Dynamic gain calibration


Unlike other experiments, the Pion-Beta Experiment is not using a light pulser for gain stabilization. Instead, Michel events are taken during normal runs. The Michel decay of stopped muons in the target produce an energy spectrum with a characteristic edge at about 50 MeV in the CsI calorimeter. If the gain in some PM tubes or the light output per MeV of any CsI crystal changes over time, this edge is shifted.

The task of the dynamic gain calibration is to analyze the michel spectra on a periodical basis and produce a gain drift table. If the gain of any channels drifts more than a certain value, the high voltage of that channel has to be adjusted.

Theory of operation

Besides Pi-Beta and pi+ -> e+ nu events, data is taken for a prescaled number of michel events at a rate of about 100 events per second. These events are identified by a specific bit pattern in the event data and histogrammed separately from other event types. For each channel, a histogram is updated with the sum of all CsI ADC's, if that specific channels contains more than 70% of the total energy. If the histograms contain a given number of events, they are compared with a saved set of reference histograms. The reference histograms were taken at an initial calibration run. The actual histograms are scaled by an variable gain factor g, which is varied to minimize the mean quadratic deviation between the reference histogram r[i] and the actual histogram h[i]:

The factor g is varied from 0.8 to 1.2 in small steps to find the minimum deviation. The error of this determination is given by the range where chi^2 increases by one. To minimize the error, the two histograms are only correlated in a region which shows a pronounced feature, because the method doesn't work at regions which are flat. Therefore, a region around the michel edge was chosen which gives a minimal error.


During our 1996 beam time, one week was dedicated for long term stability tests. During this week, Michel events were taken coninuously at a rate of 30Hz. Every five hours, the gains were calibrated against reference histograms taken at the beginning of this week. Following picture shows the Michel spectra from the beginning (red) and end of this week (black). The grey region around the Michel edge was used by the gain matching alorithm. Note how accurate the Michel edges fall together. No significant gain deviation can be observerd.

The next picture shows another channels, which shows a significant gain drift of +2.2%:

A compilation of all channels from the 1996 beam time is shown here:

Except in channel 32 no significant gain drift was observable over the period of one week. This shows that the energy resolution of our detector is stable at the per cent level over a long time and no dynamic high voltage adjustment as planned originally is necessary.

S. Ritt, 31 Oct 1995