Non-factorizable corrections to W-pair production: methods and analytic results

TL;DR

This work develops and cross-validates two methods to compute non-factorizable QED corrections in W-pair production, within a double-pole, soft-photon framework. The Modified Standard Technique (MST) decomposes five-point functions into four-point building blocks and separates virtual from real contributions, while the Direct Momentum-Integration (DMI) method provides an independent momentum-space check with explicit infrared and collinear regulation. Both approaches yield complete, gauge-invariant corrections that primarily affect W mass line shapes rather than angular distributions, and they agree to high precision across leptonic and hadronic final states. The methods are generalizable to other unstable-particle pair production scenarios and clarify the interplay between Coulomb-type near-threshold effects and non-factorizable radiative corrections.

Abstract

In this paper we present two methods to evaluate non-factorizable corrections to pair-production of unstable particles. The methods are illustrated in detail for W-pair-mediated four-fermion production. The results are valid a few widths above threshold, but not at threshold. One method uses the decomposition of $n$-point scalar functions for virtual and real photons, and can therefore be generalized to more complicated final states than four fermions. The other technique is an elaboration on a method known from the literature and serves as a useful check. Applications to other processes than W-pair production are briefly mentioned.

Figures (6)

• Figure 1: Virtual diagrams contributing to the manifestly non-factorizable $W$-pair corrections in the purely leptonic case. The scalar functions corresponding to these diagrams are denoted by $D_{0123}$, $D_{0124}$, and $E_{01234}$.
• Figure 2: The gauge-restoring "Coulomb" contribution. The corresponding scalar function is denoted by $C_{012}$. In Sect. \ref{['sec:feynman/coulomb']} we shall briefly indicate the distinction between our "Coulomb" contribution, valid outside the threshold region, and the usual one, which is also valid inside that region.
• Figure 3: Integration contour in the lower half of the complex $k_0$-plane leading to Eq. (\ref{['contourint']}).
• Figure 4: The integration area (shaded region) in the $(\xi_1,\xi_2)$ Feynman-parameter space for the calculation of the particle-pole part $D_{0123}^{\hbox{\scriptsize part}}$ of the infrared-finite scalar four-point function $D_{0123}$. The thicker curves indicate the solutions of $p^2(\xi)=0$, with $\xi_{2}^{*}=1-M_{W}^{2}/s_{122^{\prime}}$.
• Figure 5: The area of integration in the $(u,t)$-plane for the calculation of the particle pole $D_{0134}^{\hbox{\scriptsize part}}$. The shaded region is the area of integration where $E(u,t)>0$. The doubly-shaded region is the area of integration where $E(u,t)>0$ and $p^{2}(u,t)>0$. The thicker curves indicate the solutions of $p^{2}(u,t)=0$, with $u^{*}=-\zeta^{\prime}M_{W}^{2}/m_{2}^{2}$.