Probing the $CP$ nature of the Higgs coupling in $t\overline{t}h$ events at the LHC

The determination of the $CP$ nature of the Higgs coupling to top quarks is addressed in this paper, using $t\overline{t}h$ events produced in $\sqrt{s}=13\mathrm{TeV}$ proton-proton collisions at the LHC. Dileptonic final states are employed, with two oppositely charged leptons and four jets, corresponding to the decays $t\to b{W}^{+}\to b{\ell }^{+}{\nu }_{\ell }$, $\overline{t}\to \overline{b}{W}^{-}\to \overline{b}{\ell }^{-}{\overline{\nu }}_{\ell }$, and $h\to b\overline{b}$. Pure scalar ($h=H$), pure pseudoscalar ($h=A$), and $CP$-violating Higgs boson signal events, generated with MadGraph5_aMC@NLO, are fully reconstructed through a kinematic fit. We furthermore generate samples that have both a $CP$-even and a $CP$-odd component in the $t\overline{t}h$ coupling in order to probe the ratio of the two components. New angular distributions of the decay products, as well as $CP$ angular asymmetries, are explored in order to separate the scalar from the pseudoscalar components of the Higgs boson and reduce the contribution from the dominant irreducible background, $t\overline{t}b\overline{b}$. Significant differences between the angular distributions and asymmetries are observed, even after the full kinematic fit reconstruction of the events, allowing to define the best observables for a global fit of the Higgs couplings parameters.

Figure 1

Distributions of TMVA input variables for right (filled blue, labeled “Signal”) and wrong combinations (red shaded, labeled “Background”) of jets and leptons from the same parent decaying particle: $\mathrm{\Delta }R({\ell }^{+},b_t)$ (top left) and $\mathrm{\Delta }R(b_H,{\overline{b}}_H)$ (bottom left); $\mathrm{\Delta }\theta ({\ell }^{+},b_t)$ (top middle) and $\mathrm{\Delta }\theta (b_H,{\overline{b}}_H)$ (bottom middle); $\mathrm{\Delta }\mathrm{\Phi }({\ell }^{+},b_t)$ (top right) and $\mathrm{\Delta }\mathrm{\Phi }(b_H,{\overline{b}}_H)$ (bottom right). See text for details.

Figure 2

Mass distributions (left) for right (filled blue, signal) and wrong (red shaded, background) combinations of jets and leptons from the same parent decaying particle: (upper-left) the $m({\ell }^{+},b_t)$ and (lower-left) $m(b_H,{\overline{b}}_H)$; (middle top) BDT and (middle bottom) BDTG TMVA methods response for signal and background; (right-top) TMVA input variable correlations for signal and (right-bottom) background.

Figure 3

Two-dimensional distributions of $p_T$ in $t\overline{t}H$ events. The horizontal axes represent variables recorded at $\mathrm{NLO}+\mathrm{Shower}$, and the vertical axes represent the corresponding variables recorded at reconstruction level without truth-match. Upper-left: Distribution for $W^{+}$. A similar distribution is obtained for $W^{-}$, but is not shown here. Upper-right: Distribution for $t$. A similar distribution is obtained for $\overline{t}$, but is not shown here. Lower-left: Distribution for $t\overline{t}$. Lower-right: Distribution for $H$.

Figure 4

Two-dimensional distribution of the neutrino $p_T$ in $t\overline{t}H$ events. Left: The $\mathrm{NLO}+\mathrm{Shower}$ $p_T$ ($x$ axis) against the reconstructed $p_T$ without truth-match ($y$ axis) is shown. Right: Distribution of the reconstructed Higgs boson mass without truth-matched jets in $t\overline{t}H$ events.

Figure 5

$\mathrm{NLO}+\mathrm{Shower}$ versus $\mathrm{LO}+\mathrm{Shower}$ behavior of the distribution of $x_Y=\cos ({\theta }_H^{\overline{t}H})\cos ({\theta }_{{\ell }^{-}}^H)$ at the parton level with shower effects, without any selection cuts or reconstruction, for the SM signal $t\overline{t}H$ (left) and for the $t\overline{t}A$ signal (middle), each one against the main background $t\overline{t}b\overline{b}$. Notice that, for the middle plots, the sequential boost prescription was employed for the lepton. The differences between the $\mathrm{LO}+\mathrm{Shower}$ and $\mathrm{NLO}+\mathrm{Shower}$ angular distributions are shown on top. Asymmetries around $x_Y=0$ are visible in the two binned distributions (bottom). The $t\overline{t}H$, $t\overline{t}A$, and $t\overline{t}b\overline{b}$ angular distributions at NLO are compared (top right), and the corresponding two binned distributions show the asymmetries (bottom right).

Figure 6

Angle between the $t$ quark and Higgs boson ($x$ axis) at $\mathrm{NLO}+\mathrm{Shower}$ effects plotted against the angle between the $\overline{t}$ quark and Higgs boson ($y$ axis), in the $t\overline{t}H$ center-of-mass system. The SM Higgs boson ($H$) distribution (left) and the pure pseudoscalar Higgs boson ($A$) distribution (right) are shown.

Figure 7

Two-dimensional distribution at $\mathrm{NLO}+\mathrm{Shower}$ of the angle between the top quark, in the $t\overline{t}h$ center-of-mass frame, and the $t\overline{t}h$ direction in the lab frame ($y$ axis) plotted against the angle between the Higgs direction, in the $\overline{t}h$ rest frame, and the direction of several decay products (all boosted to the Higgs center of mass): (left) $b$ quark from $h$, (middle) ${\ell }^{+}$ from the top quark, and (right) ${\ell }^{-}$ from $\overline{t}$. The top (bottom) distributions correspond to $t\overline{t}H$ ($t\overline{t}A$), without any cuts.

