1204.2314 (Feng Feng)

$Apart: A Generalized Mathematica Apart Function    [PDF]

Feng Feng

We have generalized the \textsc{Mathematica} function Apart from 1 to $N$ dimension, the generalized function $Apart can decompose any linear dependent elements in $\mathcal{V}_{x}^*$ to the irreducible ones. The elements in $\mathcal{V}_{x}^*$ can be viewed as the corresponding propagators which involve loop momenta, the decomposition will be useful when one tries to perform the loop calculations using the packages like \textsc{Fire}, \textsc{Reduze}, etc. which have implemented the integration by parts (IBP) identities and Lorentz invariance (LI) identities. A description on how to use this package, combining with \textsc{Fire}, \textsc{FeynArts} and \textsc{FeynCalc} packages, to do the one-loop calculations in double quarkonium production in $e^+e^-$ colliders is given, and the full source code on a specific process: $e^+e^-\to J/\psi + \eta_c$ is also available.

View original: http://arxiv.org/abs/1204.2314