Investigation of the Violation of the Lam-Tung Relation and the Difference in Angular Distribution in Quark-Antiquark and Quark-Gluon Production of Z Boson

We study the angular coefficients A0 and A2 in Z→ℓ+ℓ− production to test the Lam–Tung relation A0 −A2 =0 in different partonic channels. Using CMS Run 2 Monte Carlo samples, the angular coefficients are extracted through forward-folding fits incorporating detector response matrices. The analysis separates quark–antiquark (QQˉ ) and quark–gluon (QG) processes and introduces an improved fit of the prediction for QG (pT) that preserves the correct low- and high-pT limits while allowing shape flexibility, as well as a new parameterization for the GG (gluon-gluon) prediction . We investigate the selection of the QG events by requiring a single b-quark in the final state (bG -> bZ).Investigation of A0 and A2 for this sample can be used to test the prediction of the angular coefficients for gluon-initiated processes.