Study on the PPS uncertainties

Introduction

PPS uncertainties are divided into three families:

• Bias: it is defined as the mean of the difference between the reconstructed value and the true one. As an example, this may be due to the incompleteness of the reconstruction formulas.
• Resolution: it is defined as the RMS of the difference between the reconstructed value and the true value.
• Systematics: this source of uncertainty is totally uncorrelated with bias and resolution and can be seen as an effect of biased conditions.

I list here the full list of sources of biases considered:

• Alignment biases:
  • Perturbation of the horizontal alignment (symmetric and anti-symmetric);
  • Perturbation of the vertical alignment (symmetric and anti-symmetric).

• Optic biases:
  • Uncertainty on the horizontal effective length;
  • Uncertainty on the derivative of the horizontal effective length;
  • Horizontal dispersion.

Note: with symmetric we mean "same deviation both in roman pot (RP) near and far", with anti-symmetric we mean "opposite deviation in roman pot (RP) near and far".

In this work, we considered a pre-existing code (https://github.com/CTPPS/proton_simulation_validation) designed to calculate the systematic uncertainties and we updated it, taking into account new possible scenarios. In this Twiki, we will describe the final output of the code, mentioning the results obtained.

The structure of the output

The output is saved in the file collect_systematics.root (see in the attachment). Note: the file provided here is just an example that was obtained using 2018_PreTS1 conditions. To study other eras, one has to produce another collect_systematics.root file, following the instructions provided in https://github.com/CTPPS/proton_simulation_validation . Therefore, the content of the folders shown in this example refers just to 2018_PreTS1 conditions.

Opening the file, one can see several other folders (single rp-2, single rp-3, ... , multi rp-0, multi rp-1). Note: depending on the Era chosen, some folders may be empty: not all RPs all used in all eras. Select the RP you want to study (as you can see also multi rp studies are possible, selecting multi rp-0 or multi rp-1, depending on the arm of interest).

The name of each folder ends with one of this strings: "_xi_vs_xi", "_t_vs_xi", "_t_vs_t". This depends on how systematics are studied:

• "_xi_vs_xi" : we study the how the quantity xi reconstructed - xi simulated varies as a function of xi simulated, supposing a perturbation at 1 sigma level of the nuisance parameters.
• "_t_vs_xi" : we study the how the quantity t reconstructed - t simulated varies as a function of xi simulated, supposing a perturbation at 1 sigma level of the nuisance parameters.
• "_t_vs_t" : we study the how the quantity t reconstructed - t simulated varies as a function of t simulated, supposing a perturbation at 1 sigma level of the nuisance parameters.

Opening the folder of interest, you will have full access to several plots, that I describe in the following lines. Note: in my description I am supposing that you are opening a folder whose name ends with the string "_X_vs_Y":

• alig-x-sym : we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the alignment on the x axis (symmetric scenario).
• alig-x-asym : we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the alignment on the x axis (asymmetric scenario). * alig-y-sym : we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the alignment on the y axis (symmetric scenario).
• alig-y-asym : we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the alignment on the y axis (asymmetric scenario).
• opt-Lx: we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the horizontal effective length;
• opt-Lpx: we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the derivative of the horizontal effective length;
• opt-Lpy: we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the derivative of the vertical effective length;
• opt-xd: we study the how the quantity X reconstructed - X simulated varies as a function of Y simulated, supposing a perturbation at 1 sigma level of the horizontal dispersion;
• combined: the combination (statistical sum) of all the above mentioned plots;
• g2_correlation: correlation matrices of the systematics, represented as 2D plot.