Initial-state parton shower kinematics for NLO event generators

We are developing NLO event generators for hadron collision interactions based on the limited leading-log (LLL) subtraction method. In this method, a boundary between non-radiative and radiative processes necessarily appears at the factorization scale ($\mu_{F}$). The radiation effects are simulated using a parton shower (PS) in non-radiative processes. It is therefore crucial in our method to apply a PS which well reproduces the radiation activities evaluated from the matrix-element (ME) calculations for radiative processes. The PS activity depends on the applied kinematics model. In this paper we introduce two models for our simple initial-state leading-log PS: a model similar to the "old" PYTHIA-PS and a $p_{T}$-prefixed model with a $p_{T}$ definition motivated by ME calculations. PS simulations employing these models are tested using $W$-boson production at LHC as an example. Both simulations show a smooth matching to the LLL-subtracted $W$ + 1 jet simulation in the $p_{T}$ distribution of $W$ bosons, and the summed $p_{T}$ spectra are stable against a variation of $\mu_{F}$, despite that the $p_{T}$-prefixed PS results in an apparently harder $p_{T}$ spectrum than the PS with the "old" PYTHIA-like kinematics. The "new" PYTHIA-PS gives a transverse activity similar to our $p_{T}$-prefixed PS. The choice of the model has to be postponed to further studies employing a comparison with experimental data