BCAL Readout Segmentation Task group Meeting: Aug 12, 2011

Meeting Info

Time:

• 3:00 JLab
• 1:00 Regina

Location:

• CC F326-327

Vid-con:

• ESNet 8542553

Agenda

Review action items from previous meeting

• Read Zisis/Andrei's note summarizing the status of the task group's activities and progress towards it goal. Send comments to Zisis. (All)
• Read Elton's Note on parametric M.C. and send comments (All)
• Continue detailed timing resolution studies on BCAL (David)
• Continue development of single cell resolution functions (Andrei/Irina)

New Agenda items

• BCAL Signal Timing Distributions (David L.)

Minutes

Participants

David L., Elton S., Curtis M., Andrei S., Matt S.

Elton's e-mail

Earlier in the week Elton circulated an e-mail (copied below) outlining a simple calculation showing that:

• single cell energy resolutions may be equal to total shower resolutions
• all single cell energy resolutions cannot simultaneously have a worse energy resolution than the total shower resolution

Andrei took exception to the e-mail indicating that the "math is not correct" (no details were given).

Andrei also pointed out that the sampling fraction in cell 3 depends on whether the shower starts in cell 1 or cell 2. Due to this effect, toy Monte Carlo and simple calculations can be misleading and so should not be trusted. He added that Irina is working on new simulations to help map out the sampling fluctuations as a function of all of the available parameters.

Hi Zisis and Andrei,

I would like to comment on the question about different resolution parameters for individual cells compared to the summed
energy. Let's make a few definitions:

E = total shower energy (lead and fiber)
sigma = a * sqrt(E), sigma2 = a2* E, denoting squares by "2" (width of visible energy due to sampling fluctuations, in units of E)
E_i = energy deposited in a cell (lead and fiber)
sigma_i = b * sqrt(E_i), sigma2_i = b2 * E_i (width of visible energy due to sampling fluctuations in cell i, in units of E_i)

Here we consider the main source of fluctuations to come from sampling, so a and b correspond to the contribution from sampling.
The sampling fluctuations are statistically independent from one another, as they come from energy depositions within geometrically
separate locations. Note: In general the E_i within the shower are highly correlated, since if more energy is deposited in cell i, less will
be deposited in cell i+1.

Let us begin with a "gedanken" set of showers, where we select a subset of showers that all have the same shower fluctuations,
namely all E_i are the same from shower to shower, (Of course the E_i can be different from E_j).  Note that this is not much different
than taking a specific GEANT event (containing shower fluctuations already and adding the sampling fluctuations in a separate step).
Given these conditions, we can deduce the following:

E = Sum_i (E_i)
sigma2 = Sum_i (sigma2_i) = Sum_i (b2* E_i) = a2*E -> a2 = (1/E) Sum_i (b2*E_i). This assumes that the sampling fluctuations are
statistically independent.

This equation is trivially satisfied if a2 = b2. It is also easy to see that b2 cannot be always be larger than a2 for all E_i, which is the
naive implication from Andrei's presentation, page 5. However, this conclusion is obtained for a set of showers with the same shower
fluctuations. If we include all subset of showers with physical shower fluctuations, then the correlations between terms with E_i and E_j
need to be taken into account and because they are negative, can lead to a situation where b2 is systematically larger than a2. But note
that this is only if shower fluctuations are included. If they already included from the GEANT MC, we should not double-count them.

Therefore, I conclude that the basic philosophy that separates shower fluctuations from sampling fluctuations is essentially correct if
one takes b = a, namely we must use the same parameters for sigma for E_i as for the full shower (E). Recall that E_i and E are the total
shower energies (not just the energy in the fiber).

Let me know if there is a flaw to this logic.  Thanks, Elton. 

BCAL Signal Timing Distributions

David showed some slides with the first results from the hdgeant-based simulation study he's been working on. The study uses individual steps for shower particles as recorded from hdgeant to develop a realistic electronic pulse shape. The point at which the pulse crosses threshold (44.7mV) is recorded as the time a TDC would have recorded.

Two calibration passes are done to correct for timewalk. The first on each layer of each end as a function of fADC value calculated from the electronic pulse shape (slide 3). The second calibration pass is done on the time difference between the two ends of the cell as a function of geometric mean (slide 4).

The corrected time difference is broken up into bins of geometric mean and fit to Gaussian shapes. The σs are then fit as a function of geometric mean to resolution functions for the time difference of each layer in the BCAL.

This procedure was performed independently for each of 3 data sets at θ=12^o, 20^o, and 90^o. In addition, the procedure was repeated for each of 5 different segmentation schemes (slide 6).

The resolution functions were used to calculate the uncertainty of the time difference in each cell of an event. The uncertainties were then combined to form an uncertainty in the time difference for the entire shower (slide 5).

A summary was presented of the results for the 5 segmentation schemes studied (slide 8). These indicated that the 1-2-3-4 segmentation scheme was very comparable to the "fine" scheme, but that all other schemes (which included summing of the first 2 layers) had significantly worse timing resolution.

Some discussion:

• Andrei pointed out that the mean time difference resolutions reported are for datasets that had flat energy distributions for the

generated particles. A more realistic input distribution would lead to a more meaningful number for the mean.

• It was noted that the outer layers do not have TDCs so the timing resolution will be different for those cells
  • It was thought that since the inner layers are driving the uncertainty, removing the outer layers from the calculation will

    likely have little affect on the whole shower resolutions

• Andrei suggested adding some mismatch in gains and time shifts to more realistically model the detector signals.

  • Elton noted that we shouldn't expect gain-matching to better than 1%

• Curtis asked if we have considered schemes to focus even more of the segmentation in the innermost layers leaving a sum

of 5 or 6 outer layers

• • Elton expressed serious concerns of adding any more than 4 SiPMs
  • Elton also reiterated Eugene's suggestion to sum sectors in some of the middle layers to save half a ring in readout electronics.
• Beni suggested a 1-3-6 configuration if we were forced to stay within the original 3-ring design budget. He noted that this is likely

  to be a viable solution only if we were able to outfit all 3 layers with TDCs

Action Items

• Read Zisis/Andrei's note and provide feedback (All)
  • (n.b. updates to previous meeting minutes are pending acceptance of this document)
• Read Elton's e-mail above and circulate comments via e-mail (All)
• Continue development of single cell resolution functions (Andrei/Irina)
• Implement the following in step-based simulation study
  • Realistic input distribution in energy
  • Remove TDC contribution from outer layers
  • Implement timing and gain shifts between SiPMs
  • Calculate t_avg