As indicated above, the primary purpose of this experiment is to determine the s quark contributions to the overall charge and magnetization densities of the nucleon. As will be demonstrated below the goal is to determine these s quark contributions at a level of a few percent of these form factors over the range of momentum transfer from about 0.1 to 1.0 GeV2.
There have been several indications that strange quarks play some role in nucleon properties:
N 
term and that determined from experiment [Be96].
production relative to that of
compared to a simple OZI rule calculation in some 
annihilation
channels can be interpreted in terms of 
knockout [Ma98].
The expectations for these contributions from the point of view of theory vary
widely [Mu94, Be96a]. In general, these measurements will tell us about the interactions of
pairs and thereby provide some constraints on 
and 
pairs as well. The measurements of the momentum fraction clearly indicate
the presence of pairs in the nucleon; the vector currents measured
here will essentially indicate whether these pairs survive long enough to
interact and become spatially separated to a degree significant compared with
the range corresponding to the momentum transfers probed. A small or zero
contribution to these currents has been described as a signal that the pairs are effectively ``inert'' [Mu98].
We cite here as examples two representative contexts for understanding the physics of the results: first, the current thinking regarding the hadronic expansion of QCD; and second, the relation to lattice QCD calculations.
Two recent papers contrast the current thinking in relation to such a picture.
First, in a calculation by Geiger and Isgur [Ge97], a study is made of the
contributions of an extended set of excited state kaons and hyperons to the
strange quark currents in the nucleon. They find strong cancellations as the
series is extended - in the pure SU(6) limit and a complete set the result is
identically zero. The authors conclude that ``If correct our conclusions rule
out the utility of a search for a simple but predictive low energy hadronic
truncation of QCD''. On the other hand, the recent data from experiment E866 at
FNAL measuring the 
- 
asymmetry in the nucleon (Gottfried Sum
Rule violation) leads to the following conclusion ``The good agreement between
the E866 - data and the virtual pion model indicates that
virtual meson-baryon components play an important role in determining the non-
singlet structure functions of the nucleon'' [Pe98]. It is clear that these
issues will remain at the center of discussion about nucleon structure for some
time to come. The detailed measurements of the sea proposed herein,
basically the complete set for this type of measurement, will have significant
impact on these questions.
One of the hopes for unraveling nucleon structure is lattice QCD. In this case,
in order to make progress with respect to understanding details of the quark
sea, one of the most vexing problems in lattice QCD - the inclusion of
dynamical fermions - must be addressed. There has been some progress recently
in ``first principles'' inclusion of dynamical fermions accruing from
developments related to ``improved'' and ``perfect'' actions [Bi98]. A
lattice calculation using these new techniques is now on the verge of being a
possibility [Ne98]. At this point there exists a lattice calculation [Do98]
with
some approximations in the treatment of the 
pairs. The results are
shown in
Figure 2. It is interesting to note that although the
calculation does not reproduce the SAMPLE measurement, it is consistent with the
HAPPEX result (in this case 
and 
are of opposite sign and the
appropriate magnitude to effectively cancel in the measured combination). A
complete set of contributions to the nucleon current as derived from
these measurements can provide an important meeting between experiment and
calculations on the lattice. Given the sheer size of these calculations, it will
in general be important to have experimental benchmarks of this sort to help
form a picture of nucleon structure from the calculational output.
and
together with the expected results from the G0
experiment (solid symbols). Overall
uncertainties are plotted for the experiment.
The electroweak probe provides a precise means of studying the currents of point-like quarks inside the nucleon. Because they are assumed to be Dirac particles in QCD, their (vector) currents are written simply as
where 
is the charge appropriate to 
(ordinary
electromagnetic charge) or 
(neutral weak ``charge'', see below)
coupling. The total electroweak current of the nucleon can then be
written as a sum of the contributions from each of the quark
flavors [Ca78, Ka88, Mc89, Be89, Na91]. For example, the
electromagnetic
form
factors can be divided up in this way
where j runs over all quark flavors and 
is the electric
charge. (We note that this is an exact statement.) In what follows
the
contributions of the quarks and antiquarks of a given flavor are
combined.
For example, 
will represent the net contribution of u
and
quarks to the charge form factor. The expression for the
electromagnetic
form factors is then
The utility of measuring the corresponding weak neutral current of
the
nucleon (in this case via parity-violating electron scattering, see
Section 
) is that it can also be written
in
terms of the 
where 
is the
weak ``charge''. This in turn suggests that the contributions of the
quark
flavors may be separated experimentally.
In order to determine
or 
, the s quark vector current matrix
elements of the
proton (``s quark form factors''), three measurements are required
(in
addition to the
assumption that c and heavier quarks do not contribute
significantly).
In addition to the form factors 
and 
it
is
possible to make use of 
if a model of the
relation
between proton and neutron structure is assumed. The simplest
relationship is that interchanging u and d
quarks
will transform a neutron into a proton and vice versa (isospin
symmetry),
i.e., in this language
The s quark form factors are then
with similar expressions for the u and d quark form factors. We note that
this
experiment will allow the three pairs of form factors 
,
and 
to be written as the set
,
and 
. The u and d form factors, combinations of
valence and sea contributions, also contain interesting information. The non-
zero
neutron charge radius, for example, suggests rather different u and d form
factors. [Be92]
It is possible that s quarks could show up in either 
or in
if they are
significant. In order to contribute to the charge form factor there
must
be a ``polarization'' of the s and 
distributions, i.e. they must
have different spatial distributions. The presence of s and
with different angular momenta - opposite 
, for example -
would
result in a contribution to . A variety of combinations is
therefore
plausible in which s quarks would contribute more to one form
factor
than the other. It should be noted that at present no microscopic
model
is capable of realistically linking the contributions to the charge and
magnetic form factors.
Electron scattering by current distributions is described by the
coherent
sum of and amplitudes
although we tend to ignore 
since it is very small, roughly
as large as 
. However, ,
unlike
, has both vector and axial-vector pieces.
Therefore, the
cross term in the cross section violates parity.
The cross term can be determined experimentally by comparing two parity-sensitive cross sections whose parity-conserving parts are identical. In this case the two cross sections are those of longitudinally polarized electrons with positive and negative helicities. Because the parity-violating terms in the cross sections are proportional to the electron helicity, the asymmetry is directly related to the cross term, i.e.
In terms of the form factors defined earlier, at tree level, the asymmetry for
elastic
scattering is [Ca78, Mc89, Be89, Na91]
where
Note that 
can be varied between zero and unity for a
fixed 
by varying the
beam energy and electron scattering angle. The ``axial-vector'' term
proportional to 
arises from the axial-vector current in the
proton
which may couple directly to the . Note that it is suppressed
relative
to the vector ``electric'' and ``magnetic'' terms because of the factor
.
The expected results for the experiment are shown in Figure 3. The uncertainties in shown in these plots include both statistical and systematic uncertainties as shown in Figure 4 and Figure 5. Also shown in Figure 3 is (1/10 times) the dipole form factor in each case to indicate the precision of the measurement of the strange quark contribution relative to the overall form factor. We note that the precision of the measurements changes very slowly as the value of the contribution moves away from zero. The statistical uncertainties shown in these Figures are determined based on 70% beam polarization and 30 day runs for the forward asymmetries and for each of the backward asymmetries. The beam polarization is a projection from what is currently available to what we expect to be possible at time the experiment runs.
from G0 experiment.
from G0 experiment.