See the previous posting 
http://stoney.phys.ualberta.ca/~e614/Projects/E614MEETINGS/00094/
for explanation of the procedure and MC parameters. 

To test Art's suggestion that angular smearing is important, the job
was rerun without multiple scattering (MULS 0), the rest of parameters
as before. Energy scale is reproduced correctly now, as you can see
from the attached picture.

Some speculations:

theta_true which I use in analysis instead of a reconstructed angle
comes from positron momentum just after muon decay.

Since phase space volume is proportional to sin(theta), it's
more probable that theta will increase due to multiple scattering.
Energy loss is proportional to 1/|cos(theta_track)| which is
systematically bigger than 1/|cos(theta_true)|

There is also a second-order in delta(theta) effect: path length
increase for a positive delta(theta) is bigger than corresponding
decrease for a negative delta(theta). This also gives systematic
bias towards bigger energy loss comparing to what is expected from
1/|cos(theta_true)|

These two effects perhaps can explain, why the answer was wrong.
However, shift of spectrum edge x_max in each angular bin can give
either negative or positive bias to the energy scale depending on how
the shift varies with theta.  The observed bias was negative. 
Is there an explanation for this?

I hope that use of reconstructed angle will give better energy
calibration than use of MC theta_true, because reconstructed angle
should be directly related to the track geometry and thus to the
amount of material passed. (Of course, biases in reconstruction can
badly affect the calibration...)

Andrei

Description: x1 based energy calibration; MULS 0. , Filename: x1-gausstep2-ec.ps

Created for the The Center for Subatomic Research E614 Project Projects Page.

Created by The CoCoBoard.