Nonrelativistic QCD for coloured scalar fields

Abstract

We present an effective field theory suitable to describe a non-relativistic particle-antiparticle pair of heavy scalars based on the gauge group SU(3). Its formulation is analogous to that of "velocity NRQCD" (vNRQCD), a non-relativistic effective theory for heavy quark pairs. The matching conditions with scalar QCD and the renormalization group evolution of the effective theory are discussed. The non-relativistic framework proposed here suffices to compute scalar-antiscalar bound state energies at next-to-next-to-leading-logarithmic (NNLL) order and next-to-leading-logarithmic (NLL) threshold production of squarks in $e^+e^-$ and $\gamma\gamma$ collisions, in particular of the lighter scalar top quark at a future Linear Collider.