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 Bremsstrahlung process. During the E89-009 experiment, a data was taken with Pb sheet blocking 0 degree Brems electrons just at the entrance of the Enge spectrometer. Although it was tricky to place a thin material at 0 degrees, it was learned that blocking 0 degree Brems electrons helps improve signal to noise ratio considerably by this 0-degree blocking technique. The Tilt method, which offers us 2 order of magnitude more hypernuclear yield and a factor of 10 better signal to noise ratio compared to the E89-009 setup.

Electron and positron rates were estimated as given in Table 4 for the beam current of 30 $\mu$A and the target thickness of 100 mg/cm$^2$. It shows that 2.6 MHz of the electron background in the Enge spectrometer which placed with 2.25 degrees to the beam axis (electron beam, 100 mg/cm$^2$ carbon target). Kaon single rate for the HKS spectrometer was estimated to be 340 Hz as shown in Table 4. With a coincidence window of 2 ns, we have accidental coincidence rate as:

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

Assuming that the accidental coincidence events spread uniformly over the energy matrix (Enge 149 MeV $\times$ HKS 240 MeV ), the largest background per bin (100 keV) projected on the hypernuclear mass spectrum will 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 6.

表 6: 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	48.4	340
$^{28}$Si	30	20.7	288
$^{51}$V	30	11.4	228