$t\overline{t}b\overline{b}$ at the LHC: On the size of off-shell effects and prompt $b$-jet identification

We investigate full off-shell effects in $t\overline{t}b\overline{b}$ production in the dilepton channel at the LHC with the center-of-mass energy $\sqrt{s}=13\mathrm{TeV}$. Specifically, we compute next-to-leading-order (NLO) QCD corrections to the $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ process and provide a prescription for $b$-jet identification to distinguish prompt $b$ jets from $b$ jets originating from the decay of the top quarks. As an important irreducible background to $pp\to t\overline{t}H(H\to b\overline{b})$, $t\overline{t}$ production in association with two prompt $b$ jets is a primary source of uncertainty in the measurement of $t\overline{t}H(H\to b\overline{b})$. In quantifying full off-shell effects, we perform comparisons between the state-of-the-art full off-shell computation and the calculation in the narrow width approximation. The former includes all double-, single- and nonresonant Feynman diagrams, interferences as well as finite-width effects of the top quarks and $W$ gauge bosons. The latter restricts the unstable top quarks and $W$ gauge bosons to on-shell states and includes for the first time NLO QCD corrections to both production and decays. We observe that full off-shell effects are subdominant compared to the scale uncertainties for the integrated fiducial cross section and for the majority of differential observables in the phase-space regions that we investigated. However, for a number of observables related to beyond the Standard Model searches, full off-shell effects are significant. Furthermore, with our $b$-jet labeling prescription, the prompt $b$ jets and the $b$ jets from top-quark decays can be successfully disentangled.

Figure 1

Representative tree-level Feynman diagrams for the $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}$ process in the NWA. The blob represents the $g\to b\overline{b}$ splitting in top-quark decays. The latter can be emitted either from the top quark or the bottom quark.

Figure 2

Reconstructed invariant mass of the top quark at NLO in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The NLO NNPDF3.1 PDF set and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. We compare the full off-shell predictions, obtained using the charge-aware and charge-blind labeling in combination with different choices for the discriminator ($p_T$ and $\mathrm{\Delta }R$), to the ${\mathrm{NWA}}_{\mathrm{full}}$ prediction.

Figure 3

Differential cross section distributions as a function of $p_T(b_1)$, $p_T(b_4)$, $H_T^{\mathrm{had}}$, and $H_T^{\mathrm{vis}}$ at NLO in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The NLO NNPDF3.1 PDF set and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. In the upper panel, off-shell results are presented together with their scale uncertainties while only the central scale predictions are given for the ${\mathrm{NWA}}_{\mathrm{full}}$ and ${\mathrm{NWA}}_{\text{LOdec}}$ case. In the lower panel, the ratios to the full off-shell calculation are shown along with the scale uncertainties.

Figure 4

Differential cross section distributions as a function of $M_{\min }(e^{+}b)$ at LO (left) and NLO (right) in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The LO and NLO NNPDF3.1 PDF sets and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. In the upper panel, full off-shell and ${\mathrm{NWA}}_{\mathrm{full}}$ results are presented together with their scale uncertainties. The DR, SR, and NR contributions to the off-shell prediction are also displayed in the upper panel. In the lower panel, the ratios to the full off-shell calculation are given along with the scale uncertainties.

Figure 5

Differential cross section distributions as a function of $M_{T2}(t)$ and $M_{T2}(W)$ at LO (left) and NLO (right) in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The LO and NLO NNPDF3.1 PDF sets and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. In the upper panel, full off-shell and ${\mathrm{NWA}}_{\mathrm{full}}$ results are presented together with their scale uncertainties. The DR, SR, and NR contributions to the off-shell prediction are also displayed in the upper panel. In the lower panel, the ratios to the full off-shell calculation are given along with the scale uncertainties.

Figure 6

Differential cross section distributions as a function of observables describing the $b\overline{b}$ pair coming from top-quark decays and the prompt $b\overline{b}$ pair at NLO in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The NLO NNPDF3.1 PDF set and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. In the upper panel, the ${\mathrm{NWA}}_{\mathrm{full}}$ result is presented together with its scale uncertainty while only the central scale predictions are shown for the full off-shell predictions. The latter are obtained using the charge-aware and charge-blind labelings in combination with different choices for the discriminator ($p_T$ and $\mathrm{\Delta }R$). In the lower panel, the ratios to the ${\mathrm{NWA}}_{\mathrm{full}}$ calculation are given along with the scale uncertainty of the ${\mathrm{NWA}}_{\mathrm{full}}$ case.

Figure 7

Differential cross section distributions as a function of observables describing the $b\overline{b}$ pair coming from top-quark decays and the prompt $b\overline{b}$ pair at NLO in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The NLO NNPDF3.1 PDF set and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. In the upper panel, the ${\mathrm{NWA}}_{\mathrm{full}}$ result is presented together with its scale uncertainty while only the central scale predictions are shown for the full off-shell predictions. The latter are obtained using the charge-aware and charge-blind labelings in combination with different choices for the discriminator ($p_T$ and $\mathrm{\Delta }R$). In the lower panel, the ratios to the ${\mathrm{NWA}}_{\mathrm{full}}$ calculation are given along with the scale uncertainty of the ${\mathrm{NWA}}_{\mathrm{full}}$ case.

Figure 8

Differential cross section distributions as a function of observables describing the $b\overline{b}$ pair coming from top-quark decays and the prompt $b\overline{b}$ pair at NLO in QCD for $pp\to e^{+}{\nu }_e{\mu }^{-}{\overline{\nu }}_{\mu }b\overline{b}b\overline{b}+X$ at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The NLO NNPDF3.1 PDF set and the dynamical scale, ${\mu }_R={\mu }_F={\mu }_0=H_T/3$, are employed. The distributions for the two $b\overline{b}$ pairs are reported in the same plot. The ${\mathrm{NWA}}_{\mathrm{full}}$ results are presented together with the full off-shell predictions, which are obtained using the charge-aware and charge-blind labelings with the $p_T$ discriminator. The scale uncertainty bands for the charge-aware predictions are also displayed.