The cross section for the BHT3 trigger is likely to change over time, both from beam-related backgrounds we can't identify and from changes in the gains of the individual towers which we can't easily correct for.  We do, however, expect the cross section to be stable over shorter time period, and to be consistent to within some reasonably wide range over the whole course of the 500GeV running.  At the moment, I'm focusing just on the simple calculation of the cross section from numbers that can be found in the runlog browser.

1) Calculating the cross section using a known luminosity:

If we have the luminosity from an external source, we can use the rates to calculate the cross section for a given trigger.  In run 10097098, C-AD reported an instantaneous luminosity of L=5.3x10^31cm^-2s^-1.  

1a) The ZDC scaler xs:

From the trigger details page for that run, we see a base ZDC (scaler) coincidence rate of R=128226Hz.  According to Bill Christie (powerpoint attached below) after correcting for ZDC singles, the true coincidence rate is closer to Rc=122200Hz (representing a ~5% correction).  From these two values, we get a corrected ZDC scaler cross section of Rc/L=2.3mb.

This number is in good agreement with the value we get from the vernier scan.

1b) The BHT3 xs:

There are some problems in finding the BHT3 trigger rate.  

- From the same trigger details page, we see a 'scaler/base_rate' for the BHT3 trigger of 1.56e-4.  The base_rate is the ZDC scaler rate, 128226Hz, meaning the BHT3 trigger rate is ~ 20Hz.  

- The runlog page for that run shows that the run was approximately 6 minutes long (=360s) and had 2854 BHT3 triggers, yielding ~7Hz.  

- From the l2btowCal plots, it seems like the run is closer to 150s long instead.  This would yield ~19Hz.  

- In Bill's powerpoint presentation, he quotes 2854 events and a run length of 90s, meaning a BHT3 rate of 31.7Hz.  

We can see there are gaps in the run from the DAQ rates plots for that run, but unfortunately there's no marker for the end of the run, and not enough markers on the horizontal axis to estimate how long the data was actually being taken.  We do see an average BHT3 rate closer to 30Hz, so that seems reasonable.  

Using 31.7Hz and the luminosity of 5.3e31, we get a BHT3 cross section of 598nb.  From the vernier scan, though, we expect there to be 1.7Hz of Single Beam background, which would reduce the BHT3 rate to 30.0Hz, and result in a non-SBB cross section of 566nb.

2) If we don't have a luminosity number for a given run, we can use the assumed-constant cross section for the ZDC to calculate the cross section for a given trigger.

...but we first have to have confidence in the scaler/base_rate value we have access to.

2a) In run 10097094, we see the same disagreement between different measures of the BHT3 rate:

- The trigger details page shows a scaler/base_rate for the BHT3 trigger of 1.68e-4 and a ZDC scaler rate of 138k.  This would yield a BHT3 rate of 22.8Hz, or assuming a similar 5% ZDC correction, 21.7Hz.  

- If we divide the number of BHT3 events from the runlog page, 1172, by the time we can roughly gauge from the l2btowCal plots, ~40s, we get 29.3Hz.

Since the run should have luminosity very close to the 10097098 run above, R=29.3Hz yields a very similar cross section, while the 20Hz number that comes from the scaler/base_rate value will be significantly off.  It seems we're suffering from the same issue in this run as the previous - the trigger details page shows a scaler/base_rate value that is averaged over a time period longer than the length that we were taking data in.

Still, if there is some constant being added to the denominator, it should be a small effect on a long run.  To test this I looked at run 10094019, which ran for over half an hour.  

1) The rate reported by the  trigger details page is 103062*1.56e-4, or 16Hz.  

2) From the runlog page and the DAQ rates plots we see 42612 events over the course of ~34min=2040s, yielding ~21Hz.

These numbers differing by ~30% as in the previous examples, suggesting the differences is not a constant being added to one of the values.

Before calculating the cross section of this, we can assume a ~5% correction to the ZDC rate from singles  (singles should be more common at higher rates, so this is probably an overestimate here), yielding Rc=97909Hz

Following the equation above, the cross section for the BHT3 trigger should be the ratio of rates (assuming it's roughly correct) times the ZDC scaler cross section, meaning here it should be 2.3mb*21/97909, or 493nb.  If we correct for the Single Beam Background, this number will get smaller.  We seem to be on the outer edge of reasonable agreement with the 566nb number in the previous section.  In order to be in very good agreement, the length of the run would need to be ~200s shorter, which is large enough that is should be noticable by eye.