Constraints on anomalous Higgs boson couplings to vector bosons and fermions from the production of Higgs bosons using the $\tau \tau$ final state

A study of anomalous couplings of the Higgs boson to vector bosons and fermions is presented. The data were recorded by the CMS experiment at a center-of-mass energy of pp collisions at the LHC of 13 TeV and correspond to an integrated luminosity of $138{\mathrm{fb}}^{-1}$. The study uses Higgs boson candidates produced mainly in gluon fusion or electroweak vector boson fusion at the LHC that subsequently decay to a pair of $\tau$ leptons. Matrix-element and machine-learning techniques were employed in a search for anomalous interactions. The results are combined with those from the four-lepton and two-photon decay channels to yield the most stringent constraints on anomalous Higgs boson couplings to date. The pure $CP$-odd scenario of the Higgs boson coupling to gluons is excluded at 2.4 standard deviations. The results are consistent with the standard model predictions.

Figure 1

Illustrations of $H$ production in VBF ($q{q}^{\prime }\to q{q}^{\prime }H$) (left) and $VH$ ($q{q}^{\prime }\to V^{*}\to VH\to q{q}^{\prime }H$) (right) in the rest frame of the $H$. The decay $H\to \tau \tau$ is shown without illustrating the further decay chain. The incoming partons and fermions in the $V$ decay are shown in brown and the intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [32, 34]. The illustration for H production via $ggH$ in association with two jets is identical to the VBF diagram, except with $V=g$.

Figure 2

The $m_{\tau \tau }$ (left) and $p_{\mathrm{T}}$ (right) distributions for $H$ candidate di-τ lepton pairs in the VBF category. All events selected in the $e\mu$, $e{\tau }_{\mathrm{h}}$, $\mu {\tau }_{\mathrm{h}}$, and ${\tau }_{\mathrm{h}}{\tau }_{\mathrm{h}}$ final states are included. The yields of the $H$ processes are scaled to match 50 times the SM predictions. Only statistical uncertainties are shown.

Figure 3

Examples of data and signal and background predictions for mela and neural network discriminants in the ${\tau }_{\mathrm{h}}{\tau }_{\mathrm{h}}$ and $\mu {\tau }_{\mathrm{h}}$ channels. Events passing the selections outlined in Sec. 6 and allocated to the VBF category are included. The yields of the $H$ processes are scaled to match 50 times the SM predictions. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalization of the background distribution. The expectation in the ratio panel is the sum of the estimated backgrounds and the SM $H$ signal. For the ${\mathcal{D}}_{0-}^{ggH}$ discriminant the distribution expected for a pseudoscalar $H$ hypothesis (labeled “PS” in the legend) is overlaid to be compared to the SM signal. Similarly, for the ${\mathcal{D}}_{CP}^{ggH}$ discriminant the distribution for a $CP$-violating scenario with the maximum-mixing between $CP$-even and $CP$-odd couplings (labeled “MM” in the legend) is shown.

Figure 4

The observed and predicted 2D distribution of (${\mathcal{D}}_{0-}^{ggH}$, ${\mathcal{D}}_{\mathrm{NN}}$) before the fit to data in the most sensitive VBF category region with $0.3<{\mathcal{D}}_{2\text{jet}}^{\mathrm{VBF}}<0.7$ in the ${\tau }_{\mathrm{h}}{\tau }_{\mathrm{h}}$ channel. The total $H$ signal, including VBF, $ggH$, and $VH$ processes, is shown stacked on top of the background in the solid red histogram. The $ggH$ signal for the $CP$-even ($CP$-odd) scenario is also shown overlaid by the red (blue) line. Only the statistical uncertainties are included in the uncertainty band.

Figure 5

Observed and predicted 2D distributions after the fit to data in the VBF high-$m_{\mathrm{jj}}$ boosted category in the ${\tau }_{\mathrm{h}}{\tau }_{\mathrm{h}}$ channel. The total $H$ signal, including VBF, $ggH$, and $VH$ processes, is shown stacked on top of the background in the solid red histogram. The $ggH$ signal for the $CP$-even ($CP$-odd) scenario is also shown overlaid by the red (blue) line. The uncertainty band accounts for all sources of systematic uncertainty in the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.

Figure 6

Observed (solid) and expected (dashed) likelihood scans of $f_{a3}^{ggH}$ obtained with the mela method (left) and the $\mathrm{\Delta }{\varphi }_{\mathrm{jj}}$ method used as a cross check (right).

Figure 7

Observed (solid) and expected (dashed) likelihood scans of ${\alpha }^{Hff}$ (in degrees) obtained with the mela method (left) and the $\mathrm{\Delta }{\varphi }_{\mathrm{jj}}$ method used as a cross check (right).

Figure 8

The observed and predicted 3D distribution of (${\mathcal{D}}_{0-}$, ${\mathcal{D}}_{\mathrm{NN}}$, ${\mathcal{D}}_{2\text{jet}}^{\mathrm{VBF}}$) before the fit to data in the ${\tau }_{\mathrm{h}}{\tau }_{\mathrm{h}}$ channel for the most sensitive VBF category. The total $H$ signal, including VBF, $ggH$, and $VH$ processes, is shown stacked on top of the background in the solid red histogram. The $\mathrm{VBF}+VH$ signal for the $CP$-even ($CP$-odd) scenario is also shown overlaid by the red (blue) line. Only the statistical uncertainties are included in the uncertainty band.

Figure 9

Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ (upper left), $f_{a2}$ (upper right), $f_{\mathrm{\Lambda }1}$ (lower left), and $f_{\mathrm{\Lambda }1}^{Z\gamma }$ (lower right) in Approach 1 ($a_i^{WW}=a_i^{ZZ}$).

Figure 10

Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ in Approach 2.

Figure 11

Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ (upper left), $f_{a2}$ (upper right), $f_{\mathrm{\Lambda }1}$ (lower left), and $f_{\mathrm{\Lambda }1}^{Z\gamma }$ (lower right) in Approach 1 ($a_i^{WW}=a_i^{ZZ}$) obtained with the combination of results using the $H\to \tau \tau$ and $H\to 4\ell$ [21] decay channels.

Figure 12

Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ in Approach 2 (defined in Sec. 2) obtained with the combination of results using the $H\to \tau \tau$ and $H\to 4\ell$ [21] decay channels.

Figure 13

Left: the observed (solid) and expected (dashed) likelihood scans of $f_{a3}^{ggH}$ obtained with the combination of results using the $H\to \tau \tau$ and $H\to 4\ell$ [21] decay channels. Right: The observed (solid) and expected (dashed) likelihood scans of $f_{CP}^{Htt}$ obtained with the combination of results using the $H\to \tau \tau$, $H\to 4\ell$ [21], and $H\to \gamma \gamma$ [20] decay channels.

Figure 14

Observed (solid) and expected (dashed) likelihood scans of $c_{gg}$ (left) and ${\tilde{c}}_{gg}$ (right) with ${\kappa }_t$ and ${\tilde{\kappa }}_t$ profiled (upper) and fixed to SM expectation (lower) using the $H\to \tau \tau$, $H\to 4\ell$ [21], and $H\to \gamma \gamma$ [20] decay channels.