Top Quark Pair Production in Association with a Jet with Next-to-Leading-Order QCD Off-Shell Effects at the Large Hadron Collider

We present a complete description of top quark pair production in association with a jet in the dilepton channel. Our calculation is accurate to next-to-leading order (NLO) in QCD and includes all nonresonant diagrams, interferences, and off-shell effects of the top quark. Moreover, nonresonant and off-shell effects due to the finite $W$ gauge boson width are taken into account. This calculation constitutes the first fully realistic NLO computation for top quark pair production with a final state jet in hadronic collisions. Numerical results for differential distributions as well as total cross sections are presented for the Large Hadron Collider at 8 TeV. With our inclusive cuts, NLO predictions reduce the unphysical scale dependence by more than a factor of 3 and lower the total rate by about 13% compared to leading-order QCD predictions. In addition, the size of the top quark off-shell effects is estimated to be below 2%.

Figure 1

Representative Feynman diagrams, involving two (first diagram), one (second diagram), and no top quark resonances (third diagram), contributing to the leading-order $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}j$ process at $O({\alpha }_s^3{\alpha }^4)$. The last diagram with a single $W$ boson resonance contributes to the off-shell effects of the $W$ gauge boson.

Figure 2

Scale dependence of the LO and NLO cross sections for the $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}j+X$ process at the LHC for $\sqrt{s}=8\mathrm{TeV}$. The scale is set to a common value ${\mu }_R={\mu }_F=\xi {\mu }_0$, where ${\mu }_0=m_t$.

Figure 3

Transverse momentum of the hardest light jet, $\mathrm{\Delta }{R}_{e^{+}{\mu }^{-}}$, and the minimal $M_{b{e}^{+}}$ for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}j+X$ at the LHC, with $\sqrt{s}=8\text{TeV}$. The uncertainty bands depict the scale variation. The lower panel displays the differential $\mathcal{K}$ factor and its uncertainty band.