Precise simulation of the initial-state QCD activity associated with $Z$-boson production in hadron collisions

The $\phi_{\eta}^{*}$ distribution of the $Z/\gamma^{*} \rightarrow \ell^{+}\ell^{-}$ production in hadron collisions is simulated using a leading-order event generator, GR@PPA. The initial-state parton shower, which simulates the multiple QCD-radiation effects in the initial state, plays the dominant role in this simulation. The simulation in the default setting agrees with the high-statistics measurement by ATLAS at LHC with the precision at the level of 5%. The observed systematic deviation, which can be attributed to the effects of ignored higher-order contributions, can be reduced by adjusting the arbitrary energy scales in the simulation. The agreement at the level of 1% can be achieved over a very wide range without introducing any modification in the implemented naive leading-logarithmic parton shower.