A study on energy resolution of CANDLES detector

In a neutrino-less double-beta-decay ($0\nu\beta\beta$) experiment, an irremovable two-neutrino double-beta-decay ($2\nu\beta\beta$) background surrounds the Q-value of the double beta decay isotope. The energy resolution must be improved to differentiate between $0\nu\beta\beta$ and $2\nu\beta\beta$ events. CAlcium fluoride for studies of Neutrino and Dark matters by Low Energy Spectrometer (CANDLES) discerns the $0\nu\beta\beta$ of $^{48}$Ca using a CaF$_2$ scintillator as the detector and source. Photomultiplier tubes (PMTs) collect scintillation photons. Ideally, the energy resolution should equal the statistical fluctuation of the number of photoelectrons. At the Q-value of $^{48}$Ca, the current energy resolution (2.6%) exceeds this fluctuation (1.6%). Because of CaF$_2$'s long decay constant of 1000 ns, a signal integration in 4000 ns is used to calculate the energy. The baseline fluctuation ($\sigma_{\rm baseline}$) is accumulated in the signal integration, degrading the energy resolution. Therefore, this paper studies $\sigma_{\rm baseline}$ in the CANDLES detector, which has a severe effect (1%) at the Q-value of $^{48}$Ca. To avoid $\sigma_{\rm baseline}$, photon counting can be used to obtain the number of photoelectrons in each PMT; however, a significant photoelectron signal overlapping probability in each PMT causes missing photoelectrons in counting and reduces the energy resolution. "Partial photon counting" reduces $\sigma_{\rm baseline}$ and minimizes photoelectron loss. We thus obtain improved energy resolutions of 4.5--4.0% at 1460.8 keV ($\gamma$-ray of $^{40}$K), and 3.3--2.9% at 2614.5 keV ($\gamma$-ray of $^{208}$Tl). The energy resolution at the Q-value shows an estimated improvement of 2.2%, with improved detector sensitivity by factor 1.09 for the $0\nu\beta\beta$ half-life of $^{48}$Ca.