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The Standard Model (SM) has been extensively verified and all of its prediction has been substantiated by the experiments. But still, some physical phenomena cannot be explained by it. For the more complete theory, a plethora of models has been predicted and all of them have their own merits. The concept that SM can be used as an effective theory here is widely held. We can add higher dimensional terms to its Lagrangian and trying to capture the footprint of the more complete UV theory, this is commonly known as the bottom-up approach. We have developed a tool named GrIP that builds higher dimensional operators of any mass dimension given information about the underlying symmetry. On the other hand, we can choose a complete UV theory, identify the heavy degrees of freedom, integrate them out and obtain operators of higher mass dimension, known as the top-down approach. Covariant Derivative Expansion (CDE) is one of the methodologies that integrate out heavy fields and generate the effective operator and their Wilson coefficient. The two most intriguing traits of CDE are, firstly, the method is manifestly gauge-invariant so the effective operators generated at the end are also gauge invariant. Secondly, its applicability is universal. Encapsulating these features there is a formula dubbed as the universal one-loop effective action (UOLEA) which has algorithmic essence to it. The Mathematica based package CoDEx based on the UOLEA is one of the tools that can integrate out heavy particles from the tree as well as one-loop diagrams and generate effective operators of mass dimension-6. Explaining any deviation from the SM prediction incorporating effective operators has been a common practice nowadays but it is difficult to trace back the origin of those effective operators and connect them to some UV complete scenario. We have developed a diagrammatic approach based on symmetry arguments to address this problem.
Andrea Pelloni, Tanjona Rabemananjara, Tommaso Giani