Comment on Richard's note (non-uniform response & energy resolution)

[Andrei Semenov <semenov@jlab.org>]

Elton:

I read Richard's note, and I see a few serious problems in it:

1. The most serious problem is with eq.18 (and with resulting eq.20). The
last term in the eq.18 is NOT proportional to E^2. The combination
(<Ei^2>-<Ei>^2) is the variation of the energy that was deposited in the
cell #i (by definition). Taking into account the statistical nature of the
energy deposition in the shower, it's more natural to expect this value to
be proportional to E, that makes it just a part of the statistical term of
energy resolution (viz. IT HAS NO CONNECTION WITH THE FLOOR TERM.)

2. The E^2-like scaling of the last term (eq.18) was introduced
artificially by Richard when he used the gaussian with the CONSTANT sigma
parameter in the "Concrete Case" section. The "size" of the shower depends
strongly on the energy, and using of the no-energy-dependent distribution
is absolutely unrealistic. And this UNREALISTIC distribution is the ONLY
origin of the E^2-dependence of the last term in eq.18 that allows to
Richard consider it as a "floor-term".

"Shape" parameter of the real distribution must be a function of energy;
and the real transverse distribution is not a gaussian. The simulation
shows very sharp and narrow (less than or about 1 cm FWHM - depends on
the energy) peak in the center accompanied with more wide wings (about
100-1000 times lower than the peak amplitude). Indeed, some experimental
papers report wide gaussian shape for the transverse distribution, but
careful analysis of the measurement procedure indicates that these
distributions were faked by finite photon-beam size convoluted with space
resolution of the detectors used (both these factors were not taken into
account in the experimental data analysis).

3. The real origin of the floor term is the sampling of energy in the
calorimeter. It's important to understand that this calorimeter is VERY
DIFFERENT from the lead-glass calorimeter model. Here, the "sampling" is
not just distribution of energy between calorimeter cells. The major
fraction of energy deposited in the lead and glue is absolutely invisible
for readout. Only 12-13% of the total energy is deposited to fibers; the
simulation shows that the variation of the energy deposition to the fibers
explains the WHOLE floor term and 50-70% of the statistical term from
Blake's analysis of experimental data (2006). Talking about Richard's
note, it means that eq.2 and 3 are not correct, and the most important
correction is that it must be big enough floor term in eq.3 .

4. The most interesting question here is: WHY WE START THIS DISCUSSION AT
ALL? Indeed, the gain of cells in 4x4 SiPM array might be different, but
when we use the conventional PMT insdead of SiPM, the quantum efficiency
of the PMT photocathode is also not a constant but a function of
coordinate; and center-to-side variation of the efficiency is at least
15-20% (or more) for the most PMTs. And PMT-to-PMT gain difference is
significant too. It means that the use of non-uniform (at the level of
10-15% cell-by-cell variation) SiPM introduce NO additional problems
compared with the use of NORMAL conventional PMT with the SAME
calorimeter. Actually, the conventional PMT case is slightly worse because
while we hope to have a random pattern of gains in 4x4 array, the PMT
quantum efficiency dependence has a center-side structure usually; so if
we will have problems with SiPMs, it means that not a single
electromagnetic calorimeter in the history worked properly :)

Thank you,
Andrei








On Fri, 11 Apr 2008, Elton Smith wrote:

> Hi Andrei and Beni,
>
> Richard has summarized his work on the effect of non-uniform response on
> energy resolution. It was suggested this morning that a couple of persons
> look at the document carefully and comment on it in advance of our working
> group meeting next Tuesday at 11:00 ET. I thought it might be useful for
> somebody from the fcal and bcal do this. Would you two be willing to take
> a look at it?  (Zisis indicated that Andrei has already looked at the
> document).
>
> The GlueX document is #1012 on the portal.
> http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1012
>
> Thanks, Elton.
>