Higgs-Stoponium Mixing Near the Stop-Antistop Threshold

Supersymmetric extensions of the standard model contain additional heavy neutral Higgs bosons that are coupled to heavy scalar top quarks (stops). This system exhibits interesting field theoretic phenomena when the Higgs mass is close to the stop-antistop production threshold. Existing work in the literature has examined the digluon-to-diphoton cross section near threshold and has focused on enhancements in the cross section that might arise either from the perturbative contributions to the Higgs-to-digluon and Higgs-to-diphoton form factors or from mixing of the Higgs boson with stoponium states. Near threshold, enhancements in the relevant amplitudes that go as inverse powers of the stop-antistop relative velocity require resummations of perturbation theory and/or nonperturbative treatments. We present a complete formulation of threshold effects at leading order in the stop-antistop relative velocity in terms of nonrelativistic effective field theory. We give detailed numerical calculations for the case in which the stop-antistop Green's function is modeled with a Coulomb-Schr\"odinger Green's function. We find several general effects that do not appear in a purely perturbative treatment. Higgs-stop-antistop mixing effects displace physical masses from the threshold region, thereby rendering the perturbative threshold enhancements inoperative. In the case of large Higgs-stop-antistop couplings, the displacement of a physical state above threshold substantially increases its width, owing to its decay width to a stop-antistop pair, and greatly reduces its contribution to the cross section.