/67531/metadc899754/m1/2/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.