Prospects of constraining the Higgs boson’s $CP$ nature in the tau decay channel at the LHC

We investigate how precisely the $CP$ nature of the 125 GeV Higgs boson $h$, parametrized by a scalar-pseudoscalar Higgs mixing angle ${\varphi }_{\tau }$, can be determined in $h\to {\tau }^{-}{\tau }^{+}$ decay with subsequent $\tau$-lepton decays to charged prongs at the Large Hadron Collider (LHC). We combine two methods in order to define an observable ${\phi }_{CP}^{*}$ which is sensitive to ${\varphi }_{\tau }$: We use the $\rho$-decay plane method for ${\tau }^{\mp }\to {\rho }^{\mp }$ and the impact parameter method for all other major $\tau$ decays. For estimating the precision with which ${\varphi }_{\tau }$ can be measured at the LHC (13 TeV) we take into account the ${\tau }^{-}{\tau }^{+}$ background from Drell-Yan production and perform a Monte Carlo simulation of measurement uncertainties on the ${\phi }_{CP}^{*}$ signal and background distributions. We obtain that the mixing angle ${\varphi }_{\tau }$ can be determined with an uncertainty of $\mathrm{\Delta }{\varphi }_{\tau }\simeq 15°$ (9°) at the LHC with an integrated luminosity of $150{\mathrm{fb}}^{-1}$ ($500{\mathrm{fb}}^{-1}$), and with $\mathrm{\Delta }{\varphi }_{\tau }\approx 4°$ with $3{\mathrm{ab}}^{-1}$. Future measurements of ${\varphi }_{\tau }$ yield direct information on whether or not there is an extended Higgs-boson sector with Higgs-sector $CP$ violation. We analyze this in the context of a number of two-Higgs-doublet extensions of the Standard Model, namely the so-called aligned model and conventional two-Higgs-doublet extensions with tree-level neutral flavor conservation.

Figure 1

(Left panel) Definition of 3-vectors and the angle ${\phi }_{CP}^{*}$ in the $a^{-}{a^{\prime }}^{+}$ ZMF (here ${\pi }^{-}{\pi }^{+}$ ZMF) for the impact parameter method. (Right panel) Normalized ${\phi }_{CP}^{*}$ distribution for $pp\to h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\pi }^{+}+2{\nu }_{\tau }$ at the LHC (13 TeV) at NLO QCD with $q_T^{\pi \pm }\ge 20\mathrm{GeV}$ and $|{\eta }_{\pi \pm }|<2.5$, and $m_h=125\mathrm{GeV}$. The blue dashed, the black dotted, and the black long-dashed line shows the distribution for a $CP$-even Higgs boson (${\varphi }_{\tau }=0$), a $CP$-odd Higgs boson (${\varphi }_{\tau }=\pm \pi /2$), and a $CP$ mixture $({\varphi }_{\tau }=-\pi /4)$, respectively. The solid black flat line is the distribution due to the $Z^{*}/{\gamma }^{*}\to \tau \tau$ background.

Figure 2

Illustration of ${\phi }_{CP}^{*}$ in the $\rho$-decay plane method as defined in (14) for $pp\to h^0\to {\tau }^{-}{\tau }^{+}\to {\rho }^{-}{\rho }^{+}+2\nu$.

Figure 3

Normalized ${\phi }_{CP}^{*}$ distribution obtained with the $\rho$-decay plane method (14) for $pp\to h\to {\tau }^{-}{\tau }^{+}\to {\rho }^{-}{\rho }^{+}+2{\nu }_{\tau }$ at the LHC (13 TeV). The left and right plots are for events with $y^{\tau }>0$ and $y^{\tau }<0$, as defined in (15). The cuts $p_T^{\rho \pm }\ge 20\mathrm{GeV}$ and $|{\eta }_{\rho \pm }|$, $|{\eta }_{\pi \pm }|\le 2.5$ were applied. The blue dashed, black dotted, and black long-dashed lines show the distribution for a $CP$-even Higgs boson (${\varphi }_{\tau }=0$), a $CP$-odd Higgs boson (${\varphi }_{\tau }=\pm \pi /2$), and a $CP$ mixture (${\varphi }_{\tau }=-\pi /4$), respectively. The flat lines are the distributions due to Drell-Yan production.

Figure 4

${\phi }_{CP}^{*}$ distribution defined in Eq. (14) for $pp\to h\to {\tau }^{-}{\tau }^{+}\to {\rho }^{-}{\rho }^{+}+2\nu$ at LHC (13 TeV) for a $CP$-even Higgs boson using the $\rho$-decay plane method. The black dotted and black dashed line (solid red line and dot-dashed red line) show the distribution if the cut on $y=y_1{y}_2$ is performed in the corresponding $\tau$ rest frames (in the laboratory frame). For the distributions displayed by the solid red line and black dotted line an additional cut of $p_{T\rho }\ge 20\mathrm{GeV}$ on the hadronic $\tau$-jet was applied.

