Systematic errors

In Fig. 3 it can clearly be seen that there are systematic offsets between the relative peak positions at the different energies. These are likely due to a combination of residual effects from imperfections in the calibration procedure (which is carried out on a subsample of the data) and small deficiencies in the fit function and fitting procedure. From the observed spreads we estimate that the extracted relative kaon position has an uncertainty of about $2\cdot10^{-3}$ and the proton position $1.5\cdot10^{-3}$. Systematic uncertainties on the yields are calculated by repeating the fits with parameters fixed to these upper and lower bounds on the relative positions. These fits are performed by the macro fit_syst_shifts_chisq.C . There are four sets of fits, cycling through all permutations where one of the two relative positions is set to the nominal value (from the free fit) and the other is set to the upper and lower bounds respectively (as indicated in Fig. 3). The resulting uncertainties in the yield are correlated as a function of $p_T$, because the relative kaon and proton position are independent of $p_T$ in our fit. Since in addition possible offsets are expected to vary slowly with rapidity, we assume full correlation of those effects in rapidity. For more details see the section spectra calculation 3.5.