The two cutoff phase space slicing method

TL;DR

The paper presents a detailed exposition of the two-cutoff phase-space slicing method for next-to-leading-order QCD corrections. It partitions the real-emission phase space into soft and hard regions using a soft cutoff δ_s and further splits the hard region into hard-collinear and hard non-collinear sectors with a collinear cutoff δ_c, enabling analytic treatment of soft and collinear singularities in dimensional regularization and numerical Monte Carlo integration for the non-singular region. The authors provide explicit derivations for soft and collinear contributions across various final-state configurations (including massive and massless quarks, tagged hadrons, and initial-state factorization), introduce fragmentation and tilde functions to absorb singularities, and validate the method with five representative processes, showing cutoff independence and agreement with known results. They also compare the approach to subtraction methods and discuss practical convergence improvements. The technique offers a straightforward, process-agnostic framework for applying NLO corrections to diverse hard-scattering processes with minimal process-dependent input, suitable for integration into Monte Carlo tools and IR-safe observables.

Abstract

The phase space slicing method of two cutoffs for next-to-leading-order Monte-Carlo style QCD corrections has been applied to many physics processes. The method is intuitive, simple to implement, and relies on a minimum of process dependent information. Although results for specific applications exist in the literature, there is not a full and detailed description of the method. Herein such a description is provided, along with illustrative examples; details, which have not previously been published, are included so that the method may be applied to additional hard scattering processes.

Figures (15)

• Figure 1: Leading order contribution to electron-positron annihilation via photon exchange.
• Figure 2: Real emission contribution to electron-positron annihilation.
• Figure 3: Loop and counterterm corrections to electron-positron annihilation via photon exchange.
• Figure 4: The vertex correction.
• Figure 5: The next-to-leading order contribution to the total cross section for producing a massive quark pair in electron-positron annihilation via single photon exchange. The two- and three-body contributions together with their sum are shown as a function of the soft cutoff $\delta_s$. The bottom enlargement shows the sum (open circles) relative to $\pm5\%$ (dotted lines) of the analytical result (solid line) given in Eq. (\ref{['eqn:anal_massive']}).