Hard matching for boosted tops at two loops

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 a two-loop order, namely the matching coefficient at the scale μ ≃ mt. Our extraction also yields the final ingredients needed to carry out logarithmic re-summation at next-to-next-to-leading logarithmic order (or N[superscript 3]LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at Oα[subscript s][superscript 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 μ ≃ m[subscript t].