Figure 8

The same as Fig. 7, after all selection cuts and full kinematic reconstruction.

Figure 9

Normalized $\beta \mathrm{\Delta }{\theta }^{\ell h}(\ell +,\ell -)$ distributions at $\mathrm{NLO}+\mathrm{Shower}$ without cuts (top left), with cuts (top middle), and after cuts and full kinematic reconstruction (top right). The $\mathrm{NLO}+\mathrm{Shower}$ $b_4$ distribution is also shown at the parton level without cuts (bottom left), with cuts (bottom middle), and after cuts and full kinematic reconstruction (bottom right). The dashed line represents the $t\overline{t}h$ SM model signal ($h=H$ and $CP=+1$) and the dashed-dotted line corresponds to the pure pseudoscalar distribution $t\overline{t}h$ ($h=A$ and $CP=-1$). The shadowed region corresponds to the $\mathrm{NLO}+\mathrm{Shower}$ $t\overline{t}b\overline{b}$ dominant background.

Figure 10

Distributions of $x_Y=\sin ({\theta }_h^{t\overline{t}h})\sin ({\theta }_{{\overline{b}}_{\overline{t}}}^{\overline{t}})$ (top) and $x_Y=\sin ({\theta }_h^{t\overline{t}h})\cos ({\theta }_{b_h}^{\overline{t}})$ (bottom). The distributions at $\mathrm{NLO}+\mathrm{Shower}$ (left), after cuts (middle), and after cuts and full kinematic reconstruction (right) are shown. The dashed line represents the $t\overline{t}h$ SM model signal ($h=H$ and $CP=+1$) and the dashed-dotted line corresponds to the pure pseudoscalar distribution $t\overline{t}h$ ($h=A$ and $CP=-1$). The shadowed region corresponds to the $\mathrm{NLO}+\mathrm{Shower}$ $t\overline{t}b\overline{b}$ dominant background. The laboratory four-momentum of $b$ quarks is boosted sequentially to the Higgs center-of-mass system (see text for details).

Figure 11

$\mathrm{NLO}+\mathrm{Shower}$ angular distributions at the parton level before selection cuts (left) and after all cuts and full kinematic reconstruction (right) of (top) $x_Y=\sin ({\theta }_t^{t\overline{t}H})\sin ({\theta }_{W+}^H)$, (middle) $x_Y=\sin ({\theta }_{\overline{t}}^{t\overline{t}H})\sin ({\theta }_{b_H}^H)$, and (bottom) $x_Y=\sin ({\theta }_H^{t\overline{t}H})\sin ({\theta }_{\overline{t}}^{t\overline{t}})$. The dashed line represents the $t\overline{t}h$ SM model signal ($h=H$ and $CP=+1$), the dashed-dotted line corresponds to the pure pseudoscalar distribution $t\overline{t}h$ ($h=A$ and $CP=-1$), and the shadowed region corresponds to the $\mathrm{NLO}+\mathrm{Shower}$ $t\overline{t}b\overline{b}$ dominant background (see text for details).

Figure 12

Distributions of $x_Y=\sin ({\theta }_H^{t\overline{t}H})\sin ({\theta }_{\overline{b_{\overline{t}}}}^{\overline{t}})$ (top), $x_Y=\sin ({\theta }_H^{t\overline{t}H})\cos ({\theta }_{b_H}^{\overline{t}})$ (middle), and $x_Y=m_{b\overline{b}}$ (bottom) after final selection at 13 TeV for $100{\mathrm{fb}}^{-1}$. The distributions on the left (right) correspond to events with at least three (four) jets from the hadronization of $b$ quarks.

Figure 13

Normalized distributions of the BDTG output discriminant variable (first row), the invariant mass of the two $b$-tagged jets with minimum $\mathrm{\Delta }R$ ($m_{bb}^{\min \mathrm{\Delta }R}$) (second row), the $\sin ({\theta }_h^{t\overline{t}h})\sin ({\theta }_{\overline{t}}^{t\overline{t}})$ (third row) and the $b_4$ variable (fourth row), after final selection at 13 TeV. The distributions on the left (right) correspond to pure scalar (pseudoscalar) Higgs bosons.

Figure 14

Expected limits at 95% C.L. in the background-only scenario, as a function of $\cos (\alpha )$. Limits on $\sigma \times \mathrm{BR}(h\to b\overline{b})$ (top left) and $\mu$ (top right) obtained with the BDTG output discriminant for integrated luminosities of 100, 300, and $3000{\mathrm{fb}}^{-1}$ are shown. The lines correspond to the median, while the narrower (wider) bands correspond to the $1\sigma$ ($2\sigma$) intervals. Limits on $\sigma \times \mathrm{BR}(h\to b\overline{b})$ at $300{\mathrm{fb}}^{-1}$ are also shown, using the individual observables $\sin ({\theta }_h^{t\overline{t}h})\sin ({\theta }_{\overline{t}}^{t\overline{t}})$ (center left) and ${\beta }_{b\overline{b}}\mathrm{\Delta }{\theta }^{\ell h}({\ell }^{+},{\ell }^{-})$ (center right), $m_{bb}^{\min \mathrm{\Delta }R}$ (bottom left), and $b_4$ (bottom right).

Figure 15

Comparison between limits on $\sigma \times \mathrm{BR}(h\to b\overline{b})$ at $300{\mathrm{fb}}^{-1}$ obtained from each of the individual distributions used in the BDTG [${\beta }_{b\overline{b}}\mathrm{\Delta }{\theta }^{\ell h}({\ell }^{+},{\ell }^{-})$, $b_4$, $m_{b\overline{b}}$] and angular distributions (top), and remaining distributions used as input for the BDTG (bottom). The ratios with respect to the limit obtained from the BDTG distribution are also represented.