Background and signal/noise ratios

One of the major sources of background in the proposed setting that facilitates detection of very forward particles is electrons associated with bremstrahlung process. During the E89-009 experiment, a data was taken with lead sheets blocking 0 degree bremstrahlung electrons just at the entrance of the Enge spectrometer. It was learned that the blocking of the 0 degree bremstrahlung electrons improved signal to noise ratio considerably. The tilt method offers us greater hypernuclear yield by more than a order of magnitude and better signal to noise ratio by a factor of ten compared to the E89-009 setup.

Electron rates at the focal plane of the Enge spectrometer were estimated as given in Table 8 for the beam current of 30 $\mu$A and the target thickness of 100 mg/cm$^2$. When the "Tilt method" is employed, the bremstrahlung electron rate is estimated to be 2.6 MHz for the beam intensity of 30 $\mu$A. The rate is much less than that of E89-009 of a few times 100 MHz.

Kaon single rate of the HKS spectrometer was estimated to be 340 Hz for the carbon target as shown in Table 8. With a coincidence window of 2 ns, the accidental coincidence rate will be:

$$N_{ACC} = (2.6 \times 10^6 {\rm Hz}) \cdot (2 \times 10^{-9} {\rm sec}) \cdot (340 {\rm Hz}) \sim 1.8 {\rm /sec}.$$

Assuming that the accidental coincidence events are spread uniformly over the energy matrix (Enge 149 MeV $\times$ HKS 240 MeV), the accidental background rate per bin (100 keV) projected on the hypernuclear mass spectrum can be estimated to be 8 $\times$ 10$^{-4}$ /sec. A typical hypernuclear ($^{12}$C target) event rate will be 48.4 / (100 nb/sr) / h = 1.3 $\times 10^{-2}$ / (100 nb/Sr) / sec as shown in Table 3. The ratio of the signal to accidental background is expected better than an order of magnitude. It is noted that we can further suppress the accidental rate by sacrificing the hypernuclear yields with lower beam intensity.

表 3: Expected hypernuclear production rates in the (e,e'K$^+$) reaction

Target	$\begin{array}{c}{\rm beam}\\ {\rm Intensity}\\ {\rm (\mu A)}\end{array}$	$\begin{array}{c}{\rm Counts}\\ {\rm per}\\ {\rm 100nb/sr \cdot hour}\\ \end{array}$	$\begin{array}{c}{\rm Qfree}\\ {\rm K^+~in}\\ {\rm HKS(Hz)}\end{array}$
$^{12}$C	30	48	340
$^{28}$Si	30	21	288
$^{51}$V	30	11	228