FC charge per DST file fails to account for charge between last and first scaler readouts

[c-dilks]

As part of the RG-A inclusive cross section analysis, we have noticed an issue
with the FC charge in the QADB: in summary, there is a systematic uncertainty
associated with the scale of the accumulated charge.

The FC charge was read out for the RG-A F18 dataset at a rate of 30 Hz, which
defines a time bin of the scaler readout of 33 ms. Since the QADB applies QA
filters per reconstructed DST HIPO file, the total accumulated beam charge is
determined by summing over each of the DST HIPO files' charge values, including
only the files that pass the analyzer's preferred QA criteria filter.

The charge readouts in the data are accumulative, so a DST HIPO file's total
charge is determined by the difference between its maximum and minimum charge
readouts; however, this strategy does not include the small amount of charge
accumulation before and after the file's first and last charge readouts,
respectively, leading to an underestimate of the total accumulated charge for a
DAQ run. At maximum, this underestimate should be the amount of charge
accumulated in one time bin, and therefore much smaller than the total charge.
Furthermore, sometimes the maximum charge readout value of a particular DST
file may be larger than the minimum charge readout value of the subsequent
file, which leads to an overestimate of the total charge. Therefore, computing
the charge per DAQ run by summing each of its DST files' charge values is not
quite accurate and contributes a scale systematic uncertainty.

The updated QADB procedure, which will be applied to pass-2 data, instead uses
time bins and does not suffer these issues. Analyzers who plan to publish
results based on pass-1 data, that need the QA-filtered accumulated charge,
should be aware of the above issue and systematic uncertainty.

For RG-A F18 inbending data, we have estimated a scale systematic of 0.6% on
the total accumulated charge; this is based specifically on the set of runs
used in Valerii's analysis (and is therefore now included in his analysis).
Since we have the tools to estimate such a systematic for any runs in Run
Groups A, B, K, and M, please ask @c-dilks to do an estimation if you need it
for your analysis; the code for this is found in util/gap_charge_systematic.

Since Run Groups A, B, and K have pass-2 data produced, this charge issue will
be fixed when the QADB is reproduced using the new time bins method on pass-2
data. For RG-M pass-1 data, if needed, we can redo the QA using the new time
bins method.