Abstract
We study the resummation of the 0-jettiness resolution variable mathcal{T} 0 for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the mathcal{T} 0 → 0 limit. We then calculate the mathcal{O} (αs) corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL′, NNLL and approximate NNLL′ ( {mathrm{NNLL}}_{mathrm{a}}^{prime } ). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the t overline{t} +jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at {mathrm{NNLL}}_{mathrm{a}}^{prime } +NLO accuracy.
Highlights
There is an abundance of experimental measurements of the ttprocess at all LHC run energies and with a range of luminosities, for example refs. [1,2,3,4,5,6,7,8,9,10,11]
We study the resummation of the 0-jettiness resolution variable T0 for the top-quark pair production process in hadronic collisions
We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL, next-to-next-to-leading logarithmic (NNLL) and approximate NNLL (NNLLa)
Summary
We discuss the factorisation theorem for T0 and the calculation of the perturbative ingredients necessary to achieve NNLL and approximate NNLL accuracy. We report on the calculation of the relevant soft function at one-loop order, which is a necessary ingredient beginning at NLL accuracy. It is convenient to work with two additional variables: the velocity of the top-quarks in the ttrest frame βt and the scattering angle θ of the top-quark in the centre-of-mass frame of the event. These can be expressed via the invariants above as βt =
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