中国物理学会高能物理分会第十三届全国粒子物理学术会议（2021）

The finite modular symmetry provides us with an attractive and novel way to understand lepton flavor mixing, and has recently attracted a lot of attention. In a class of neutrino mass models with modular flavor symmetries, it has been observed that CP symmetry is preserved at the stabilizer of the modulus parameter $\tau = {\rm i}$, whereas significant CP violation emerges within the neighbourhood of this stabilizer. In this work, we first construct a viable model with the modular $A^\prime_5$ symmetry, and explore the phenomenological implications for lepton masses and flavor mixing. Then, we introduce explicit perturbations to the stabilizer at $\tau = {\rm i}$, and present both numerical and analytical results to understand why a small deviation from the stabilizer leads to large CP violation. As low-energy observables are very sensitive to the perturbations to model parameters, we further demonstrate that the renormalization-group running effects play an important role in confronting theoretical predictions at the high-energy scale with experimental measurements at the low-energy scale.