BGV Calibration

06/05/03: Initial Plans:

Please let us know if you've got any input- I'll update this page as we reproduce what has already been done and build on it.

Use Downstream and Upstream TDC information to reconstruct z coordinates for any given channel
Match all Upstream PMTs and all Downstream PMTs to each other, making careful use of pedestals;
- Use either IU's recent approach, Teige's approach ca. 7/99, or "bump matching" in the raw spectra
- Select Data with only 1 TDC hit within ADC gate
Obtain overall energy scale using one or more methods, listed below....

Physical events for possible use in calibrating energy scale:

Select protons (?) in BGV using BSD; Preferably single hits in both detectors
- Correlate pixel z in BSD and BGV, as check for BGV Down-Up TDC diff -> z method (Amplitude time-walk a problem?)
- Clean sample by conserving p_T² in single-pixel omega events?
- Look for recognizable proton signal in BGV- MIP? Energy spectra?
- Balance Upstream detectors vs Downstream detectors; Obtain physical conversion factor
Select "unmasked" BGV showers (not present in BSD); Should be gammas....
- With azimuthal symmetry from above, balance Upstream vs Downstream
- Do showers themselves have spectra to calibrate on?
Look for exclusive eta production, shared between BGV and LGD
- Events with 1 or 2 LGD photons but no successful particle reconstruction, preferably 1 BGV photon
- Purify sample: Conserve p_T² between "eta" and single BSD pixel
- Purify sample: Make use of CPV timing, veto on charged particles in LGD
- Purify sample: Fiducial cut on LGD?
- Look for eta characteristics in LGD/BGV using GEANT simulations

06/11/03: I've been re-working the libBGV/bgvClusterize function to operate with the newly calibrated time_list. The existing version does not work well on intial examination, showing a large bias towards "low-angle" phi; I believe this is due to the ordering of the hitlist (nClusters, phi). I took out the actual clusterizing, which makes this a straight conversion to physical units, and the low-phi bias fell away. Using the upstream and downstream timing information from bgv_hits I reconstruct a z-coordinate and cluster time with the existing (but incorrectly executed) strategy:

z = 1/2 [ L_BGV + (t_up - t_down) c_effective ]

t = t_up - ( z / c_effective )

Number of BGV "Clusters"; Cluster Time
Reconstructed BGV z; BSD Pixel z; Note the increase of BGV hits at ~0cm, keep in mind that the BGV is 86.5 cm long
BGV z-coord (x-axis) v BSD z-coord: Single BGV Cluster and BSD Pixel events; Note that there is some correlation, with offset in z between two detectors
BGV Cluster phi; Phi difference between clusters in event; Note the absence of positive delta phi in the bottom plot, and the sharp peak corresponding to 15^o of cluster separation
Difference in z between event clusters; Same, for clusters closer than 20^o in phi
Difference in t between event clusters; Same, for clusters closer than 20^o in phi
Note the sharper peak at zero in these bottom plots, corresponding to similar hits in neighboring clusters

It should be noted that the effective speed of light I used for the BGV is ~9.4 cm/ns. The correlation in z between BGV and BSD is encouraging, but needs work. It seems clear to me that showers in the BGV frequently strike multiple detector elements; clusterizing these hits in hope of obtaining accurate values for z, phi, and t (much less energy) will likely require an overall energy calibration for weighting.

06/16/03: Employing the energy calibration method of Teige '99, which will scale the channels to each other.... Briefly summarizing, the ratio of pulse heights measured by a given upstream and downstream detector for a hit can be expressed as:

R = [ G_U / G_D ] e^{K(2z' - 1)},

where -1/K is the attentuation length within a detector element, z' is a z-coordinate normalized to the length of the detector, and G_U (G_D) is a gain factor for the upstream (downstream) phototube. The log of this ratio has a linear relationship to z':

ln[R] = a₀ + a₁ z'

a₀ = ln [ G_U / G_D ] - K
a₁ = 2 K

Note that:

G_U / G_D = e^{a₀ - a₁/2},

which means we can not only normalize the upstream and downstream ends of a given element, but can also normalize the energy measurements of the detector elements to each other. Further analysis will obtain an overall factor to translate these normalized measurements into physical energy units.

A typical channel showing this linear relationship: 06_16_03_01.jpeg

At this point, my results resemble those displayed by Scott in his '99 tech note. His showed much more variation in y-intercept than mine do.... The slopes look similar, which tells me that the gains I'm measuring are probably different than his. I'll clean up the sample and run this analysis with much higher statistics (over different run periods) and see how things change- The runset used in the original analysis (6268-6271) isn't currently available on the UConn cluster, which may account for significant variation in gain.

