# BEMC Calibration Uncertainty

Goal:

To calculate the systematic uncertainty on the cross section due to the BEMC calibration uncertainty.

Justification:

Clearly, the BEMC energy scale is of vital importance to this measurement.  The energies measured by the BEMC are used to calculate many of physics level quantities (photon energy, pion pt, pion mass, Zgg) that directly enter into the determination of the cross section.  Since the calibration of the BEMC is not (and indeed could not be) perfect, some level of uncertainty will be propagated to the cross section.  This page will try to explain how this uncertainty is calculated and the results of those calculations.

Method:

Recently, the MIT grad students (lead by Matt Walker) calculated the gain calibration uncertainty for the BEMC towers.  The results of this study can be found in this paper.  For run 6, it was determined that the BEMC gain calibration uncertainty was 1.6% (in the interest of a conservative preliminary estimate I have gone with 2%).  In the analysis chain, the BEMC gains are applied early, in the stage where pion candidate trees are built from the MuDSTs.  So if we are to measure the effect of a gain shift, we must do so at this level.  To calculate the systematic uncertainty, I recalculated the cross section from the MuDSTs with the BEMC gain tables shifted by plus or minus 2%.  I recreated every step of the analysis from creating pion trees to recreating MC samples, calculating raw yields and correction factors, all with shifted gain tables.  Then, I took the ratio of new cross section to old cross section for both shifts.  I fit these ratios after the first two bins, which are not indicative of the overall uncertainty.  I used these fits to estimate the systematic for all bins.  The final results of these calculation can be found below.

Plots:

1) All three cross secton plots on the same graph (black = nominal, red = -2%, blue = +2%) 2)  The relative error for the plus and minus 2% scenarios. Discussion:

This method of estimating the systematic has its drawbacks, chief among which is its maximum-extent nature.  The error calculated by taking the "worst case scenario," which we are doing here, yields a worst case scenario systematic.  This is in contrast to other systmatics (see here) which are true one-sigma errors of a gaussian error distribution.  Gaussian errors can be added in quadrature to give a combined error (in theory, the stastical error and any gaussian systematics can be combined in this manner as wel.)  Maximum extent errors cannont be combinded in quadrature with gaussian one-sigma errors (despite the tendency of previous analyzers to do exactly this.)  Thus we are left with separate sources of systematics as shown below.  Furthermore, clearly this method accurately estimates the uncertainty for low pt points.  Consider, for example, the +2% gain shift.  This shift increases the reconstructed energies of the towers, and ought to increase the number of pion candidates in the lower bins.  However, trigger thresholds are based on the nominal energy values not the increased energy values.  Since we cannot 'go back in time' and include events that would have fired the trigger had the gains been shifted 2% high, the data will be missing some fraction of events that it should include.  I'm not explaining myself very well here.  Let me say it this way: we can correct for thing like acceptence and trigger efficiency because we are missing events and pions that we know (from simulation) that we are missing.  However, we cannot correct for events and candidates that we don't know we're missing.  Events that would have fired a gain shifted trigger, but didn't fire the nominal trigger are of the second type.  We only have one data set, we can't correct for the number of events we didn't know we missed.

All this being said, this is the best way we have currently for estimating the BEMC energy scale uncertainty using the available computing resources, and it is the method I will use for this result.

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