Higher-order corrections for tW production at high-energy hadron colliders

Abstract

We discuss cross sections for tW production in proton-proton collisions at the LHC and at higher-energy colliders with energies of up to 100 TeV. We find that, remarkably, the soft-gluon corrections are numerically dominant even at very high collider energies. We present results with soft-gluon corrections at approximate NNLO and approximate N3LO matched to complete NLO results. These higher-order corrections are large and need to be included for better theoretical accuracy and smaller scale dependence. Total cross sections as well as top-quark and W-boson transverse-momentum and rapidity distributions are presented using various recent sets of parton distribution functions.

Top-quark production at approximate N3LO

“…The associated production of a top quark with a boson, i.e. production [5][6][7][8], has the second largest cross section among single-top processes at the LHC.…”

“…), where Γ (1) is the oneloop result. Soft-gluon corrections were calculated at aNNLO in [5] and at aN 3 LO in [6,8]. While it has long been known that soft-gluon corrections dominate the cross section at LHC energies, it has recently been shown in [8] that this is also true at much higher energies through 100 TeV.…”

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

“…The next-to-leading order (NLO) corrections have been obtained for stable tW final state [12][13][14][15] as well as the process including the decay of the top quark and the W boson [16]. The approximate next-to-next-to-next-toleading order total cross section has been derived by expanding the threshold resummation formula [17][18][19][20]. The all-order corrections induced by soft gluons are considered in [21].…”

Observation of tW production in the single-lepton channel in pp collisions at $$ \sqrt{s} $$ = 13 TeV

“…The leading-order (LO) Feynman diagrams for the tW process are shown in figure 1. The production cross section in proton-proton (pp) collisions at √ s = 13 TeV, assuming a top quark mass m t of 172.5 GeV, has been computed to be 71.7 ± 1.8 (scale) ± 3.4 (PDF) pb at approximate next-to-next-to-LO (NNLO) [17], and 79.5 +1.9 −1.8 (scale) +2.0 −1.4 (PDF) pb at approximate next-to-NNLO (aN 3 LO) [18]. The first uncertainties are due to scale variations in the calculation, and the second correspond to the choice of parton distribution functions (PDFs).…”