We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed technique based on prime invariants. In addition, we employ an alternative method that utilises the generators of each symmetry in the bi-adjoint representation and show how this method can be used to identify operators of any higher dimension. The accidentally symmetric 2HDMEFT potentials exhibit two classes of symmetries: (i) continuous symmetries and (ii) discrete symmetries. The number of continuous symmetries in the 2HDMEFT remains the same as in the 2HDM. However, the introduction of higher-order operators allows additional higher-order discrete symmetries, such as $Z_n$ and CPn. We classify the full list of the 17 accidental symmetries in the 2HDMEFT including dimension-6 and dimension-8 operators, and derive the relations that govern the theoretical parameters of the corresponding effective potentials.

我们在两个希格斯模型有效场论（2HDMEFT）的框架中构造了意外对称的电势，其中包括维度6和维度8的高阶算符。我们的构建得到了基于素不变性的较早开发技术的推动。此外，我们采用一种替代方法，该方法利用双伴随表示中每个对称的生成器，并说明如何使用此方法来识别任何更高维的算子。意外对称的2HDMEFT势表现出两类对称：（i）连续对称和（ii）离散对称。2HDMEFT中连续对称的数量与2HDM中相同。但是，引入高阶算子可以实现其他高阶离散对称，例如${ž}_{ñ}$和CP n。我们对2HDMEFT中的17个意外对称的完整列表进行分类，包括6维和8维算符，并得出控制相应有效电位理论参数的关系。