@annav I am aware of papers about effective operators such the one you linked: "Learning to pinpoint effective operators at the LHC: a study of the tt¯bb¯ signature", my question was what actually are effective operators?

Okay thanks - I have looked into the resources provided. I have my own form of the PMNS matrix and then the form given in the wikipedia page, but how do I actually extract $sin(\theta_{23})$ for example? All the terms in the PMNS matrix are a product of other variables - is it possible to isolate the $sin(\theta_{23})$ term?

Well the context is sterile neutrinos scattering with electrons in direct dark matter detection, which I believe is Lbar N --> Lbar N?

Thanks for the answer - so how does renormalisation affect this? I thought renormalisation would quash the divergence but if it's important for vacuum polarisation effects then is this still the case?