$CP$ violation effects in the diphoton spectrum of heavy scalars

In a class of new physics models, an extended Higgs sector and new $CP$-violating sources are simultaneously present in order to explain the baryon asymmetry in the Universe. The aim of this work is to study the implications of beyond the Standard Model (SM) $CP$ violation for the searches of heavy scalars at the LHC. In particular, we focus on the diphoton channel searches in the $CP$-violating two-Higgs-doublet model (CPV 2HDM). To have a sizable CPV in the scalar sector, the two heavy neutral scalars in 2HDM tend to be nearly degenerate. The theoretical constraints of unitarity, perturbativity and vacuum stability are considered, which requires that the heavy scalars $M_H\lesssim 1\mathrm{TeV}$ in a large region of the parameter space. The experimental limits are also taken into account, including the direct searches for heavy neutral scalars in the final state of the SM $h$, $W$ and $Z$ bosons; the differential $t\overline{t}$ data; those from the charged scalar sector which is implied by the oblique $T$ parameter; and the precise measurements of the electric dipole moments of electrons and mercury. The quantum interference effects between the resonances and the SM background are crucially important for the diphoton signals, and the CPV mixing of the quasidegenerate heavy scalars could enhance significantly the resonance peak. With an integrated luminosity of $3000{\mathrm{fb}}^{-1}$ at the LHC, almost the whole parameter space of CPV 2HDM could be probed in the diphoton channel, and the CPV could also be directly detected via the diphoton spectrum.

Figure 1

Representative examples of BRs of the heavy scalars $H_{2,3}$ in CPV 2HDM of type I (left) and type II (right), as functions of scalar mass $M_H$, with a small mass splitting of $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) or 10 GeV (lower), and $\tan \beta =0.5$. With the maximal mixing ${\alpha }_c=\pi /4$, the BRs of the two heavy scalars $H_{2,3}$ are almost the same.

Figure 2

$\mathrm{BR}(H_{2,3}\to \gamma \gamma )$ in CPV 2HDM of type I (left) and type II (right), as functions of scalar mass $M_H$, with the mass and mixing parameters varying in the ranges given in Eq. (36).

Figure 3

Left: Limits on the cross sections of $gg\to H_{2,3}$ at the LHC, in the subsequent different decay modes. The solid, dashed, and dotted-dashed red lines are the limits from the decays $H\to ZZ$ in Ref. [64] and $H\to WW/ZZ$ in Refs. [65, 66]; the solid, dashed and dotted-dashed green lines are from $H\to hh$ [68, 69, 70]; the solid and dashed blue lines are from $H\to hZ$ [72, 74]. In this plot we show also the direct charged scalar search limits from $pp\to H^{\pm }X$ [84] (dashed purple). Right: The 95% C.L. uncertainties of the differential cross section $\mathrm{d}\sigma /\mathrm{d}{M}_{tt}$ [85], which is used to constrain the (CPV) couplings of $H_{2,3}$ to the top quark. See text for more details.

Figure 4

Lower limits on the mass of charged scalar $H^{\pm }$ in 2HDM, as functions of $\tan \beta$, from the direct searches at the LHC [84] and the observations of rare decay $B\to X_s\gamma$ [91]. The solid and dashed lines are respectively for the type-I and type-II models. These limits could be used to constrain the heavy quasidegenerate neutral scalars $H_{2,3}$ when combined with the experimental limits on oblique parameter $T$ [87].

Figure 5

Experimental limits on the CPV 2HDM of type I (left) and type II (right) with maximal $CP$ violation ${\alpha }_c=\pi /4$ and two quasidegenerate scalars $H_{2,3}$ with a small mass splitting of $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) or 10 GeV (lower). The red, green and blue shaded regions are respectively from the direct searches of heavy neutral scalars in the final states of $WW/ZZ$, $hh$ and $hZ$ collected in Fig. 3 [64, 65, 66, 68, 69, 70, 72, 74], with the same line legends as in that figure, e.g. the solid red line represents the limits from Ref. [64]. In this figure we also show the limits from the uncertainties of differential cross section $\mathrm{d}\sigma /\mathrm{d}{M}_{tt}$ at the parton level (solid pink line) [85], the limits from the direct searches of charged scalars at the LHC (dashed purple) [84] and precise measurements of $B\to X_s\gamma$ (dashed orange) [91]. The short-dashed, long-dashed and dotted-dashed gray lines are respectively from the limits of theoretical arguments of unitarity, perturbativity and stability of the scalar potential. All the regions below the unshaded lines (and the regions above the upper short and dashed gray lines in the two lower panels) are excluded. See text for more details.

Figure 6

The same as in Fig. 5 in the $M_H-{\alpha }_c$ plane, with ${\alpha }_b={10}^{-3}$ and $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$. The scenarios with larger splitting $\mathrm{\Delta }{M}_H=10\mathrm{GeV}$ are excluded by the theoretical arguments of perturbativity, unitarity and stability.

