The experimentally measured 
and 
can be
expressed as the linear combination of the asymmetries in the cross sections
and 
,
The cross section asymmetries are given as;
where 
is the virtual photoabsorption cross section
when the projection of the photon-nucleon system spin along
the virtual photon axis is J, and 
is a term
arising from the interference between transverse and longitudinal
amplitudes.
represents the probability of the depolarization of the photon
and described as
where 
representing the fraction of the energy
transferred to the target nucleon.
d is expressed as
The kinematical factor 
is defined as
and goes to 0 in Bjorken limit.
In the above equations, we took the limit of
and neglected the term
of 
, since 
is small as shown in Figure 2.
Figure 2: Kinematical factor 
as a function of x for several choices of
. Overplotted are the data points of EMC, SMC, and SLAC-E143.
The 
and 
can be expressed as
In Figure 3, the difference between the exact expression
of 
and approximate expression are plotted as a function
of x for the data points of three latest measurements for
proton, EMC, SMC, and SLAC-E143. The difference is order of 10
for CERN energies, and the use of approximate expression is justified.
Figure 3: Difference between the exact expression of 
and
approximate expression by neglecting 
are plotted
as a function of x for the data points of three latest measurements
for proton.
R is a ratio of the longitudinal to transverse cross sections;
where the total transverse cross section 
is defined by;
and 
is the corresponding cross section for
the longitudinally polarized photon.
The cross sections, 
, 
,
and 
, are related to the structure functions
as follows;
and 
is denoted by;
where K is an arbitrary factor representing the incoming photon flux. The Hand's convention chooses K as;
By substituting above equations into eqs. (7) and
(7), the asymmetries 
and 
are expressed as;
The ratio R is given by substituting eqs. (18) and (19) into eq. (13);
In the Breit frame it can be shown by helicity and angular momentum
conservation that R should be zero when scattering on quarks of
spin 
.
The early SLAC experiments showed that R was small and that quarks are fermion. In this case, Callan-Gross relation,
is concluded.
The longitudinal and transverse structure functions, 
and 
,
are defined as;
to satisfy;
By substituting above equations into eq. (13), R is expressed as;
Those formulae relate the measured asymmetries
and 
to
the cross section asymmetries 
and 
. From these cross section
asymmetries, two spin-dependent structure functions can be obtained as
In this note, we will try to tabulate all available data in the form of
for further usage of the data tables.
