Dips at Colliders

We categorize new physics signatures that manifest themselves as a "dip" structure at colliders. One potential way to realize a dip is to require interactions to be zero when all particles are mass on-shell, but not if one or more are mass off-shell. For three particle interactions, we have found three interesting cases: one massive gauge boson with two identical scalars; one massless gauge boson with two different scalars; one massive gauge boson with two identical massless gauge bosons. For each case, we identify the relevant effective operators to explore its dip signature at the LHC. Unfortunately, the unstable particle with a vanishing mass-on-shell interaction has a complex mass which is coincident with the complex pole in its propagator. As a result, a contact-like amplitude without a dip is produced. We then point out two other interesting ways that generate a dip in the cross section. The first way has a dip signature due to a zero in the vertex form factor of the time-like momentum in the s-channel. In the second way, the dip plus bump signature appears because there is destructive interference among processes of exchanging different s-channel particles.