In case of the two-photon Bethe-Heitler
process,  we can factorize the process: u(x)*|A(u)|^2 + d(x)*|A(d)|^2
= [u(x)+d(x)/4]*|A(u)|^2 (A : Feynman amplitude) neglecting the mass difference.
But in case of the electroweak (EW) process where Z0 couples to a quark line, 
coupling structures are different between u and d quarks, i.e. the ratios of
vector and pseudo-vector coupling constants are different.  Therefore
we cannot do such a factorization. Also in case of the QED process where two
types of diagrams exist: (1) one photon connected to a quark line and (2)
two photons connected to a quark line,  again we cannot do such a factorization.
Anyway using the MERGE card as seen in Table1
of the GRAPE paper is the best we can do for saving time.
Comments  to  Tetsuo ABE (tetsuo.abe@kek.jp)
Last  updated  on  July 11,  2001