A study on energy resolution of CANDLES detector

In a neutrinoless double-beta decay ($0\nu\beta\beta$) experiment, energy resolution is important to distinguish between $0\nu\beta\beta$ and background 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. At the Q-value of $^{48}$Ca, the current energy resolution (2.6%) exceeds the ideal statistical fluctuation of the number of photoelectrons (1.6%). Because of CaF$_2$'s long decay constant of 1000 ns, a signal integration within 4000 ns is used to calculate the energy. The baseline fluctuation ($\sigma_{baseline}$) is accumulated in the signal integration, thus degrading the energy resolution. This paper studies $\sigma_{baseline}$ in the CANDLES detector, which severely degrades the resolution by 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 $\sigma_{baseline}$ and minimizes photoelectron loss. We 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 is estimated to be improved from 2.6% to 2.2%, and the detector sensitivity for the $0\nu\beta\beta$ half-life of $^{48}$Ca can be improved by 1.09 times.