Towards the two-loop electroweak corrections to the Drell-Yan process: the infrared structure

TL;DR

This work addresses the challenge of computing two-loop electroweak corrections to the Drell-Yan lepton-pair production by focusing on a QED subset as a stringent test bed. It introduces OCEANN, a framework that achieves exact two-loop amplitudes with arbitrary numerical precision by combining diagram generation, master-integral reduction, and a series-expansion treatment of integrals, ensuring precise UV renormalisation and IR subtraction. The paper explicitly validates the IR structure through the process $u\bar{u}\to e^+e^-$, demonstrating controlled cancellation of IR poles and compatibility with existing literature, while detailing scheme-dependence and the practicalities of working with $\alpha_{\overline{MS}}(\mu_R)$ versus $\alpha(0)$. The results establish a robust, scalable path toward full two-loop EW corrections to Drell-Yan processes, pivotal for percent-level precision at current and future collider experiments and for probing potential beyond-Standard-Model physics.

Abstract

We discuss the lepton-pair production process in Quantum Electrodynamics. We present the ultraviolet-renormalised and infrared-subtracted finite contribution of the second-order virtual corrections to the inclusive lepton-pair production cross section $u\bar u\to e^+e^-$. The results are obtained within a new computational framework, OCEANN, developed in view of the evaluation of the exact two-loop electroweak virtual corrections to high-energy scattering processes. One of the key methodological features in this approach is the representation of the scattering amplitude with arbitrary precision at every stage of the calculation. The analysis in QED allows us to address the treatment of the infrared structure of the process and it can be easily extended to the complete electroweak Standard Model case. The perfect agreement with the literature, for this subset of corrections, provides a non trivial validation of the general framework.

Figures (3)

• Figure 1: Sample two-loop Feynman diagrams: 1-particle irreducible and factorisable one-loop $\times$one-loop contributions.
• Figure 2: Sample Feynman diagrams with the insertion of a closed fermionic loop along a photon line and the associated electric charge counterterm diagrams.
• Figure 3: We plot the contribution to $\langle\mathcal{M}|\mathcal{M}\rangle$ coming from one- and two-loop diagrams for different values of $\sqrt{s}$ and $t=-s/4$. In particular, in solid blue we present $(4\pi\alpha_{\overline{\text{MS}}}^3)\;2\text{Re}\langle {\cal M}^{(0,0)}|{\cal M}^{(0,1),fin}\rangle$, while in dashed orange $\alpha_{\overline{\text{MS}}}^4\; 2\text{Re}\langle {\cal M}^{(0,0)}|{\cal M}^{(0,2),fin}\rangle$, with $\alpha_{\overline{\text{MS}}}=1/128$. The two-loop contributions have been multiplied by a factor $10$ to improve the readability.