Contribution of the Direct Interaction Vertex to the Z → l⁺l^–γ Process

The contribution of the direct interaction vertex to the \(Z \to {{l}^{ + }}{{l}^{ - }}\gamma \) process is extracted on basis of a measurement of differential distributions over the invariant mass \({{l}^{ \pm }}\gamma \) at the ATLAS detector. Models of CP-violating effective interaction and CP-preserving effective interaction are considered. The direct vertex can be seen as an effective description of loop corrections within the Standard Model. The contribution of the direct vertex in the CP-preserving model lead to \({\text{Br}}\left( {Z \to {{e}^{ + }}{{e}^{ - }}\gamma } \right) = \left( {3.81 \pm 0.53} \right) \times {{10}^{{ - 5}}},\) \({\text{Br}}\left( {Z \to {{\mu }^{ + }}{{\mu }^{ - }}\gamma } \right) = \left( {3.99 \pm 0.47} \right) \times {{10}^{{ - 5}}}.\) Adding an effective model to predictions of the modern PowHeg+PHOTOS and Sherpa 2.2 generators significantly improves the agreement with experimental results. The significance of the additive was 5 and 4.7 standard deviations for PowHeg+PHOTOS and Sherpa 2.2, respectively. The PowHeg+PHOTOS generator with the effective interaction additive describes the experimental data slightly better than other generators with the same type of effective additive.