Effective field theory for type II seesaw model --symmetric phase v.s. broken phase--

Effective field theory is an effective approach to parameterizing effects of high energy scale physics in low energy measurements. The two popular frameworks for physics beyond the standard model are the so-called standard model effective field theory (SMEFT) and the Higgs effective field theory (HEFT). While the description by the SMEFT deteriorates when the scale of new physics is not so high or it participates in spontaneous electroweak symmetry breaking, the HEFT makes use of nonlinear realization of spontaneously broken symmetry in which there are practically no restrictions on the Higgs field as a singlet. In this work we present another framework, called broken phase effective field theory (bEFT), in which we deal directly with mass eigenstate fields after spontaneous symmetry breaking without employing nonlinear realization. We take the type-II seesaw model as an example to demonstrate our approach. By matching the model to both the bEFT and the SMEFT at tree level, we compare the results for two processes, the Higgs pair production via vector boson fusion which appears as a subprocess at the LHC and the Higgs-strahlung process at a future electron-positron collider. We find that the bEFT reproduces the type-II seesaw model more accurately than the SMEFT in the regions where the bare mass of the Higgs triplet becomes close to the electroweak scale. Therefore, the bEFT serves as a useful framework that can compensate for the shortcomings in both the SMEFT and the HEFT when dealing with UV models that involve Higgs mixing or new particles with a mass close to the electroweak scale.