Operator Basis and RGEs of the SMEFT LNV Operators
Di Zhang (Technical University of Munich)

In this talk, a new physical basis and a Green’s basis for dimension-seven (dim-7) operators are proposed, which are suitable for the matching of ultraviolet models onto the Standard Model Effective Field Theory (SMEFT) and the deviation of renormalization group equations (RGEs) for the SMEFT dim-7 operators. The reduction relations to convert operators in the Green’s basis to those in the physical basis are achieved as well, where some redundant dim-6 operators in the Green’s basis are involved if the dim-5 operator exists. Working in these two bases, we work out the one-loop RGEs resulting from the mixing among different dimensional operators for the SMEFT dim-7 operators for the first time, and also revisit those from the mixing among dim-7 operators. These results complete the full one-loop RGEs of dim-7 operators and can be used for a consistent one-loop analysis of the SMEFT. On the other hand, we accomplish the full two-loop RGE of the dim-5 Weinberg operator and discuss its effects on the initially massless neutrino.