无中微子双贝塔衰变是当前核物理与粒子物理中的一个前沿热点问题，对人们理解中微子的自然属性、轻子数不守恒的弱相互作用过程和中微子的质量排序等问题有重要的物理意义。要解决这些重大物理问题，就需要理论计算的高精度的原子核矩阵元。目前这些原子核矩阵元存在非常大的不确定性。这些不确定性主要有两个来源：即来自原子核多体波函数与来自衰变算符本身。本项目将在以往工作的基础上进一步力图在国际上率先彻底解决来自衰变算符本身不确定性的问题。一方面，发展角动量投影方法以研究以往工作中所采用的closure近似的适用性。即不忽略中间核的贡献，直接计算母核基态到中间核各激发态、中间核各激发态到子核基态的过程。另一方面，在手征有效场理论的框架下研究手征两体流对相应衰变算符的修正。最终，力争在理论上给出高精度的原子核矩阵元，为相应的大型实验的设计提供理论指导。

Neutrinoless double-beta decay is one of the hot topics in modern nuclear and particle physics, which plays crucial roles in our understanding of the nature of neutrinos, lepton-number violation in weak-interaction process as well as the neutrino mass hierarchy. Theoretical nuclear matrix elements with very high precision are indispensable for such studies. However, predicted nuclear matrix elements by different nuclear methods have very large uncertainties, which have two kinds of sources, i.e., from the nuclear many-body wave functions and from the decay operator itself. This project aims to solve the latter source of uncertainty for the first time in the world based on our previous works. On one hand, by developing a angular-momentum-projection method, we will check the closure approximation used in many previous studies, i.e., we will not neglect the contribution of the intermedium nucleus but calculate matrix elements from the ground state of parent nucleus to all low- and high-lying states of the intermedium nucleus and then to the ground state of the daughter nucleus. On the other hand, we will study the effects of chiral two-body currents in the chiral effective field theory on the neutrinoless double beta decay operators. Finally, we are expected to provide nuclear matrix elements with high precision, which would be helpful for corresponding experimental design.