Anatomy of inclusive $t\overline{t}W$ production at hadron colliders

In LHC searches for new and rare phenomena the top-associated channel $pp \to t\overline{t}W^\pm +X$ is a challenging background that multilepton analyses must overcome. Motivated by sustained measurements of enhanced rates of same-sign and multi-lepton final states, we reexamine the importance of higher jet multiplicities in $pp \to t\overline{t}W^\pm +X$ that enter at $\mathcal{O}(\alpha_s^3\alpha)$ and $\mathcal{O}(\alpha_s^4\alpha)$, i.e., that contribute at NLO and NNLO in QCD in inclusive $t\overline{t}W^\pm$ production. Using fixed-order computations, we estimate that a mixture of real and virtual corrections at $\mathcal{O}(\alpha_s^4\alpha)$ in well-defined regions of phase space can arguably increase the total $t\overline{t}W^\pm$ rate at NLO by at least $10\%-14\%$. However, by using non-unitary NLO multi-jet matching, we estimate that these same corrections are at most $10\%-12\%$, and at the same time exhibit the enhanced jet multiplicities that are slightly favored by data. This seeming incongruity suggests a need for the full NNLO result. We comment on implications for the $t\overline{t}Z$ process.