$P$-even, $CP$-violating signals in scalar-mediated processes

Most studies of Higgs sector $CP$ violation focus on the detection of $CP$-violating neutral Higgs-fermion Yukawa couplings, which yield $P$-odd, $CP$-violating phenomena. There is some literature on purely bosonic signatures of Higgs sector $CP$ violation, where the simultaneous observation of three processes (suitably chosen) constitutes a signal of $P$-even $CP$ violation. However, in the examples previously analyzed, some of the processes are strongly suppressed in the approximate Higgs alignment limit (corresponding to the existence of a Standard Model-like Higgs boson as suggested by LHC data), in which case the proposed $CP$-violating signals are difficult to observe in practice. In this paper, we extend the existing literature by examining processes that do not vanish in the Higgs alignment limit and whose simultaneous observation would provide unambiguous evidence for scalar-mediated $P$-even $CP$ violation. We assess the discovery potential of such signals at various future multi-TeV lepton (and $\gamma \gamma$) colliders. The potential for detecting loop-induced $P$-even, $CP$-violating phenomena is also considered.

Figure 1

$\sigma ({\ell }^{+}{\ell }^{-}\to h_2{h}_3)$ as a function of the CM energy for $m_{h_2}=m_{h_3}=200\mathrm{GeV}$ and $m_{h_2}=m_{h_3}=600\mathrm{GeV}$.

Figure 2

$\sigma ({\ell }^{+}{\ell }^{-}\to h_2{h}_2{h}_3)$ (left) and $\sigma ({\ell }^{+}{\ell }^{-}\to h_2{h}_3{h}_3)$ (right) as a function of the CM energy, with $m_{h_2}=200\mathrm{GeV}$.

Figure 3

$\sigma (e^{+}{e}^{-}\to e^{+}{e}^{-}{H}^{+}{H}^{-}{h}_i)$, $\sigma ({\mu }^{+}{\mu }^{-}\to {\mu }^{+}{\mu }^{-}{H}^{+}{H}^{-}{h}_i)$, and $\sigma ({\ell }^{+}{\ell }^{-}\to H^{+}{H}^{-}{h}_i)$ as a function of the CM energy. In the left panel, $m_{h_i}=125\mathrm{GeV}$ and $m_{H^{\pm }}=150\mathrm{GeV}$, and in the right panel, $m_{h_i}=m_{H^{\pm }}=300\mathrm{GeV}$. The scalar potential parameters are chosen such that ${\mathrm{\Lambda }}_i=2\pi$.

Figure 4

$\sigma ({\ell }^{+}{\ell }^{-}\to H^{+}{H}^{-}{h}_i)$ as a function of the charged Higgs mass for four CM energies of $\sqrt{s}=1.5$, 3, 10 and 14 TeV. In the left panel $m_{h_i}=125\mathrm{GeV}$, and in the right panel $m_{h_i}=300\mathrm{GeV}$. The scalar potential parameters are chosen such that ${\mathrm{\Lambda }}_i=2\pi$.

Figure 5

$\sigma (e^{+}{e}^{-}\to e^{+}{e}^{-}{H}^{+}{H}^{-}{h}_i)$ via $\gamma \gamma$ fusion as a function of the charged Higgs mass (left) and of the neutral Higgs mass (right) for two CM energies of $\sqrt{s}=1.5\mathrm{TeV}$ and $\sqrt{s}=3\mathrm{TeV}$. The scalar potential parameters are chosen such that ${\mathrm{\Lambda }}_i=2\pi$.

Figure 6

$\sigma ({\mu }^{+}{\mu }^{-}\to {\mu }^{+}{\mu }^{-}{H}^{+}{H}^{-}{h}_i)$ as a function of the charged Higgs mass for three CM energies of $\sqrt{s}=3$, 10, and 14 TeV. In the left panel, $m_{h_i}=125\mathrm{GeV}$, and in the right panel, $m_{h_i}=300\mathrm{GeV}$. The scalar potential parameters are chosen such that ${\mathrm{\Lambda }}_i=2\pi$.

Figure 7

The cross section $\sigma (\gamma \gamma \to H^{+}{H}^{-}{h}_i)$ as a function of the charged Higgs mass for two CM energies, $\sqrt{s}=1.25\mathrm{TeV}$ (left panel) and $\sqrt{s}=2.5\mathrm{TeV}$ (right panel), for two values for the neutral Higgs masses, $m_{h_i}=125\mathrm{GeV}$ and $m_{h_i}=300\mathrm{GeV}$. The scalar potential parameters are chosen such that ${\mathrm{\Lambda }}_i=2\pi$.

Figure 8

Sample one-loop diagrams contributing to the decay process $h_{2,3}\to Z\gamma \gamma$.

Figure 9

Representative box diagrams [graphs (a) and (c)] and triangle diagrams [graphs (b) and (d)] with an internal charged Higgs boson, $H^{\pm }$, for the $h_i\to \gamma \gamma \gamma$ ($i=2$, 3) process. The arrows on the charged Higgs propagator denote the flow of electric charge.

Figure 10

Sample diagrams for two-loop contributions to the decay process $h_3\to \gamma \gamma \gamma$.