Resummation of soft and Coulomb corrections for $t\bar{t}h$ production at the LHC

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 $t\bar{t}$ production process. We show that up to the next-to-leading power, the total cross section for $t\bar{t}h$ production admits a similar factorization formula in the threshold limit as that for $t\bar{t}$ 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.