Speaker
Description
Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree level, but would become more obscure when loop effects are important. Using scalar theories as examples, we carefully exam the positivity bounds in a case where the leading contribution to a forward elastic amplitude arises at the one-loop level, and point out certain subtleties in terms of the implications of positivity bounds on the theory parameter space. In particular, the one-loop generated dimension-8 operator coefficients and their beta functions are generally not subject to positivity bounds as they might correspond to interference terms of the cross sections under the optical theorem, which could have either sign. A strict positivity bound can only be implied when all contributions at the same loop order are considered, including the ones from dim-4 and dim-6 operator coefficients, which have important effects at the one-loop level. We also consider similar examples in scalar QED, where gauge invariance puts strong constraints on the form of the UV completion and plays an important role in the interpretation of positivity bounds.
