The relevant processes are classified into 3 categories using
the invariant mass of the hadronic system(
),
where 
and 
are the 4-momenta of
the incoming 
and the proton after ISR, respectively.
and 
are those of the scattered and
the produced lepton before FSR, respectively.
The 3 categories are
(elastic),
(quasi-elastic) and
(DIS),
and 
are the masses of the proton and the neutral pion, respectively.
The default value for 
is set to 5GeV.
For the elastic process, the diagrams in Fig.1 are calculated.
The elastic proton vertex is described using a dipole form factor.
The general form of the proton-proton-photon (
) vertex (
)
where protons are on-shell can be written as
where 
indicates the electric charge of the proton,
q means the 4-momentum transfer (
),
and 
are two independent form factors,
is the anomalous magnetic moment of the proton
and
is the mass of the proton (see, for example, [8].).
The electric and magnetic form factors (
and 
respectively)
are defined as follows,
Using the Gordon decomposition and the scaling law,
the following formula which is used in this program is obtained,
where 
and 
indicates the Bohr magneton.
is calculated according to the dipole fit,
The only difference between the elastic and the quasi-elastic processes is
the treatment of the proton vertex and the final state hadronic system.
The quasi-elastic proton vertex can be described using the hadron tensor in the following form assuming parity and
current conservation (for example, see [8]),
where
.
and 
are
the electromagnetic proton structure functions.
To obtain the cross-section formula, the hadron tensor is contracted with
the lepton tensor 
which is calculated using amplitudes generated by GRACE,
In this version, the structure functions in
EPVEC are used for 
and 
.
The functions were parameterized fitting the experimental data [9]
in the following kinematic region,
where 
.
The exclusive hadronic system is simulated in the event generation step
with the method used in the generator EPSOFT [10] for proton dissociative processes.
For the DIS process, the Quark-Parton Model (QPM) is used, and
the diagrams in Fig.2 are calculated.
The PDFLIB [11] is linked to get parton densities.
The simulation of the proton remnant and the hadronization are performed by PYTHIA.
It should be noted that the lowest order calculation in this process is valid only
in the region,
where 
is the 4-momentum of the incoming quark.
The value of u corresponds to the virtuality of the u-channel quark in the diagram
in Fig.2-(b).
When it is around or smaller than 25 GeV
, large QCD corrections are needed,
so that the lowest order calculation is not correct as explained in [4].
