Meeting No. 11

Systematic uncertainty

Let's discuss systematic uncertainties. As we discussed last week, not all of them effect the proton charge radius. Here are my notes on the contributions to the systematic uncertainty. I believe, that majority of them do belong in the final fit.

SystematicUncertainties.pdf

Determination of the proton radius:

Last week I have shown you the prodecude for calculating the radius. I also calculated the model dependend uncertainty using simple MC simulation. As an alternative to this procedure, Harald suggested to use error propagation in order to obtain this result analytically. I have done this, but this is not simple. When looking at the functions, we can not use the derivative of the FF to get out the error of the radius, because then all the dependencies cancel out. One needs to check the FF it self. Here I have the Q2 dependence of points. Hence, I get out the uncertainty for each Q2 point. Considering that the last point contributes most, the errors are comparable.

FitFormFactorsEducated2.pdf

Here are my notes on the calculation of the Radius:

NotesOnRadius.pdf

The Vertex correction:

Last week I reported on the effects of the Vertex correction. As discussed the consistent correction works for the 495MeV and 330MeV settings. However, as shown on the plot below, it does not work for the last setting. Here, approx 2% are missing. If I normalize data to the elastic setting, the remaining points are too high - but consistent. This is disturbing. I revisited all my steps and I can not find a step, where I could bring in sich difference.

The External Radiative Correction:

Now I have received already several times questions about external corrections. Hence, I checked their contribution to the result. Interrestingly, their effect is not negligible and their E' dependece is very similar to the one of the vertex corrections. Hence, a mistake here could also bring the missing correction for the 195MeV setting. To be happy the correction would have to be a bit larget. (The cyan points show result, when I change the density for +10%. magenta show results, when I leave out the contributions in the target walls. )

Optics:

The SVD algorithm is now done for the 195MeV and 360MeV settings. Now I need to determine the matrices for A and B for the last 495MeV setting. Here are the results for the 360MeV and 195MeV settings: