Background estimation

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, data was taken with a lead sheet blocking 0 degree bremsstrahlung electrons just at the entrance of the Enge spectrometer. It was learned that blocking 0 degree bremsstrahlung electrons improves considerably signal to noise ratio. The ``Tilt method'' offers greater hypernuclear yield by more than an order of magnitude and better signal to noise ratio by a factor of 10 compared to the E89-009 setup.

Electron rates at the focal plane of the Enge spectrometer were estimated as given in table 10 for a beam current of 30 $\mu$A and a target thickness of 100 mg/cm$^2$. When the ``Tilt method'' is employed, the bremsstrahlung electron rate is estimated to be less than 1 MHz for a beam intensity of 30 $\mu$A. This rate is much less than a few times 100 MHz observed during E89-009.

We assume the integrated singles rate of the electron arm as 1 MHz for the estimation of signal to accidental background ratio. The kaon singles rate of the HKS spectrometer was estimated to be 380 Hz for the carbon target as shown in table 10. With a coincidence window of 2 ns in the off-line analysis, the accidental coincidence rate in the final spectrum will be:

$$N_{ACC} = (1 \times 10^6 {\rm Hz}) \cdot (2 \times 10^{-9} {\rm sec}) \cdot (380 {\rm Hz}) \sim 0.8 {\rm /sec}.$$

Assuming that the accidental coincidence events are spread uniformly over the energy matrix (Enge 190 MeV $\times$ HKS 270 MeV), the accidental background rate per bin (100 keV) projected on the hypernuclear mass spectrum can be estimated to be:

$$\frac{0.8\mbox{/sec}}{190\mbox{MeV}\times300\mbox{MeV/$c$}\fr... ...}{dP_K})^2} \times0.1\mbox{MeV} = 4 \times 10^{-4}\mbox{/sec},$$

where $dM_{Hy}/dP_K = 0.899$ is the kaon momentum dependence of the hypernuclear energy; 186 MeV and 200 MeV/$c$ are coming from the $^{12}_\Lambda$B(g.s.) position in energy matrix (see figure 7).

A typical hypernuclear ($^{12}$C target) event rate will be 33 / (100 nb/sr) / h = 9.2 $\times 10^{-3}$ / (100 nb/sr) / sec as shown in table 5. The cross section of $^{12}_\Lambda$B(g.s.) doublet was measured as 140 nb/sr in E89-009. Therefore signal to noise ratio can be estimated assuming the ground state peaks are distributed in 3 bins (300 keV):

$$S/N \sim (9.2 \times 10^{-3}\mbox{/s} \times \frac{140}{100}) / ( 4 \times 10^{-4}\mbox{/s/bin} \times 3\mbox{bin}) = 10.7.$$

The ratio of the signal to accidental background is expected almost an order of magnitude improved compared with E89-009 ($S/N = 1.4$). It is noted that we can further suppress the accidental rate by sacrificing the hypernuclear yields with lower beam intensity.

表 5: 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	33	380
$^{28}$Si	30	14	320
$^{51}$V	30	8	290