Application of a computer algebra systems to the calculation of the \(\pi\pi\)-scattering amplitude

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Abstract

The aim of this work is to develop a set of programs for calculation the scattering amplitudes of the elementary particles, as well as automating the calculation of amplitudes using the appropriate computer algebra systems (Mathematica, Form, Cadabra). The paper considers the process of pion-pion scattering in the framework of the effective Nambu-Iona-Lasinio model with two quark flavours. The Package-X for Mathematica is used to calculate the scattering amplitude (starting with the calculation of Feynman diagrams and ending with the calculation of Feynman integrals in the one-loop approximation). The loop integrals are calculated in general kinematics in Package-X using the Feynman parametrization technique. A simple check of the program is made: for the case with zero temperature, the scattering lengths \(a_0 = 0.147\) and \(a_2 = -0.0475\) are calculated and the total cross section is constructed. The results are compared with other models as well as with experimental data.

About the authors

Yuriy L. Kalinovsky

Joint Institute for Nuclear Research; Dubna State University

Author for correspondence.
Email: kalinov@jinr.ru

Doctor of Physical and Mathematical Sciences, senior researcher

6, Joliot-Curie St., Dubna, Moscow region, 141980, Russian Federation; 19, Universitetskaya St., Dubna, Moscow Region, 141982, Russian Federation

Alexandra V. Friesen

Joint Institute for Nuclear Research

Email: avfriesen@theor.jinr.ru

Candidate of Physical and Mathematical Sciences, researcher of Joint Institute for Nuclear Research

6, Joliot-Curie St., Dubna, Moscow region, 141980, Russian Federation

Elizaveta D. Rogozhina

Joint Institute for Nuclear Research; Dubna State University

Email: liorinoff@mail.ru

Student of Dubna State University; Senior laboratory assistant of Joint Institute for Nuclear Research

6, Joliot-Curie St., Dubna, Moscow region, 141980, Russian Federation; 19, Universitetskaya St., Dubna, Moscow Region, 141982, Russian Federation

Lyubov’ I. Golyatkina

Joint Institute for Nuclear Research; Dubna State University

Email: lubovgolyatkina@mail.ru

Student of Dubna State University; Senior laboratory assistant of Joint Institute for Nuclear Research

6, Joliot-Curie St., Dubna, Moscow region, 141980, Russian Federation; 19, Universitetskaya St., Dubna, Moscow Region, 141982, Russian Federation

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