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. h c,b , χ 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.
PROGRAM SUMMARYProgram title: HELAC-Onia.
Catalogue number:Program obtainable from: http://helac-phegas.web.cern.ch/helac-phegas
Licensing provisions: noneOperating system under which the program has been tested: Windows, Unix.
Programming language: FORTRAN 90Keywords: quarkonium helicity amplitudes, NRQCD, Dyson-Schwinger equations, off-shell currents.
Nature of physical 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 paly a crucial role in unveiling its production mechanism.
Method of solution:A labor-saved 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.