Abstract
In this paper, a combined resummation of soft and Coulomb corrections is performed for the associated production of the Higgs boson with a top quark pair at the LHC. We illustrate the similarities and critical differences between this process and the toverline{t} production process. We show that up to the next-to-leading power, the total cross section for toverline{t}h production admits a similar factorization formula in the threshold limit as that for tt production. This fact, however, is not expected to hold at higher powers. Based on the factorization formula, we perform the resummation at the improved next-to-leading logarithmic accuracy, and match to the next-to-leading order result. This allows us to give NLL′+NLO predictions for the total cross sections at the LHC. We find that the resummation effects enhance the NLO cross sections by about 6%, and significantly reduce the scale dependence of the theoretical predictions.
Highlights
(NLO) quantum chromodynamics (QCD) corrections were calculated in [13,14,15,16,17,18], while the NLO electroweak contributions were calculated in [19,20,21]
In the left plot of figure 8, we show the dependence of the NLL′+NLO cross section on μh, μs and μJ
A major difference between the two processes is that for tth production, the ttpair is recoiled by the Higgs boson and has a residue momentum of the potential scaling; while for ttproduction, the residue momentum of the top quark pair is of the ultrasoft scaling
Summary
The total cross section for inclusive tth production at hadron colliders can be expressed as [29]. In figure 1, we numerically compare the approximate Born partonic cross sections for tth production with the exact ones, i.e, σq(0q)(Eggx)a→cttth. While the above analyses show that the small-β region for tth production is not as important as that for ttproduction, it is still interesting to study the small-β behavior of the cross section at higher orders in QCD. We find that up to βcut 0.3, σc(0u)tApp provides a rather good approximation to the exact result This fact should be kept in mind when we later combine the small-β resummation and the fixed-order calculation. At higher orders in perturbation theory, exchanges of Coulomb gluons and soft gluons lead to threshold-enhanced terms such as 1/βn and lnn β For small βcut, these terms represent the dominant contributions to the constrained cross section σcut. The rest of the paper will be devoted to deriving a factorization formula for the partonic cross section in the threshold limit, and resumming these enhanced terms to all orders in perturbation theory
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