Maximizing the azimuthal-angle correlation in the decay of vector boson pairs

Spin correlation observables of particles produced at colliders generally depend on the coordinate basis. While spin correlations and their associated basis dependence have been studied in top-quark pair production, the basis dependence of spin correlations of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>W</a:mi><a:mo>±</a:mo></a:msup></a:math> pairs has not been studied. In this work, we focus on the azimuthal-angle correlation in the decay of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>W</c:mi><c:mo>±</c:mo></c:msup></c:math> pairs, which encodes spin information in the direction transverse to the rotational axis. We quantitatively describe the basis dependence of the relative azimuthal angle. We further present the optimal coordinate direction to define the azimuthal angle between the decay products of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>W</e:mi><e:mo>±</e:mo></e:msup></e:math> bosons to achieve the maximal spin correlation based on symmetry considerations. The results can be used to optimize the measurement of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>C</g:mi><g:mi>P</g:mi></g:math>-even and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math>-odd interactions, and have applications to quantum information observables in the vector boson pair system.