[Halld-cal] [EXTERNAL] FCAL calibration follow-up

[Shepherd, Matthew]

> On Apr 30, 2020, at 4:15 PM, Colin Gleason <gleasonc at jlab.org> wrote:
> 
> Some one correct me if I'm wrong, but I always thought of the gain calibration as the method to bring the width to its most consistent value, then the energy correction is used to shift the pi0 mass to where it should be.

The gain calibration minimizes width by looking at the pi0 mass for every block individually and it shifts the mass to be same for every block by applying a scale factor to the energy for that block.  In doing so it makes the response uniform and that consequently minimizes the pi0 width across the entire detector because individual pi0's vary less in their measured invariant mass.

A potential problem is that a block away from the beam axis tends to be populated on average by lower energy photons from pi0 decays than a block near the beam axis.  Because the response is nonlinear this means that, if one doesn't do a nonlinear correction when gain balancing, the pi0 peak in the outer blocks may be shifted from inner blocks not by a true gain variation but just by the nonlinear response.  This would then introduce some artificial position-dependent gain that would later show up as ring dependence of the response.  It is a small effect because nonlinearities are relatively small and the average energy variation is probably also small.  Because it is a small effect, I suspect just a crude non-linear correction (like the one determined from the previous run's calibration) likely reduces it to a negligible effect.

Since Igal is starting everything from scratch and aiming for sub percent precision, it is important to have an eye out for this effect.

Regarding shifting the mass in the right spot, I think you also do some gain rescaling typically to preserve the average gain, right?  

This would take out uniform gain shifts embedded in the gain constants and require they be re-incorporated into the non-linear correction (which has an asymptotic value that is not unity to absorb such effects).  If you didn't do this rescaling, I suspect that that after gain balancing you'd have a pi0 peak whose mass was in the right spot.  The non-linear correction should also be a width minimizer because it removes fluctuations in the reconstructed mass due to variations of the energies of the photons.  I suspect this nonlinear effect is relatively unchanged in the many years we've run GlueX as it is tied to things like attenuation in glass, thresholds, etc. which are largely unchanged.  And hence the change in width is not noticeable.  The dominant feature you probably see of the nonlinear correction is likely the overall shift it introduces by its asymptotic deviation from a factor of 1.

Matt