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【摘要】
The behavior of fundamental particles, such as quarks and neutrinos, is key to understanding the Standard Model of particle physics. Their mixing patterns are described by two mathematical objects: the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quarks and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix for neutrinos. In this talk, I will explain how recent advances in theory and experiments are helping to improve the precision of these matrices, providing deeper insights into the nature of particles and forces. For quarks, I will discuss how precise measurements of the neutron lifetime allow us to determine the largest CKM matrix element, Vud. I will present a modern theoretical framework that accounts for subtle effects, like radiative corrections, in low-energy processes with nucleons. These corrections are essential for achieving high precision in extracting Vud. For neutrinos, future experiments such as Hyper-Kamiokande in Japan and LBNF/DUNE in the USA aim to answer fundamental questions, such as whether neutrinos preserve charge-parity (CP) violation and the ordering of their masses. These experiments depend on accurate predictions of how neutrinos interact with matter. I will review recent theoretical progress on radiative corrections, the structure of hadrons, and neutrino-nucleus interactions, and discuss their role in determining the elements of the PMNS matrix.