[Paper Review] Charge asymmetries of lepton transverse momenta in Drell-Yan processes at the LHC

M. W. Krasny, W. Płaczek|arXiv (Cornell University)|Sep 21, 2012

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper identifies a critical flaw in the interface between the WINHAC matrix element generator and PYTHIA 6.4 parton shower for Drell-Yan processes at the LHC: incorrect assignment of effective quark/antiquark transverse momenta in the LO matrix element leads to severely biased lepton transverse momentum ($p_T^l$) charge asymmetries. The authors propose two matching schemes—swapping quark/antiquark transverse momenta or skipping lepton momentum rotations in the $W$-boson rest frame—that restore agreement with NLO QCD predictions (e.g., MC@NLO), significantly improving the accuracy of $p_T^l$ asymmetry distributions for precision SM measurements.

ABSTRACT

Charged lepton transverse momenta in the Drell-Yan processes play an important role at the LHC in precision measurements of the Standard Model parameters, such as the W-boson mass and width, their charge asymmetries and sin^2(theta_W). Therefore, their distributions should be described as accurate as possible by the Monte Carlo event generators. In this paper we discuss the problem of matching the hard-process kinematics of the Monte Carlo generator WINHAC with the parton-shower kinematics of the PYTHIA 6.4 generator while interfacing these two programs. We show that improper assignment of the quark and antiquark effective momenta in the LO matrix element computations may affect considerably the predicted lepton transverse momenta and even completely reverse their charge asymmetries at the LHC. We propose two matching schemes in which the NLO QCD distributions of the leptonic kinematical variables can be well reproduced by the LO WINHAC generator.

Motivation & Objective

• To address inaccuracies in lepton transverse momentum ($p_T^l$) charge asymmetries arising from improper kinematic matching between the WINHAC matrix element generator and PYTHIA 6.4 parton shower in Drell-Yan processes at the LHC.
• To resolve the issue of biased $p_T^l$ distributions caused by incorrect assignment of effective quark and antiquark transverse momenta in the LO matrix element computation.
• To develop and implement matching schemes that reproduce NLO QCD predictions for $p_T^l$ and charge asymmetry distributions, ensuring reliable input for precision Standard Model measurements.
• To improve the simulation of $W$-boson polarization effects in Drell-Yan processes by correctly preserving spin correlations across the matrix element and parton shower stages.

Proposed method

• The authors analyze the kinematic mismatch between WINHAC's LO matrix element and PYTHIA 6.4's parton shower, focusing on the assignment of effective quark and antiquark transverse momenta.
• They propose a matching scheme that swaps the transverse momenta of the effective on-shell quarks and antiquarks in the PYTHIA interface to correct the $p_T^l$ asymmetry bias.
• They also propose a second scheme that skips the rotation of outgoing lepton momenta in the $W$-boson rest frame, preserving the initial-state parton shower helicity configuration.
• These schemes are implemented in a new version of the WINHAC generator to ensure consistency with NLO QCD predictions from MC@NLO and MCFM.
• The performance of the new schemes is validated by comparing $p_T^l$ and pseudorapidity ($\eta_l$) charge asymmetry distributions against MC@NLO results in both full and restricted phase spaces.

Experimental results

Research questions

• RQ1 Why do standard PYTHIA 6.4 parton shower interfaces with matrix element generators produce incorrect lepton transverse momentum charge asymmetries in Drell-Yan processes at the LHC?
• RQ2 How does the incorrect assignment of effective quark and antiquark transverse momenta in the LO matrix element affect the $p_T^l$ distributions and their charge asymmetries?
• RQ3 Can simple modifications to the event generation interface—such as swapping quark/antiquark transverse momenta or skipping lepton momentum rotations—restore agreement with NLO QCD predictions?
• RQ4 What role does the $W$-boson polarization, as encoded in the spin density matrix, play in the observed bias, and how can it be correctly preserved across the matrix element and parton shower stages?

Key findings

• The original interface between WINHAC and PYTHIA 6.4, which uses PYTHIA's default effective quark transverse momenta, produces $p_T^l$ charge asymmetries that are strongly biased and even reversed compared to NLO QCD predictions.
• Swapping the transverse momenta of the effective quark and antiquark in the event-by-event interface leads to excellent agreement with MC@NLO results for both $p_T^l$ and $\eta_l$ charge asymmetries in full and restricted phase spaces.
• Skipping the rotation of lepton momenta in the $W$-boson rest frame also improves agreement with MC@NLO, though slightly less effectively than the momentum swap, and corresponds to preserving the initial-state parton shower helicity.
• The new matching schemes implemented in WINHAC successfully reproduce the NLO QCD distributions of leptonic kinematical variables, correcting a significant source of systematic error in $W$-boson mass and $\sin^2\theta_W$ measurements.
• The results demonstrate that proper matching of matrix element and parton shower kinematics, especially for spin-1 intermediate particles, is essential for accurate simulation of polarization effects and precision measurements at the LHC.