QCD and QED Corrections to Light-by-Light Scattering

TL;DR

This work addresses light-by-light scattering ($\gamma\gamma\to\gamma\gamma$) by computing the two-loop QCD and QED corrections to fermion-loop contributions in the ultrarelativistic regime where all kinematic invariants satisfy $s,t,u \\gg m_f^2$. The authors employ a unitarity-cut–based approach to obtain massless two-loop double-box amplitudes, reduce to master integrals, and express results as helicity amplitudes $M^{(2)}_{\lambda_1\lambda_2\lambda_3\lambda_4}$, with notable simplifications such as $M^{(2)}_{--++}=-3/2$ and other amplitudes involving logarithms and polylogarithms. Numerically, QCD and QED corrections are found to be small in the relevant energy ranges (e.g., $8$–$100$ GeV for quark-box contributions) and often cancel in the unpolarized cross section, reinforcing the reliability of leading-order predictions and providing precise inputs for backgrounds in di-photon processes. The results also illuminate the structure of these amplitudes via unitarity and Ward identities, and set the stage for future extensions to massive internal lines and electroweak corrections to the $W$-box contribution, with potential relevance to high-energy tests of the Standard Model and new physics scenarios.

Abstract

We present the QCD and QED corrections to the fermion-loop contributions to light-by-light scattering, gamma gamma to gamma gamma, in the ultrarelativistic limit where the kinematic invariants are much larger than the masses of the charged fermions.