Observable phi-eta-star at LHC and second-order QED matrix element in Z/gamma to l+ l- decays

In a recent publication by ATLAS collaboration a new observable, the so-called phi-star angle, was used for precise measurement of transverse Z momentum. One of the dominant systematic errors for this measurement originates from the theoretical control of QED final-state bremsstrahlung. At present, it is estimated at the 0.3% level for the shape of the phi-star distribution. In this paper we discuss the possible effects of the second-order QED matrix element for that quantity. For that purpose, results from simulations based on the Yennie--Frautchi--Suura (YFS) exponentiation and featuring the second-order matrix elements are used and compared with the case when the matrix element is restricted to the first order. From this study we conclude that in order to reach the precision below 0.3% for the phi-star distribution at the LHC, inclusion of the second-order QED matrix element in a respective Monte Carlo event generator is necessary.