Multiple Higgs boson production from W_L W_L to distinguish SMEFT from HEFT in the presence of new physics.

If there is new electroweak physics, it may well be out of reach of the accelerator effort. In that case Effective Field Theory becomes the logic tool to parameterize the results of new physics searches, and SMEFT has become the standard. However, the most general theory with the known particle content is HEFT, and whether this is needed or SMEFT suffices should be investigated in future experimental efforts. While the San Diego and other groups have established geometric criteria to distinguish SMEFT from HEFT, which can be useful for theorists examining specific beyond-SM completions, more phenomenological understanding is needed.

We discuss various aspects of (multi-) Higgs production from longitudinal electroweak gauge bosons W_L W_L → n h in the TeV region as necessary information to make progress about which is the EFT of choice. It appears that the LHC will not be enough to decide in view of the demanding final state with several Higgs bosons.