Tuesday, 1 November 2022 at 11:15
The success of the Standard Model (SM) and the lack of direct evidence of any beyond Standard Model (BSM) particles impels us to look for indirect shreds of evidence. The effective field theory framework is just the right tool for that. We can treat the SM as an effective theory by adding 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 ef- fective 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 applica- bility 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.