  Electroweakly Interacting Massive Particles (EWIMPs), in other words, new
massive particles that are charged under the electroweak interaction of the
Standard Model (SM), are often predicted in various new physics models. EWIMPs
are probed at hadron collider experiments not only by observing their direct
productions but also by measuring their quantum effects on Drell-Yan processes
for SM lepton pair productions. Such effects are known to be enhanced
especially when the di-lepton invariant mass of the final state is close to the
EWIMP threshold, namely twice the EWIMP mass. In such a mass region, however,
we have to carefully take non-perturbative effects into account, because the
EWIMPs become non-relativistic and the prediction may be significantly affected
by e.g., bound states of the EWIMPs caused by the electroweak interaction. We
study such non-perturbative effects using the non-relativistic effective field
theory of the EWIMPs, and found that those indeed affect the differential cross
section of the Drell-Yan processes significantly, though the effects are
smeared due to the finite energy resolution of the lepton measurement at the
Large Hadron Collider experiment.
