HELAC-Onia: An automatic matrix element generator for heavy quarkonium physics Original Research Article

By the virtues of the Dyson–Schwinger equations, we upgrade the published code HELAC to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub HELAC-Onia. We rewrote the original HELAC to make the new program be able to calculate helicity amplitudes of multi image-wave quarkonium states production at hadron colliders and electron–positron colliders by including new image-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, HELAC-Onia is also sufficiently numerical stable in dealing with image-wave quarkonia (e.g. image) and image-wave color-octet intermediate states. To the best of our knowledge, it is a first general-purpose automatic quarkonium matrix elements generator based on recursion relations on the market.