Two-loop master integrals for the single top production associated with $W$ boson

Abstract

The tW associated production has the second-largest cross section among three single top production channels. A complete study of NNLO QCD corrections to tW production is still missing in literature. We present the calculation of part of the requisite two-loop master integrals for the process b + g → t + W at NNLO QCD. It turns out that the 80 master integrals in two families, involving up to three massive internal lines, can be expressed by Goncharov polylogarithms. The canonical differential equations that these integrals obey contain at most three square roots. By separating the canonical master integrals into groups according to their dependences on roots, we succeed in achieving optimization of final expressions, which are validated by independent numerical checks.

Evaluating master integrals in non-factorizable corrections to $t$-channel single-top production at NNLO QCD

“…As for the tW mode, the complete corrections at NNLO QCD are still unavailable. Only partial results have been obtained [28][29][30][31][32] and the complete two-loop QCD amplitudes for tW production were studied very recently [33].…”

One-loop squared amplitudes for hadronic tW production at next-to-next-to-leading order in QCD

“…However, the complete next-to-next-to-leading order (NNLO) QCD corrections have not been obtained yet, though a small fraction of the two-loop master integrals have recently been computed analytically [25,26]. To obtain these corrections, the double-real, real-virtual and double-virtual corrections should be calculated independently and collected together in the end to provide an infrared (IR) finite prediction.…”