HELAC-Onia: an automatic matrix element generator for heavy quarkonium physics

By the virtues of the Dyson-Schwinger equations, we upgrade the published code \mtt{HELAC} to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub \mtt{HELAC-Onia}. We rewrote the original \mtt{HELAC} to make the new program be able to calculate helicity amplitudes of multi P-wave quarkonium states production at hadron colliders and electron-positron colliders by including new P-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, \mtt{HELAC-Onia} is also sufficiently numerical stable in dealing with P-wave quarkonia (e.g. $h_{c,b},\chi_{c,b}$) and P-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.