Figure 7

The same as in Fig. 6 with ${\alpha }_b={10}^{-2}$, $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) and 10 GeV (lower).

Figure 8

The same as in Fig. 5 in the $M_H-{\alpha }_b$ plane, with ${\alpha }_c=-\pi /4$, $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) and 10 GeV (lower).

Figure 9

The same as in Fig. 8 in the $M_H-{\alpha }_b$ plane, with ${\alpha }_c=+\pi /4$.

Figure 10

Examples of the diphoton spectra $\mathrm{d}\sigma /d{M}_{\gamma \gamma }$ in the CPV 2HDM, with the heavy scalar mass $M_H=500\mathrm{GeV}$ with a small splitting $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (left) or 10 GeV (right), $\tan \beta =0.5$ and ${\alpha }_c=0$. In these plots we show both the pure resonance (blue) and real and imaginary interference (solid and dashed red) contributions, as well as the total spectra (black). For the Yukawa couplings of type I and type II, these spectra are almost the same.

Figure 11

The same as in Fig. 10, with $\tan \beta =2$.

Figure 12

Total diphoton spectra in the vicinity of the resonance peak, in the examples given in Figs. 10 and 11 with mass splitting $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$, ${\alpha }_c=0$ and $\pi /4$ (and $\pi /2$ for $\tan \beta =2$).

Figure 13

Diphoton prospects of quasidegenerate scalars $H_{2,3}$ in CPV 2HDM in the parameter space of $M_H$ and $\tan \beta$, with type-I (left) and type-II (right) Yukawa couplings, with a small mass splitting $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ and ${\alpha }_c=0$. The regions below the solid red lines are probable at the 95% C.L. at the HL-LHC with $\sqrt{s}=14\mathrm{TeV}$ and an integrated luminosity of $3000{\mathrm{fb}}^{-1}$, by searches of $gg\to H_{2,3}\to \gamma \gamma$, with the SM background $gg\to \gamma \gamma$ and the interference of background and resonance taken into consideration. (Note that the red lines go beyond 1 TeV when $\tan \beta \lesssim 1$, not shown in these plots; the small $\tan \beta$ regions are all covered implicitly.) The shaded regions are excluded, respectively, by differential $t\overline{t}$ data [85] (pink) in the right panel of Fig. 3, direct $H^{\pm }$ searches [84] (purple) and $B\to X_s\gamma$ [91] (orange) in Fig. 4. The gray regions are excluded by the theoretical arguments of perturbativity, stability and unitarity. The limits and prospects in the two plots with a larger $\mathrm{\Delta }{M}_H=10\mathrm{GeV}$ are almost the same.

Figure 14

The same as in Fig. 13, with ${\alpha }_c=\pi /4$, $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) and 10 GeV (lower). More limits are shown in these plots: the combined direct searches of $H_{2,3}\to WW/ZZ$, $hh$ and $hZ$ at the LHC (yellow) [64, 65, 66, 68, 69, 70, 72, 74] and the EDM measurements of electrons (blue) [30] and mercury (brown) [31]. Within the dark bands, we cannot find any physical solution for the relation (27).

Figure 15

The same as in Figs. 13 and 14 in the $M_H-{\alpha }_c$ plane, with ${\alpha }_b={10}^{-3}$ and $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$. The scenarios with larger splitting $\mathrm{\Delta }{M}_H=10\mathrm{GeV}$ are excluded by the theoretical arguments of perturbativity, unitarity and stability.

Figure 16

The same as in Figs. 13 and 14 in the $M_H-{\alpha }_c$ plane, with ${\alpha }_b={10}^{-2}$, $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) and 10 GeV (lower). The type-I 2HDM with $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ is excluded by the electron EDM measurements [30].

Figure 17

The same as in Figs. 13 and 14 in the $M_H-{\alpha }_b$ plane, with ${\alpha }_c=-\pi /4$, $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) and 10 GeV (lower). The type-II 2HDM with $\mathrm{\Delta }{M}_H=10\mathrm{GeV}$ is excluded by the electron EDM measurements [30].

Figure 18

The same as in Figs. 13 and 14 in the $M_H-{\alpha }_b$ plane, with ${\alpha }_c=+\pi /4$ and $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$. The scenarios with $\mathrm{\Delta }{M}_H=10\mathrm{GeV}$ are excluded by the electron and mercury EDM measurements [30, 31].

Figure 19

The same as in Figs. 13 and 14 in the $M_H-{\alpha }_b$ plane, with ${\alpha }_c=0$, $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$ (upper) and 10 GeV (lower).

Figure 20

Significance at the resonance peak with a bin width of 10 GeV for the CPV 2HDM with $\mathrm{\Delta }{M}_H=1\mathrm{GeV}$, $\tan \beta =0.5$ (left) and 2 (right), and ${\alpha }_c=0$, $\pi /4$ (and $\pi /2$ for $\tan \beta =2$). The sensitivities for type-I and type-II 2HDM are almost the same.