Hard Matching for Boosted Tops at Two Loops

TL;DR

This paper derives the two-loop matching coefficient for top quark cross sections in the boosted regime, enabling precise theoretical predictions and resummation at N$^3$LL order, accounting for rapidity logarithms from virtual top loops.

Contribution

It provides the missing two-loop matching coefficient for top cross sections in the boosted regime, facilitating advanced resummation and precision calculations.

Findings

Extracted the two-loop matching coefficient at the top mass scale.

Identified rapidity logarithms due to virtual top loops and treated them with rapidity RG.

Enabled N$^3$LL resummation for top cross sections in the boosted regime.

Abstract

Cross sections for top quarks provide very interesting physics opportunities, being both sensitive to new physics and also perturbatively tractable due to the large top quark mass. Rigorous factorization theorems for top cross sections can be derived in several kinematic scenarios, including the boosted regime in the peak region that we consider here. In the context of the corresponding factorization theorem for $e^+e^-$ collisions we extract the last missing ingredient that is needed to evaluate the cross section differential in the jet-mass at two-loop order, namely the matching coefficient at the scale $\mu\simeq m_t$. Our extraction also yields the final ingredients needed to carry out logarithmic resummation at next-to-next-to-leading logarithmic order (or N$^3$LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at $\mathcal{O}(\alpha_s^2)$ due to virtual top quark loops, which we treat using rapidity renormalization group (RG) evolution. Interestingly, this rapidity RG evolution appears in the matching coefficient between two effective theories around the heavy quark mass scale $\mu\simeq m_t$.