estimates of time resolution

[Elton Smith <elton@jlab.org>]

Calorimeter timing enthusiasts,

We spent some time yesterday picking Stefano Miscetti's brain about
various calorimeter issues, especially timing. He is clearly a walking
encyclopedia concerning KLOE detector and data. I wanted to pass on a few
thoughts before I forget.

1. Back of the envelop estimates of the time resolution.

quadruture sum of the following contributions:

1. sigma0 - electronics noise
2. sigma_sci/sqrt(Npe) - scintillator decay time
3. sigma_pmt/sqrt(Npe) - intrinsic pmt resolution
4. sigma_disp/sqrt(Npe) - dispersion

where Npe is the number of photoelectrons. Let us begin by assuming that
the electronic noise does not contribute (but clearly needs to be tracked
carefully especially for a large system). Now let us estimate each of the
other contributions in turn:

2. Sigma_sci. This is determined by the decay time of the scintillator. We
can take this from the scintillator specifications: 2.7 ns (BCF-20), 3.2
ns (BCF-12). (Recall that the rms of an exponential is equal to the decay
time). For discussion take 3 ns.

3. Sigma_pmt. This is given by the transit time spread of the pmt [See
Philips Photomultipliers Principles and Applications, p. 4-15]. The
transit time spread is dominated by the variances in transit time from the
cathode to first dynode (sig_kd1) and the electron multiplier (sig_m). For
"fast tubes" sig_kd1~0.15-0.35 ns and sig_m~0.15-0.25 ns, giving a
sigma_pmt~0.21-0.43 ns.

4. Dispersion in the scintillator. This corresponds to transit time
differences for optical photons traveling at different angles inside the
fiber. For a maximum trapping angle of 27deg, the transit time difference
is of order the distance top the pmt (~200 cm)/vsci(20 cm/ns) = 10 ns
(1/cos13deg-1/cos27deg) ~ 1 ns.

Adding these in quadrature we get 3.2 ns/sqrt(Npe). We see that the time
resolution will be dominated by the scintillator decay time.

The number of photoelectrons depends on the particle detected. For single
cells for cosmic ray muons we have measured Npe~25 per pmt. For muons
traversing 6 cells, we divide by sqrt(6). In the beamtest for 1 GeV
showers, we estimate a total of 700 p.e. per side.  (This number is
expected to be 2-4 times higher for the actual detector)

We can now estimate the estimated resolution for the calorimeter.

1 cell: sigma ~ 3.2 ns/sqrt(2*25) = 450 ps.
muons: sigma/sqrt(6) = 183 ps.
1 GeV: sigma ~ 3.2 ns/sqrt(2*700) = 86 ps/sqrt(E)

This estimate suggests that our measured time resolution for 1 GeV showers
is consistent with the energy dependent term but the constant term is a
mystery. The resolution for muons is espected to be smaller than the
measured value by a factor of about 2, but consistent with KLOE's
measurements.


Elton Smith
Jefferson Lab MS 12H5
12000 Jefferson Ave
Suite # 16
Newport News, VA 23606
elton@jlab.org
(757) 269-7625
(757) 269-6331 fax