A remark on the critical value of the lightest neutrino mass in the construction of sufficient and necessary conditions for CP conservation with Majorana neutrinos

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This Letter serves as a comment referring to the paper Yu and Zhou (2020) [1]. In Yu and Zhou (2020) [1], Yu and Zhou made a sagacious observation that whether the simultaneous vanishing of a set of weak-basis invariants constitutes the sufficient and necessary conditions for CP conservation with Majorana neutrinos depends on the lightest neutrino mass m1. However, in this Letter, we show that there exist flaws in their analysis. For their conclusion regarding I1=I2=I3=0, we give four counter examples, two for 0<m1≤m⁎ and the other two for m1>m⁎. The so-called “critical value” m⁎≈0.0265eV for I1=I2=I3=0 is not so meaningful as declared in Yu and Zhou (2020) [1]. Other less severe flaws are also mentioned.