Consistency tests of AMPCALCULATOR and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial based approach

Abstract

Ampcalculator is a Mathematica based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one-loop (upto $O(p^4)$) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling $G_{27}$. Another illustrative set of amplitudes at tree level we provide is in the context of $τ$-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. Kaon-Compton amplitude has been checked and a minor error in published results has been pointed out. This exercise is a tutorial based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and used in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.