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

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 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, HELAC-Onia is also sufficiently numerical stable in dealing with P-wave quarkonia (e. g. hc, b, χc, 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. Program title: HELAC-Onia. Catalogue identifier: AEPRᵥ1₀ Program summary URL: http: //cpc. cs. qub. ac. uk/summaries/AEPRᵥ1₀. html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http: //cpc. cs. qub. ac. uk/licence/licence. html No. of lines in distributed program, including test data, etc.: 114595 No. of bytes in distributed program, including test data, etc.: 1555550 Distribution format: tar. gz Programming language: Fortran 90. Computer: Any. Operating system: Windows, Unix. Classification: 4. 4, 11. 1, 11. 2, 11. 5. Nature of problem: An important way to explore the law of the nature is to investigate the heavy quarkonium physics at B factories and hadron colliders. However, its production mechanism is still unclear, though NRQCD can explain its decay mechanism in a sufficiently satisfactory manner. The substantial K-factor in heavy quarkonium production processes also implies that the associated production of quarkonium and a relatively large number of particles may play a crucial role in unveiling its production mechanism. Solution method: A labor-saving and efficient way is to make the tedious amplitudes calculation automatic. Based on a recursive algorithm derived from the Dyson–Schwinger equations, the goal of automatic calculation of heavy quarkonium helicity amplitudes in NRQCD has been achieved. Inheriting from the virtues of the recursion relations with the lower computational cost compared to the traditional Feynman-diagram based method, the multi-leg processes (with or without multi-quarkonia up to P-wave states) at colliders are also accessible. Running time: It depends on the process that is to be calculated. However, typically, for all of the tested processes, they take from several minutes to tens of minutes.