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We construct accidentally symmetric potentials in the framework of Two HiggsModel Effective Field Theory (2HDMEFT) including higher-order operators ofdimension 6 and dimension 8. Our construction is facilitated by an earlierdeveloped technique based on prime invariants. In addition, we employ analternative method that utilises the generators of each symmetry in thebi-adjoint representation and show how this method can be used to identifyoperators of any higher dimension. The accidentally symmetric 2HDMEFTpotentials exhibit two classes of symmetries: (i) continuous symmetries and(ii) discrete symmetries. The number of continuous symmetries in the 2HDMEFTremains the same as in the 2HDM. However, the introduction of higher-orderoperators allows additional higher-order discrete symmetries, such as $Z_n$ andCP$n$. We classify the full list of the 17 accidental symmetries in the 2HDMEFTincluding dimension-6 and dimension-8 operators, and derive the relations thatgovern the theoretical parameters of the corresponding effective potentials.

Accidental Symmetries in the 2HDMEFT