07/04/03: A study in search of an appropriate c_eff for the BGV should probably be performed.... It directly effects the values I obtain for attenuation lengths by spreading out reconstructed z-values. For c_eff = 9.4 cm/ns (as was found in the existing code; top plots) versus 16 cm/ns (as suggested by Elton in our last conference call; bottom plots):

It seems like the correct answer might be somewhere between these values.... Further evidence that 9.4 cs/ns might be a little low (the slope of the above plot is too steep) is the low attenuation lengths I'm getting, compared to those obtained in '99. The lengths are reasonably consistent between different runsets, a good sign, but are typically between 50 and 90 cm (about half of what I expected).

Gains between the upstream and downstream ends of a given channel are reasonably close, typically with 10-20% in late runs. It should be noted that the curves aren't quite linear, as can be seen in the typical fit below (all using c_eff = 9.4 cm/ns):

Sample of linear fit to ln[R] vs normalized zed
List of attenuation lengths for runs 8222 and later
List of ln[R] for runs 8222 and later

After applying the attenuation and gain corrections, the non-linearity is more readily apparent. Possibilities to explain this include an amplitude time-walk effect, which would tend to flatten the slope as it pulls hits "further out" in zed towards the ends of the detectors. This is seen in the upstream end, but the opposite occurs in the downstream until the very edge (where statistics are low). There may be some systematic error in the way I calculate zed.... This effect may also be enhanced by a low value of c_eff. Hits on the outer edges might be skewed away from high values of ln[R] by energy/pedestal considerations.... The events used here are all single multiplicity in BGV "cluster," which might bias through event selection. Some small improvement can be seen by cutting on the corrected energy values:

ln[R] vs normalized zed, w/ attenuation and gain corrections
ln[R] vs normalized zed, w/ corr's and "energy" sum > 150 units
ln[R] vs normalized zed, w/ corr's and "energy" sum < 500 units
ln[R] vs normalized zed, w/ corr's and up- or downstream "energy" < 200 units
ln[R] vs normalized zed, w/ corr's and up- or downstream "energy" < 400 units

Anyways.... The upstream vs downstream calibration seems to be close on the individual channels. The corrected energies seem to be on similar scales, but not exact. Assuming that these issue can be either solved or sidestepped in the near future, the next step is to calibrate each channel to the others. With that, a more accurate BGV clusterizer can be employed.

07/29/03: Obtaining an effective value for c in the BGV means deciding on a criteria for judgement.... At the last conference call I attended Richard suggested placing the half-max of the z-distribution at 86.5 cm (the length of the BGV). This results in a c_eff of about 18.5 cm/ns, as plotted here.

A more accurate way of determining this value might be a comparison between the z_BSD and the reconstructed z_BGV. From purely geometric considerations, one expects that any given z_BGV will be further downstream than a corresponding z_BSD because of the detectors' differing mean radii; specifically, the ratio of z_BGV to z_BSD should be equal to the ratio of r_BGV to r_BSD for a given hit. A plot of z_BSD vs z_BGV for "one-cluster" events is plotted here, with a linear fit. Assuming that the BSD rings are well understood, we can adjust c_eff until the slope of this fit reached the desired value. (Note that the axes were reversed between the top and bottom plots because I sliced in y) The current choice of 18.5 cm/ns gives a fit of:

z_BGV = 10.2 cm + 1.292 z_BSD

The 10.2 cm offset corresponds to a 1.1 ns delay on the upstream photosignal....

I've been looking into the second-order effects of ln[R] vs zed.... Richard theorized that the effect might be due to a linear increase in sigma of the zed-slices, caused by a loss of timing resolution in the downstream end. From what I can see this isn't occuring, as evidenced by the representative channel plotted here. It seems to me that the slight increase in sigma near the up- and downstream ends is a weak statistical effect.

Looking closer at the individual up- and downstream channels, I found something disturbing. If we describe the pulse heights for a BGV channel as:

P_up = E G_up e^{K z'}; P_dn = E G_dn e^{K (1 - z')},

we expect that the log of these hits will provide a linear fit in z' with a slope equal to +/- K. Looking at a representative channel:

we see the they have different absolute values (slopes of -0.373 and 1.4775, corresponding to attenuation lengths of 231 cm and 58 cm), resulting in different attenuation lengths for the two ends of a given channel. When I build in a second order term, such as:

P_up = E G_up e^{K z' + A_up z'²}
P_dn = E G_dn e^{K (1 - z') + A_dn (1 -z')²}

I obtain effective attenuation lengths of 2943 cm and 37.4 cm from the log fit. It seems to me that there's either a problem at the hits level or in my analysis.