Meeting No. 9
Vertex Corrections:
We are struggling with the discrepancy we observe for the first two (elastic)
points. The following plot that shows relative difference (please do not mind
the absolute scale) between the data and the simulation. You can see, that the
ratio is flat in the whole momentum range except for the first two points, which
sit exactly on the top of the elastic peak and are approx. 10 percent lower.
VertexCorrections.pdf
VertexCorrections2.pdf
We suspected that the problem was caused by our generator, when we hit the limit
of the numerical precision and need to introduce cut-off parameters. However, in
the last weeks we went very carefully through the generators code, and now believe
that the generator works well. The cut-off parameters are still there, but are placed
such that are at the end divided out and cause no error in the CS.
Therefore, we started to investigate other parts of the simulation, that could
cause the discrepancy and at the moment we are looking at vertex corrections:
We always assumed that vertex corrections are changing only slowly with momentum.
Therefore, we considered the contribution only at the centre of each kinematic point
(shown with blue points on the plot). However, when I performed more detailed
simulation for the first (elastic) kinematic I noticed (see red points) that very near the
elastic peak the correction starts to change very fast. If the fall-off is fast enough
this could compensate for the difference we observe. Is the effect that I see
physically meaningful or did I hit a problem with numerical instability?
I went to Marcs paper and there I noticed that amplitudes MV2 and MV3 (eq. 22 and 28)
include terms that have 1/q' dependence (1/-2k.q') on top of the 1/q' dependence of the
BH diagrams. In my opinion this could bring additional 1/q' dependence of the vertex
correction to the cross-section, which could explain what we observe.
However, the thing that is bothering me is that the integral of the correction
is not finite, but is Log[q'] divergent. I am meeting with Marc today to
discuss this problem.
Angle dependence:
Last week we were discussing possibility that the discrepancy we see
at the elastic setting comes from wrong scattering angles. I do not think that
this error could explain what we see (but please correct me if I am wrong):
The elastic cross-section indeed strongly depends on the scattering angle,
but its dependence is predominantly included in the Mott cross-section which
affects elastic peak and the tail the same way. Hence, a mistake in an
angle could cause a discrepancy between different energy settings, but
can not create a discrepancy between the peak and the tail. Here, the angle
comes into CS via Q**2 only.
Below is the simulation I made for different scattering angles.
You may see that for different angles the structure changes quite
a lot (This is probably what Adrian observed. ). However, it is not an offset,
but an oscillation around the central value, which happens because the
momentum distribution does not match the angle distribution any more.
Comparison.pdf
Multiplicity issue?
I again had doubts that something is wrong with the data at the elastic
line. There the rates were high in order to insure enough rate in spectrometer A.
I have compared the multiplicities for setting at the peak and setting at the
tail, and learned that at the peak 1 wire was less hit than at the tail setting.
Is this significant?
27. 4. 2016 in Ljubljana
Last modified 29.4.2016