Figure 5

(Left panel) Definition of the angle ${\phi }_{CP}^{*}$ in the case of the combined method. (Right panel) Normalized ${\phi }_{CP}^{*}$ distributions, Eq. (19), for $pp\to h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\rho }^{+}+2{\nu }_{\tau }$ events with $y_{+}^{\tau }>0$ at the LHC (13 TeV). The cuts $q_T^{{\pi }^{-}}$, $p_T^{{\rho }^{+}}\ge 20\mathrm{GeV}$ and $|{\eta }_{{\rho }^{+}}|$, $|{\eta }_{{\pi }^{\pm }}|\le 2.5$ were applied. The blue dashed, black dotted, and black long-dashed lines show the distribution for a $CP$-even Higgs boson (${\varphi }_{\tau }=0$), a $CP$-odd Higgs boson (${\varphi }_{\tau }=\pm \pi /2$) and a $CP$ mixture $({\varphi }_{\tau }=-\pi /4)$, respectively. The flat line is the distribution due to Drell-Yan production. The distributions for events with $y_{+}^{\tau }<0$ are shifted by ${\phi }_{CP}^{*}\to {\phi }_{CP}^{*}+\pi$.

Figure 6

Normalized ${\phi }_{CP}^{*}$ distributions for a $CP$-even Higgs boson at the LHC (13 TeV). The cuts $p_T^{{\rho }^{\pm }}\ge 20\mathrm{GeV}$, $|{\eta }_{{\rho }^{\pm }}|$, $|{\eta }_{{\pi }^{\pm }}|$, $|{\eta }_{l^{-}}|\le 2.5$ were applied. The dashed blue line (left panel) is the distribution for $h\to {\rho }^{-}{\rho }^{+}$, as in Fig. 3, left panel. The solid red and dashed red lines (left and right panels) correspond to $h\to {\pi }^{-}{\rho }^{+}$ with the additional cut $q_T^{{\pi }^{-}}\ge 20\mathrm{GeV}$. The dot-dashed black and dotted black lines (left and right panels) correspond to $h\to l^{-}{\rho }^{+}$ with the additional cut $q_T^{l^{-}}\ge 20\mathrm{GeV}$. The distributions shown in the left panel were computed with the cuts $y^{\tau }>0$ and $y_{+}^{\tau }>0$. The panel on the right shows the reduction of the height of the distributions if the laboratory-frame cut $y_{+}^L>0$ is applied.

Figure 7

Impact of measurement uncertainties on ${\phi }_{CP}^{*}$ distributions. (Left panel) $CP$-even Higgs boson $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\rho }^{+}$. (Right panel) Signal (solid black and red lines) and background (black dotted line) distributions for ${\pi }^{-}{\rho }^{+}$ and $l^{-}{\rho }^{+}$ final states.

Figure 8

Allowed regions in the space of the reduced $\tau$-Yukawa couplings $\mathrm{Re}(y_{1\tau })$, $\mathrm{Im}(y_{1\tau })$ for assumed measurements of ${\kappa }_{1\tau }=1.0\pm 0.04$ and ${\varphi }_{1\tau }=0°\pm 9°$ (grey segments) and ${\varphi }_{1\tau }=0°\pm 4°$ (red segments), respectively.

Figure 9

Aligned 2HDM with $CP$-conserving Higgs potential but $\mathrm{Im}({\zeta }_l)\ne 0$. For illustration we assume ${\varphi }_{1\tau }$ is measured with a central value of ${\varphi }_{1\tau }=15°$. The plot shows the resulting allowed areas to which the parameters $\mathrm{Re}({\zeta }_l),\mathrm{Im}({\zeta }_l)$ are restricted if $\mathrm{\Delta }{\varphi }_{1\tau }=\pm 9°$ (red areas) and $\mathrm{\Delta }{\varphi }_{1\tau }=\pm 4°$ (green areas).

Figure 10

A2HDM with $CP$-violating Higgs potential and $\mathrm{Im}({\zeta }_l)=0$. Constraints on the mixing matrix elements $R_{12}$ and $R_{13}$ assuming that measurements yield ${\varphi }_{1\tau }=0°$ (left panel) or ${\varphi }_{1\tau }=15°$ (right panel). The red (green) areas show the allowed regions which would remain if ${\varphi }_{1\tau }$ will be measured with a precision of $\mathrm{\Delta }{\varphi }_{1\tau }=\pm 9°$ ($\mathrm{\Delta }{\varphi }_{1\tau }=\pm 4°$). Notice that in the right panel the allowed regions are restricted to $|R_{12}|<1$.

Figure 11

Exclusion ranges (colored) in the $|\sin {\alpha }_b|$, $\tan \beta$ parameter space, assuming that measurements yield ${\varphi }_{1\tau }=0°\pm 4°$. The area between the solid red lines and the tops of the plots will then be excluded, irrespective of the value of the mixing angle $\alpha$. The dot-dashed blue, dashed black and dotted black lines are the boundaries of $\alpha$-dependent exclusion ranges for fixed values of $\cos (\beta -\alpha )=0.4$, 0 and $-0.4$, respectively. (Left panel) Type-I model. (Right panel) Type-II model.