running without the CP veto

Figure 18: Coincidence peak in the tdc spectrum of the CPV OR for a run during the June period where the CP vetoes were removed from the trigger. The level 2 trigger was still present.

From Fig. 16 it is clear that to make further progress in reducing our electronics dead-time we have no choice but to compromise on our original wish for a online clean neutral trigger. The tdc spectrum for the CPV OR is shown in Fig. 18, taken during a run where the CP veto was removed from the trigger. All of the events in this sample passed the level 2 trigger condition. This figure shows that a veto window of 15ns is necessary in order to reject CP events online with full efficiency. Examination of the spectra for the individual counters shows that this peak width is essentially all coming from intrinsic time spread of the CP signals in the individual counters and not from timing misalignment.

There is no absolute reason why the CP veto must be done online. Several have suggested that we could reduce the width of the online CP veto window and accept a certain fraction of the CP events, and then reject them offline using the tdc data. The model presented above can be generalized to cover this possibility, albeit at the expense of some additional complication. Eq. 12 above takes on its simple form because it is assumed that CP events are completely rejected at all beam intensities (see Eqs. 6, 9). Relaxing this assumption turns the two terms of Eq. 12 into the eight terms of Eq. 18.

$$S_{_0} = r_{_R}\,I\,f_{_{ {T}\not{C}\not{U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Umiss})\,{\cal F}_{true} +$$ (18)

$$r_{_R}\,I\,f_{_{\not{T}\not{C}\not{U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Umiss})\,{\cal F}_{acc.} +$$

$$r_{_R}\,I\,f_{_{ {T} {C}\not{U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Umiss})\,{\cal F}_{true} +$$

$$r_{_R}\,I\,f_{_{\not{T} {C}\not{U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Umiss})\,{\cal F}_{acc.} +$$

$$r_{_R}\,I\,f_{_{ {T}\not{C} {U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Uhit})\,{\cal F}_{true} +$$

$$r_{_R}\,I\,f_{_{\not{T}\not{C} {U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Uhit})\,{\cal F}_{acc.} +$$

$$r_{_R}\,I\,f_{_{ {T} {C} {U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Uhit})\,{\cal F}_{true} +$$

$$r_{_R}\,I\,f_{_{\not{T} {C} {U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Uhit})\,{\cal F}_{acc.} +$$

where I have used an obvious notation for the fractions $f_{XXX}$ of the RPD OR rate that belong to each category. For example, $f_{_{\not{T}CU}}$ represents the fraction of RPD OR hits that were generated by a reaction chain that also includes particles that produced hits over threshold in the CPV and UPV counters, but nothing over threshold in the left-side tagger readout. In Eq. 18 $f_s$ is denoted $f_{_{T\not{C}\not{U}}}$ and $f_n$ is equivalent to $f_{_{T\not{C}\not{U}}}+f_{_{\not{T}\not{C}\not{U}}}$. Eq. 12 is simply the first two lines of Eq. 18; the subsequent lines enter as soon as ${\cal F}_{Uhit}$ and ${\cal F}_{Chit}$ deviate from unity.

Actually we have no reason to decrease the veto window width for the UPV OR, the problem is with the CPV OR. Therefore let ${\cal F}_{Uhit}=1$. This gets rid of the last four lines of Eq. 18 and leaves only $f_{_{TC\not{U}}}$ and $f_{_{\not{T}C\not{U}}}$ as additional inputs to extend the range of applicability of the model to $t_{_C}<15$ns. The formula for ${\cal F}_{Chit}$ now becomes

$${\cal F}_{Chit} = 2\left(1-\mbox{Erf}\,(\frac{t_{_C}}{\sigma_{_C}})\right)$$ (19)

where $\sigma_{_C}$ is the standard deviation of the CPV coincidence peak, 2.6ns in Fig. 18. Carrying on the generalization of the model to Eqs. 17,14 we obtain

$${\cal F}_1 =\;\;\left(\frac{r_{_R}\;I}{S_{_0}}\right) [ f_{1_{ {T}\not{C}\not{U}}}\,f_{_{ {T}\not{C}\not{U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Umiss})\,{\cal F}_{true} +$$ (20)

$$f_{1_{\not{T}\not{C}\not{U}}}\,f_{_{\not{T}\not{C}\not{U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Umiss})\,{\cal F}_{acc.} +$$

$$f_{1_{ {T} {C}\not{U}}}\,f_{_{ {T} {C}\not{U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Umiss})\,{\cal F}_{true} +$$

$$f_{1_{\not{T} {C}\not{U}}}\,f_{_{\not{T} {C}\not{U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Umiss})\,{\cal F}_{acc.}\;\; ]$$

$${\cal F}_2 =\;\;\left(\frac{r_{_R}\;I}{S_{_0}}\right) [ f_{2_{ {T}\not{C}\not{U}}}\,f_{_{ {T}\not{C}\not{U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Umiss})\,{\cal F}_{true} +$$ (21)

$$f_{2_{\not{T}\not{C}\not{U}}}\,f_{_{\not{T}\not{C}\not{U}}}\, (1-{\cal F}_{Cmiss})\,(1-{\cal F}_{Umiss})\,{\cal F}_{acc.} +$$

$$f_{2_{ {T} {C}\not{U}}}\,f_{_{ {T} {C}\not{U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Umiss})\,{\cal F}_{true} +$$

$$f_{2_{\not{T} {C}\not{U}}}\,f_{_{\not{T} {C}\not{U}}}\, (1-{\cal F}_{Chit})\,(1-{\cal F}_{Umiss})\,{\cal F}_{acc.}\;\; ]$$

where $f_{1_{XXX}}$ and $f_{2_{XXX}}$ are the level 1 and level 2 pass fractions, respectively, for level 0 event class $XXX$.

