[Paper Review] Screened-Coulomb ansatz for the non-factorizable radiative corrections to the off-shell W^+ W^- production

A.P. Chapovsky, V. A. Khoze|arXiv (Cornell University)|Feb 15, 1999

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes a screened-Coulomb ansatz that effectively reproduces non-factorizable QED radiative corrections to off-shell W⁺W⁻ production in e⁺e⁻ collisions. By introducing a damping factor into the width-dependent part of the first-order Coulomb correction, the ansatz captures screening effects from non-Coulomb mechanisms, achieving excellent agreement with full one-loop calculations without explicit loop integrations.

ABSTRACT

We demonstrate that the results of the complete first order calculation of the non-factorizable QED corrections to the single-inclusive cross-sections for $e^+e^- o W^+W^- o 4$ fermions could be very well reproduced by a simple physically motivated ansatz. The latter allows to take into account effectively the screening role of the non-Coulomb radiative mechanisms by introducing a dampening factor in front of the width-dependent part of the known first-order Coulomb correction, the so-called screened-Coulomb ansatz.

Motivation & Objective

• To develop a simplified yet accurate method for computing non-factorizable radiative corrections in e⁺e⁻ → W⁺W⁻ → 4 fermions processes.
• To address the challenge of computing intricate one-loop QED corrections involving off-shell W bosons and complex phase space structures.
• To capture the screening effects of non-Coulomb radiation mechanisms that are difficult to include in standard factorized approaches.
• To provide a practical, phenomenologically viable approximation that avoids full one-loop calculations while preserving accuracy.
• To validate the ansatz against exact first-order QED calculations for the single-inclusive cross-sections.

Proposed method

• Introduces a screened-Coulomb ansatz by modifying the known first-order Coulomb correction with a damping factor.
• The damping factor effectively accounts for non-Coulomb radiative mechanisms that suppress long-range Coulomb-like interactions.
• The ansatz retains the width-dependent structure of the standard Coulomb correction but suppresses it at large momentum transfers via the screening factor.
• The screening factor is derived from physical considerations of radiation recoil and soft-photon emission patterns.
• The method is tested by comparing its predictions against the complete one-loop calculation of the single-inclusive cross-sections.
• The approach avoids explicit loop integrations by embedding non-factorizable effects into a phenomenological correction term.

Experimental results

Research questions

• RQ1 Can a simple ansatz accurately reproduce the non-factorizable QED corrections to off-shell W⁺W⁻ production in e⁺e⁻ collisions?
• RQ2 How do non-Coulomb radiation mechanisms affect the structure of the one-loop corrections in this process?
• RQ3 To what extent can screening effects from virtual and real photon emissions be captured by a modified Coulomb correction?
• RQ4 Does the screened-Coulomb ansatz maintain accuracy across the full phase space of off-shell W bosons?
• RQ5 Can the ansatz replace full one-loop calculations in phenomenological studies without significant loss of precision?

Key findings

• The screened-Coulomb ansatz reproduces the results of the complete one-loop calculation of the non-factorizable QED corrections with high accuracy.
• The damping factor successfully models the screening of Coulomb-like interactions due to non-Coulomb radiation mechanisms.
• The agreement between the ansatz and full calculation is excellent across the relevant kinematic region of off-shell W⁺W⁻ production.
• The method provides a computationally efficient alternative to full one-loop calculations for phenomenological applications.
• The ansatz remains valid even when the W bosons are far off-shell, indicating robustness in the full phase space.
• The approach demonstrates that non-factorizable corrections can be effectively captured by a physically motivated modification of the standard Coulomb term.