Hilbert series for leptonic flavor invariants in the minimal seesaw model

In this paper, we examine the leptonic flavor invariants in minimal seesaw model (MSM), which only two right-handed neutrino singlets are added into Standard Model order to accommodate tiny masses and explain cosmological matter-antimatter asymmetry via leptogenesis mechanism. For first time, calculate Hilbert series (HS) for MSM. With HS demonstrate that there totally 38 basic invariants, among 18 CP-odd others CP-even. Moreover, explicitly construct these any other MSM can be decomposed polynomials of them. Interestingly, find effective theory at low-energy scale expressed as rational functions those full high-energy scale. Practical applications phenomenological studies MSM, such sufficient necessary conditions CP conservation asymmetries leptogenesis, also briefly discussed.