Fit QA

After running the fit, some QA needs to be done. There is a number of options to explore here. The minimum is to verify that the fitted kaon and proton peak position and asymmetry vs $p$ make sense.

Figure 3: Relative kaon and proton positions as a function of total momentum $p$ for the different energies. The left panel shows the relative positions as extracted from the fit and the right panels show the results after subtracting the Bethe-Bloch parameterisation. The error bars shown are statistical only. The lines indicate the estimated limits for systematic error calculation.

Fig. 3, left panel, shows the relative kaon and proton position as extracted by the combined fit, as a function of total momentum $p$. The different marker styles and colors indicate results for different beam energies. The line shows the parameterisation of the Bethe-Bloch curve that is used to initialise the fit. The relative positions of the electron and deuteron peak are fixed to this curve as well. The right panel Fig. 3 shows the difference between the fitted values and the parameterisations, for kaons and protons separately (upper and lower right panels). The fits all agree with the parameterisation at the level of 0.001-0.002 units in relative position. At that same level, some systematic deviations are seen between the different energies. The dashed curves show the uncertainty band that is assigned for the systematic error calculation.

Figure 4: Asymmetry parameter $\delta$ as a function of total momentum $p$ for the different energies.

Fig. 4 shows the values of the asymmetry parameter $\delta$ as extracted from the combined fit in each total momentum bin. The different marker styles and colors indicate the different energies. The asymmetry parameter has only a weak dependence on the total momentum and beam energy. This is consistent with the idea that the asymmetry arises from the intrinsic tail of the Landau-distribution that governs energy loss.

In addition to those basic checks, it is a good idea to verify the $p$ and $p_T$ dependence of the fitted resolution parameter. The $p$-dependence should reflect the change in peak position, and also shows some effect of the transition from standard resolution to high resolution sectors in the TPC. The $p_T$-dependence should be weak, but a rather large spread of values in each $p,p_T$-bin may be observed, mainly due to differences between tracks above the $y=0$ plane and below (two different $\phi$-bins). Another cross-check is to compare the extracted yields in the different $\phi$-bins. I have always observed a modest systematic difference between both bins, but never followed up in detail. There might be a difference in acceptance/efficiency between those bins as well.