Single Higgs production in association with a photon at electron-positron colliders in extended Higgs models

We study associated Higgs production with a photon at electron-positron colliders, $e^{+}{e}^{-}\to h\gamma$, in various extended Higgs models, such as the inert doublet model, the inert triplet model, and the two Higgs doublet model. The cross section in the standard model (SM) is maximal around $\sqrt{s}=250\mathrm{GeV}$, and we present how and how much the new physics can enhance or reduce the production rate. We also discuss the correlation with the $h\to \gamma \gamma$ and $h\to Z\gamma$ decay rates. We find that, with a sizable coupling to a SM-like Higgs boson, charged scalars can give considerable contributions to both the production and the decay if their masses are around 100 GeV. Under the theoretical constraints from vacuum stability and perturbative unitarity as well as the current constraints from the Higgs measurements at the LHC, the production rate can be enhanced from the SM prediction at most by a factor of 2 in the inert doublet model. In the inert triplet model, in addition, we find a particular parameter region where the $h\gamma$ production significantly increases by a factor of about 6 to 8, but the $h\to \gamma \gamma$ decay still remains as in the SM. In the two Higgs doublet model, possible deviations from the SM prediction are minor in the viable parameter space.

Figure 1

Total cross section for $e^{+}{e}^{-}\to h\gamma$ in the SM as a function of the collision energy. The total rate (red solid) is decomposed into two contributions; triangle loops (blue solid) and box loops (green solid). The contribution from the triangle loops is further decomposed into the ones from top quarks (blue dashed) and from $W$ bosons (blue dotted).

Figure 2

Representative Feynman diagrams for $e^{+}{e}^{-}\to h\gamma$.

Figure 3

Theoretical constraints on the ${\lambda }_3–{\lambda }_2$ plane in the IDM (left) and in the ITM (right).

Figure 4

Theoretical constraints on the ${\lambda }_3^{\prime }\text{−}\tan \beta$ plane in the THDM.

Figure 5

(Left) Total cross sections for $e^{+}{e}^{-}\to h\gamma$ in the IDM as a function of ${\lambda }_3$ at $\sqrt{s}=250\mathrm{GeV}$ with different charged Higgs-boson masses. The contributions only from the $hV\gamma$ (dashed lines) or box (dotted) diagrams are also shown as a reference. Gray lines denote the SM prediction. (Right) Correlations between $\mathrm{\Delta }R(h\to \gamma \gamma )$ and $\mathrm{\Delta }R(e^{+}{e}^{-}\to h\gamma )$, defined in Eqs. (35) and (34). Vertical blue lines indicate the $h\to \gamma \gamma$ signal strength from the LHC Run-I data with the $1\sigma$ and $2\sigma$ uncertainties.

Figure 6

(Left) Total cross sections for $e^{+}{e}^{-}\to h\gamma$ in the ITM as a function of ${\lambda }_3$ at $\sqrt{s}=250\mathrm{GeV}$ with different charged Higgs-boson masses. The right regions shown by dotted lines for $m_{H^{++}}=m_{H^{+}}=90$, 100, 125 GeV indicate parameter regions excluded by the requirement of the existence of the inert vacuum. A gray line denotes the SM prediction. (Right) Correlations between $\mathrm{\Delta }R(h\to \gamma \gamma )$ and $\mathrm{\Delta }R(e^{+}{e}^{-}\to h\gamma )$. Vertical blue lines indicate the $h\to \gamma \gamma$ signal strength from the LHC Run-I data with the $1\sigma$ and $2\sigma$ uncertainties.

Figure 7

(Left) Total cross sections for $e^{+}{e}^{-}\to h\gamma$ in the THDM as a function of ${\lambda }_3$ at $\sqrt{s}=250\mathrm{GeV}$ for $m_{H^{+}}=90\mathrm{GeV}$, where we fix $\tan \beta =2$ and vary $c_{\beta -\alpha }$ from 0 to 0.3. Gray lines denote the SM prediction. (Right) Correlations between $\mathrm{\Delta }R(h\to \gamma \gamma )$ and $\mathrm{\Delta }R(e^{+}{e}^{-}\to h\gamma )$. Vertical blue lines indicate the $h\to \gamma \gamma$ signal strength from the LHC Run-I data with the $1\sigma$ and $2\sigma$ uncertainties.

Figure 8

Correlations between $\mathrm{\Delta }R(h\to \gamma \gamma )$ and $\mathrm{\Delta }R(h\to Z\gamma )$ in the IDM (left) and in the ITM (right).

Figure 9

Same as Fig. 5, but at $\sqrt{s}=500\mathrm{GeV}$. Total cross sections for $e^{+}{e}^{-}\to h\gamma$ as a function of ${\lambda }_3$ (left) and correlations between $\mathrm{\Delta }R(h\to \gamma \gamma )$ and $\mathrm{\Delta }R(e^{+}{e}^{-}\to h\gamma )$ (right) in the IDM.

Figure 10

Correlations between $\mathrm{\Delta }R(h\to \gamma \gamma )$ and $\mathrm{\Delta }R(e^{+}{e}^{-}\to h\gamma )$ in the ITM (left) and in the THDM (right) at $\sqrt{s}=500\mathrm{GeV}$.

Figure 11

Real and imaginary parts of the loop function $(C_{12}+C_{23})(p_1^2,p_2^2,p_h^2;m_S,m_S,m_S)$ as a function of the mass of the scalar particle $m_S$. External momenta are fixed at $p_1^2=0$, $p_2^2=(0,250,500\mathrm{GeV}{)}^2$, and $p_h^2=m_h^2$.