Study of SVT occupancies for various background conditions

Introduction

Definitions

Results

Occupancies

These plots show the expected Phi and Z occupancies for B Bbar events only (no background); these, for nominal background mixed in with B Bbar events, and these, for background 10 x nominal + B Bbar events. The occupancies have been divided by two, for reasons explained in the next section. For reference, this table gives the occupancies for noise hits only (no B Bbar events or background).

One can see that the maximal occupancies are 3-4 times lower than what was assumed at the TDR time (see, e.g., p.556).

Trigger jitter update

The present simulation assumes a 1 microsecond jitter window. According to Fred Kral, the expected trigger jitter is ~180 ns. We have accepted a conservative estimate of 500 ns as a more realistic jitter window to be downloaded to the chips. Consequently, the occupancy plots have been divided by two.

Al Eisner has written a thorough note on the occupancies with a particular emphasis on the impact on the dataflow. He used a 1 microsecond window; and still saw a significant reduction of the occupancies compared to the TDR results.

Time of event and time stamp (or corrected time) correlation

This plot shows the correlation between the time of event and the digis' time stamp for B Bbar events and for background (10 x nominal). The event time was obtained via the BunchT0 package which in our case returned the best estimated time from the L1 trigger simulation. The distribution was fitted, and the results of the fit were used to compute the "expected" time stamp for a given event time. The quantity (time stamp - expected time stamp) can be used for discriminating signal from background. As one can infer from these plots, a loose cut of | time stamp - expected time stamp | < 2.5 (corresponding to about 300 ns time window) results in a more than 50% background rejection and a reduction of occupancies by about a factor of two!

Gerry Lynch pointed out that the time stamp may not be the best quantity to use, and the "corrected" time (which is essentially time stamp minus the time shift from the TOT for a given channel) might do better. This plot shows the correlation between the time of event and the corrected time, this, the fit to it, and this, the distributions for corrected time minus expected corrected time for both B Bbar and background. They do indeed look very promising. However, one should remember that the present TOT simulation may be rather optimistic, and studies with a more realistic TOT modelling may be needed for truly conclusive answers.

Using timing information in reco clustering

High occupancies obviously lead to hit finding inefficiencies (for example, an early hit from noise or background can "mask off" a good hit). Using the correlation between the time of event and the time stamp (or the corrected time), which, as was discussed in the previous section, is capable of effectively reducing the occupancies by half, can therefore be very helpful for offline reconstruction. We should be able to obtain this number from Level 3 trigger to within a 10 ns accuracy (which is certainly good enough for our purposes).
Thanks to Anders Ryd, it is now possible to use Level 3 trigger sequence in offline reconstruction. The first tests revealed some problems in trigger software (see, for example, this posting). However, there is no doubt that this will eventually work.



A note on the simulation

While doing these studies, we've noticed a few effects that may need some attention in the simulation. One is the following: let's suppose we have a background hit that comes earlier than the good hit. What loss of efficiency do we expect?
Here's a simple argument due to Claudio Campagnari. Let b = background occupancy in 500 ns; f = rate of background hits = b/500ns; p = probability that the shaper output is positive when the a good hit occurs (which leads to inefficiency). p = f (delta t), where (delta t) = typical length of the background hit. As one can estimate from these plots due to Amedeo Perazzo, the typical delta t's are:


Shaping Time	Typical delta t	p at 1% backgr. occupancy
100ns	~250ns	~0.5%
200ns	~550ns	~1%
300ns	~700ns	~1.4%
400ns	~850ns	~1.7%


So at higher occupancies there might be a significant efficiency loss. But if we interpret this plot correctly, the typical times for background hits do not extent beyond ~ -500 ns. This is not sufficient for higher shaping times.

Another effect that is not in the simulation is "overshoot". Please refer again to these plots. The overshoot is ~30% of signal for slow decay const. Let t_1/2 = time over which overshoot is >15% of signal. Then the fraction r of real hits for which threshold is affected significantly due to a previous background hit is ~ f t_1/2. So, for b = 1% occupancy, we have:


Shaping Time	t1/2	r
100 ns	800 ns	1.6%
200 ns	1.4 micros	2.8%
300 ns	2.8 micros	5.6%
400 ns	3.2 micros	6.4%


Amedeo Perazzo proposed the following preliminary version of the simulation of the shaper overshoot at 100 ns.

Energy deposition for B Bbar and background hits

This plot shows the dE/dx spectra for B Bbar and background hits. One can see that background tends to have larger energy deposition than B Bbar hits (which is unfortunate). The units are keV.