NNLO soft function for electroweak boson production at large transverse momentum

TL;DR

This work computes the NNLO soft function for electroweak boson production at large transverse momentum, the last missing piece required for NNLO threshold accuracy. The calculation handles three lightlike Wilson lines, exploiting rescaling invariance to show color structure is diagonal and most jet-line attachments vanish, and provides the bare and renormalized soft function up to two loops. The resulting two-loop non-log coefficient c_2^S confirms non-abelian exponentiation and enables N^3LL threshold resummation when combined with known hard and jet functions. The findings lay the groundwork for significantly improved predictions of p_T spectra for photons, W, Z, and Higgs production in hadron collisions.

Abstract

The soft function relevant for the production of an electroweak boson (photon, W, Z or H) with large transverse momentum at a hadron collider is computed at next-to-next-to-leading order. This is the first two-loop computation of a soft function involving three light-cone directions. With the result, the threshold resummation for these processes can now be performed at next-to-next-to-next-to-leading logarithmic accuracy.

Figures (3)

• Figure 1: The three Wilson-line configurations relevant for electroweak boson production.
• Figure 2: Feynman diagrams that contribute to the soft function up to NNLO. In addition there are mirror symmetrical graphs, which we take into account by multiplying each diagram $D_i$ with a symmetry factor $f_i$, where $f_1=f_2=f_3=f_5=2$, $f_4=1$ and $f_6=f_7=4$. Additional diagrams, in which gluons attach to the jet Wilson line, vanish, see text.
• Figure 3: Additional diagrams that turn out to be zero. Graphs (a) and (b) vanish because the associated integrals are scaleless, (c) because of its color structure.