Figure 19: Decomposition of signal losses among various stages of the event pipeline as a function of the width of the CPV veto window $t_{_C}$ at a beam current of 250nA, with the upper-level trigger improvements foreseen for 1999 running in place. The large increases in trigger and data acquisition dead-time at low values of $t_{_C}$ reflect the onset of leakage from charged reactions that enter as the veto efficiency decreases from unity.

Figure 20: Comparison between ideal and actual rates of recording signal events on tape as a function of beam intensity, under the conditions of a level 1 trigger and improved DAQ, and with the online CPV veto disabled.

Figure 21: Same as Fig. 20 but with expanded vertical scale.

The input parameters for the model used to generate Figs. 19-21 are listed in Table 2.3. For some of the input values to the generalized model I had to make an educated guess. For example, $f_{_{TC\not{U}}}$ is measured directly in a run with the UPV veto enabled but the CPV veto removed. It appears that we did not take any data under these conditions. By looking at data with both CPV and UPV vetoes disabled, it is possible to check how many of the events come with a coincident UPV signal and subtract them off, but most of that data sample is completely skewed by the presence of the level 2 trigger condition. Taking what I believe to be reasonable estimates for the inputs that cannot be directly extracted from the data, it is now possible to produce a realistic prediction for the yield of signal events on tape as a function of $t_{_C}$ all the way down to zero CPV window width. The result is shown in Fig. 19. The conclusion from this plot is that the best yield is obtained with no online CPV veto at all!

Table 2: Input parameters to the model for 1999 running conditions, together with information about how the value for the parameter was obtained.

	parameter		value		method
	$r_{_T}$		$1.94\cdot 10^5$		/s/nA		fit to scaler data
	$r_{_R}$		$1.45\cdot 10^3$		/s/nA		fit to scaler data
	$r_{_U}$		$1.4\cdot 10^4$		/s/nA		fit to scaler data
	$r_{_C}$		$2.7\cdot 10^5$		/s/nA		fit to scaler data
	$t_{_T}$		$1.0\cdot 10^{-8}$		s		to be chosen
	$t_{_U}$		$1.5\cdot 10^{-8}$		s		to be chosen
	$t_{_C}$		$0$		s		no CPV in trigger
	$\sigma_{_C}$		$2.6\cdot 10^{-9}$		s		measured with UPV OR tdc
	$d_{_T}$		$1.0\cdot 10^{-8}$		s		fit to scaler data
	$d_{_C}$		$1.0\cdot 10^{-8}$		s		fit to scaler data
	$d_1$		$1.2\cdot 10^{-6}$		s		fast-clear specifications
	$d_2$		$1.4\cdot 10^{-5}$		s		measured on scope
	$d_{_{DAQ}}$		$3.0\cdot 10^{-4}$		s		promised by DAQ gurus
	$f_{_{T\not{C}\not{U}}}$		$2.6\cdot 10^{-3}$				measured at low rate
	$f_{_{\not{T}\not{C}\not{U}}}$		$5.5\cdot 10^{-1}$				measured with veto in/out
	$f_{_{TC\not{U}}}$		$5.0\cdot 10^{-3}$				pure guess (should be small)
	$f_{_{\not{T}{C}\not{U}}}$		$2.2\cdot 10^{-1}$				reasonable guess
	$f_{1_{T\not{C}\not{U}}}$		1.0				conservative estimate
	$f_{1_{\not{T}\not{C}\not{U}}}$		$3.0\cdot 10^{-2}$				reasonable guess
	$f_{1_{TC\not{U}}}$		1.0				conservative estimate
	$f_{1_{\not{T}{C}\not{U}}}$		$2.0\cdot 10^{-1}$				reasonable guess
	$f_{2_{T\not{C}\not{U}}}$		$1.3\cdot 10^{-1}$				fit to scaler data
	$f_{2_{\not{T}\not{C}\not{U}}}$		$3.5\cdot 10^{-3}$				fit to scaler data
	$f_{2_{TC\not{U}}}$		$1.0\cdot 10^{-1}$				reasonable guess
	$f_{2_{\not{T}{C}\not{U}}}$		$2.5\cdot 10^{-2}$				reasonable guess

The fact that we are writing all of this signal to tape does not necessarily mean that it will be possible to recover offline the set of events with accidental CPV hits within the coincidence peak. However the CPV is highly segmented, which makes it possible to recover events with a CPV inside the coincidence region provided that it does not physically overlap with a cluster in the LGD. Hence the expectation is that many of these events will in fact be usable. Fixing $t_{_C}=0$, the yield of signal events to tape under 1999 conditions, as a function of beam current, is shown in Figs. 20-21. These two are the same figure shown with different vertical scales. It is true that most of the 800 events/s being written to tape at 250nA have charged particles in the forward region. Most of them could be eliminated during a crude one-pass reduction made offline. The most important conclusion of this report is that only by disabling the online CPV veto can Radphi make effective use of 250nA of beam, that corresponds to $5\cdot 10^7$ tagged photons/s.