Re: estimates of time resolution

["Fernando J. Barbosa" <barbosa@jlab.org>]

Hi Elton,

There was another subject that we discussed with Stefano and that is of 
interest to the calorimeter: temperature and calibrations.

No attempt was made to specifically control temperature in KLOE (just 
the building temp control) and they observe cyclical changes over a day 
[jokingly, Stefano said that they could find the time of the 24-hour day 
by looking at the data] - significant changes have been attributed to 
the PMTs and cables. As a result, they perform calibrations every two 
(2) hours.

Regards,
Fernando

Elton Smith wrote:
> 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
>   
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