Email from Mike:

From jmichaelfinn@cox.net Thu Sep 23 11:38:25 2004
Date: Tue, 21 Sep 2004 16:46:51 -0400
From: John M. Finn 
Reply-To: finn@physics.wm.edu
To: 'Yongguang Liang' , 'Mark Pitt' 
Cc: 'Roger Carlini' , 'Jim Birchall' ,
     'Juliette Mammei' , 'Klaus Grimm' ,
     'Neven Simicevic' , 'Greg Smith' ,
     'Allena Opper' , 'Tony Forest' ,
     'Norman Morgan' , 'Mike Finn' ,
     'David Armstrong' ,
     'Shelley Page' , 'Dave Mack' ,
     'Richard Jones' 
Subject: Measurements of Q2

        For the benefit of the young members of the collaboration, I thought
it would be useful to summarize the algorithms that I use in calculating Q2.
Keep in mind that there are two completing definitions of Q2 that are in
play. Both can be well defined only in the peaking or "effective radiatot"
approximations, since we have no direct knowledge of nucleon form factors
far off-mass-shell. They are:
        
        1) The Q2 of the scattering vertex: This is the Q2 of interest,
since it relates directly to the scattering asymmetry, but is not directly
measurable. It needs to be corrected for all energies losses (virtual and
real Bremstralung, as well as ionization energy losses) occurring before the
scattering, i.e., along the incoming electron direction. The definition of
the initial electron energy at the scattering vertex (x) is given by
        
        		E_vertex = E_0 - dE_Before(x) -dW_Before
        
        Here, E_0 is the Beam energy, dE_Before(x) is the most probable
energy loss up to the scattering vertex, and dW_Before is the radiative
energy loss along the incident electron direction.
        
        2) The measured Q2: This is much more of a matter of how one chooses
to define it. I generate it by assuming trace-back from the front Region I
and II chambers. This defines Q2 in terms of a direction and a point in the
target. The final electron energy is ignored. Using this definition, one can
correct the Q2 for the most probable energy loss up to the scattering
vertex, but there is no way to account for real and virtual radiative
losses. Therefore the calculations assume the most probable value for this,
i.e., zero radiation.  The definition of the electron energy at the vertex
is given by
        
         		E_vertex(0) = E_0 - dE_Before(x)
        
        With either of these definitions of the vertex energy, and knowledge
of the scattering angle, Q2 can be calculated for elastic scattering at the
vertex.  Note that both definitions are defective in that they ignore the
possibility of large angle Bremstralung. Fortunately, this is extremely
small (except possibly for very large radiative losses that won't appear in
our cuts). Multiple scattering can be treated as a resolution effect in the
simulations.
        It is of interest, ideally, to generate both, to see how much they
differ. For all cases that I have analyzed, the difference is small <= 1%,
and the Monte Carlo routines can reliably be used to reduce the residual
error due to the correction to negligible proportions. 
        
        I hope that this summary is of use.
        
        Best Regards,
        Mike