大亞灣反應堆微中子實驗—利用慢信號中子被氫捕獲訊號測量微中子振盪混合角

Abstract

目前已知的微中子有三種類型：電子微中子、緲子微中子和濤子微中子。微中子在傳播的過程中會由一類轉變成另外兩類，此現象稱為微中子震盪 ( neutrino oscillation ) 現象。

微中子弱作用態(weak interaction state)是質量本征態 ( mass eigenstate ) 和矩陣 ( unitary matrix ) 的線性組合。這個矩陣帶有四個參數分別是三個混合角 ( mixing angle$-\ \theta_{12},\ \theta_{23},\ \theta_{13}$ ) 以及一個CP破壞相位角(CP-violating phase, $\delta_{CP}$)。微中子震盪實驗目標是測量這四個參數以及另外兩個與微中子質量相關的參數 ( mass-squared differences, $\Delta m^2_{32},\ \Delta m^2_{21}$ )。一般預測，混合角 $\theta_{13}$ 非常小，能夠精準的測量混合角 $\theta_{13}$ 在物理的研究上是非常重要的，它可幫助我們了解混合矩陣以及測量CP破壞相位角，進而解開現今物理未知的領域！

反應堆微中子實驗是利用反 $\beta$ 衰變 ( Inverse-beta decay, IBD ) 來量測微中子的事例。反 $\beta$ 衰變 ( Inverse-beta decay, IBD ) 的過程是一個反電子微中子 ( electron anti-neutrino ) 與探測器中的質子反應產生一個正電子 (positron, $e^+$) 與一個中子。正電子在極短時間內透過正負電子的煙滅效應 ( annihilation process ) 放出兩道伽瑪 ( $\gamma$ )，此信號是判別微中子的快信號 ( prompt signal )。另外一方面，中子可被氫或釓捕獲放出另一道伽瑪，能量分別為 2.2 MeV 或 8 MeV ，此信號則為慢信號( delayed signal )。

大亞灣反應堆微中子實驗是為了測量混合角 $\theta_{13}$ 而設計的，目標是測量精準度達到 0.01 或是 $\sin^2 2\theta_{13}$ 在百分之九十的信心水準之上。在二零一二年三月期間，大亞灣合作組發表了混合角 $\theta_{13}$ 的測量結果：$\sin^2 2\theta_{13}=0.092 \pm 0.016(\mathrm{stat.}) \pm 0.005(\mathrm{syst.})$，利用釓捕獲的訊號以及 55 天的數據分析而達到 5.2的標準偏差，因此可以排除 $\theta_{13}$ 為零的可能性，是一項重要的結果！同年六月，大亞灣再度更新測量結果 $\sin^2 2\theta_{13} = 0.089 \pm 0.010(stat.) \pm 0.005(syst.)$。

本篇論文，利用中子被氫捕獲的訊號進行混合角 $\theta_{13}$ 的測量。此方法有別於釓捕獲的分析，由於中子被氫捕獲時所產生的能量較低，因此容易受到許多低能量的輻射影響；其次，中子被氫捕獲所需的時間較長，因此也引入了不少雜訊。上述的種種因素，為此分析增加了不少挑戰！為解決這些因素，我們使用許多不同於釓捕獲分析的方法。目前，氫捕獲的分析結果是 $\sin^2 2\theta_{13}=0.083 \pm 0.018$，結合兩種分析方式，混合角則為 $\sin^2 2\theta_{13}=0.089 \pm 0.008$。

The neutrino oscillation arises because the neutrino weak interaction states are the linear combination of the mass eigenstates with a unitary matrix. The matrix contains four parameters, three mixing angles $(\theta_{12}, \theta_{23}, \theta_{13})$ and a CP-violating phase $\delta_{CP}$. Neutrino oscillation experiments are expected to determine these parameters and two mass-squared differences $\Delta m_{32}^2$ and $\Delta m_{21}^2$. $\theta_{13}$ was predicted to be very small. The precision measurement of $\theta_{13}$ is very important for the understanding of neutrino mixing matrix and the measurement of the CP-violating phase $\delta_{CP}$.

The reactor neutrino measurement is performed via the inverse-beta decay (IBD) process, $\overline{\nu_e} + p \rightarrow n + p^+$. The positron-electron annihilation emits gammas, which is the prompt signal in the IBD process. The delayed signal is from neutron capture on Gadolinium or Hydrogen and emits gamma with approximately 8 MeV or 2.2 MeV energies, respectively.

The Daya Bay Reactor Neutrino Experiment was designed to measure the mixing angle $\theta_{13}$ with a sensitivity at 0.01 or better in $\sin^2 2 \theta_{13}$ at the 90$\%$ confidence level. By using the 55-days antineutrino data, the Daya Bay Experiment first published the non-zero result of the mixing angle $\theta_{13}$, $\sin^2 2\theta_{13}=0.092 \pm 0.016(\mathrm{stat.}) \pm 0.005(\mathrm{syst.})$, with the significance of 5.2 standard deviations in March 2012 and updated the result in June 2012 with $\sin^2 2\theta_{13} = 0.089 \pm 0.010(stat.) \pm 0.005(syst.)$.

In this thesis, the $\theta_{13}$ mixing angle is measured by an independent method, which is based on the neutron capture on hydrogen signals. Several new techniques are developed to meet challenges from the higher background and different systematics, such as those due to the lower neutron capture energy (2.2 MeV), the longer capture time (200 $\mu s$), and the energy loss at the detector boundary.

With 217 days of antineutrino data, from December 24, 2011 to July 28, 2012, the rate-only analysis for the neutron capture on hydrogen gives $\sin^2 2\theta_{13}=0.083 \pm 0.018$. The combination with the gadolinium-capture result provides the double statistics to the $\theta_{13}$ measurement. The combined measurement gives $\sin^2 2\theta_{13}=0.089 \pm 0.008$.