[Paper Review] Demonstration of One Cutoff Phase Space Slicing Method: Next-to-Leading Order QCD Corrections to the $tW$ Associated Production in Hadron Collision

Qing-Hong Cao|ArXiv.org|Jan 10, 2008

High-Energy Particle Collisions Research16 citations

TL;DR

This paper presents a detailed next-to-leading order (NLO) QCD calculation for top-quark–W-boson associated production in hadron collisions using the one cutoff phase space slicing (OC-PSS) method. It provides the first complete set of virtual corrections not previously published, offering a critical third-party cross-check against two earlier independent calculations that reported discrepancies, thereby enhancing confidence in the theoretical prediction for this process at the LHC.

ABSTRACT

We present a detailed calculation of next-to-leading order QCD corrections to the $tW$ associated production using the one cutoff phase space slicing method. Such QCD corrections have been calculated independently by two groups already, however, a number of differences were found. It is desirable to have a third party calculation to make a crossing check. In this note, we present our complete results of the virtual corrections which are not shown in the literature so far. The numerical comparison will be presented in the forthcoming paper. As a demonstration of the one cutoff phase space slicing method, we also show in details how to organize the color ordered amplitudes and how to slice the soft and collinear phase space regions.

Motivation & Objective

• To provide a third-party calculation of NLO QCD corrections for top-quark–W-boson associated production in hadron collisions to resolve discrepancies between two earlier independent calculations.
• To present the full set of virtual corrections for the tW process, which had not been published in the literature before.
• To demonstrate the application of the one cutoff phase space slicing method in handling infrared divergences in a multi-parton final state.
• To enable precise numerical comparisons with existing results by providing a complete and publicly available framework for the virtual amplitudes.
• To support the development of flexible Monte Carlo event generators for high-precision LHC physics by detailing the organization of color-ordered amplitudes and phase space slicing procedures.

Proposed method

• The one cutoff phase space slicing (OC-PSS) method is employed to regulate both soft and collinear infrared divergences in the real emission corrections.
• The method separates the phase space into regions based on the energy and momentum configurations of unresolved partons, using a single cutoff parameter to define the boundary between resolved and unresolved regions.
• Color-ordered amplitudes are systematically organized to simplify the computation of helicity amplitudes and facilitate efficient phase space integration.
• Virtual corrections are calculated using dimensional regularization with the $ar{ ext{MS}}$ scheme, and ultraviolet divergences are isolated and renormalized.
• Infrared divergences from virtual and real corrections are systematically canceled by slicing the phase space and integrating analytically in the singular regions.
• The method allows for a fully differential cross section calculation by combining analytic results in singular regions with Monte Carlo integration in the regular regions.

Experimental results

Research questions

• RQ1 How can the one cutoff phase space slicing method be systematically applied to compute NLO QCD corrections for the tW associated production process?
• RQ2 What are the complete virtual corrections for the tW production amplitude, and how do they compare with previously published results?
• RQ3 Can the OC-PSS method accurately handle the interplay between soft and collinear singularities in a process with multiple final-state partons?
• RQ4 What are the quantitative differences between the current calculation and the two earlier independent NLO calculations of tW production?
• RQ5 How can the color-ordered amplitude structure be efficiently organized to enable automated and precise NLO computations?

Key findings

• The paper presents the first complete set of virtual corrections for the tW associated production process, which were not available in the literature prior to this work.
• The one cutoff phase space slicing method successfully isolates and cancels infrared divergences between virtual and real corrections, enabling a finite and infrared-safe cross section.
• The virtual amplitude contributions are explicitly decomposed into self-energy, vertex, triangle, box, and bubble diagrams, each with their respective UV and IR divergences expressed in terms of $\epsilon_{UV}$ and $\epsilon_{IR}$ poles.
• The divergent parts of the virtual amplitudes are analytically derived, with explicit expressions for $f_i^{V_j}$, $f_i^{B_k}$, and $f_i^{S_m}$ in terms of Mandelstam variables and poles in $\epsilon_{UV}$ and $\epsilon_{IR}$.
• The box and bubble diagrams contribute the dominant infrared divergences, with $B_3$ showing complex logarithmic and pole structures in $\epsilon_{IR}$, particularly involving $\ln(-t_1/m_t^2)$ and $\ln(s/m_t^2)$ terms.
• The final result provides a benchmark for future comparisons, with numerical validation expected in a forthcoming publication, thus enabling a critical cross-check of earlier conflicting results.