Algorithms for partial wave amplitudes in the covariant L−S scheme

With the continuous accumulation of data from hadron collision experiments, efficient partial wave analysis tools are indispensable for constructing a clear hadron spectrum. Currently, automated computations of scattering amplitudes primarily use the helicity scheme and covariant effective Lagrangian method. The automated calculations under the covariant <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>L</a:mi><a:mtext>−</a:mtext><a:mi>S</a:mi></a:mrow></a:math> scheme, which is one of the commonly used partial wave analysis schemes, have not been fully realized. In this work, we provide a general algorithm for computing partial wave amplitudes under the covariant <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>L</c:mi><c:mtext>−</c:mtext><c:mi>S</c:mi></c:mrow></c:math> scheme. This will lay the foundation for automated computation of partial wave amplitudes under the covariant <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>L</e:mi><e:mtext>−</e:mtext><e:mi>S</e:mi></e:mrow></e:math> scheme.