Higgs boson production in $e$ and real $\gamma$ collisions

We investigate the Standard Model Higgs boson production in $e^{-}\gamma$ collisions. The electroweak one-loop contributions to the scattering amplitude for $e^{-}\gamma \to e^{-}H$ are calculated and expressed in analytical form. We analyze the cross section for the Higgs boson production in $e^{-}\gamma$ collisions for each combination of polarizations of the initial electron and photon beams. The feasibility of observing the Higgs boson in the $e^{-}+\gamma \to e^{-}+b+\overline{b}$ channel is examined.

Figure 1

${\gamma }^{*}\gamma$ fusion diagrams: top-quark loop contributions.

Figure 2

${\gamma }^{*}\gamma$ fusion diagrams: $W$-boson loop contributions.

Figure 3

“$W{\nu }_e$” diagrams.

Figure 4

“$Ze$” diagrams.

Figure 5

The differential cross section for Higgs boson production $d{\sigma }_{(e\gamma \to eH)}/d(t/m_h^2)$ (black solid line) together with $d{\sigma }_{(\gamma \gamma )}/d(t/m_h^2)$ (blue dashed line), $d{\sigma }_{(Z\gamma )}/dt$ (red dotted line), $d{\sigma }_{(W{\nu }_e)}/d(t/m_h^2)$ (green dot-dashed line) and $d{\sigma }_{(Ze)}/d(t/m_h^2)$ (orange thin solid line) as a function of $-t/m_h^2$ with $\sqrt{s}=200\mathrm{GeV}$ for four cases of polarizations of the initial electron and photon beams, $(P_e=+1,P_{\gamma }=+1)$, $(P_e=+1,P_{\gamma }=-1)$, $(P_e=-1,P_{\gamma }=+1)$ and $(P_e=-1,P_{\gamma }=-1)$. In the plot of $(P_e=+1,P_{\gamma }=-1)$, $d{\sigma }_{(Ze)}/dt$ is too small and is out of the plot range.

Figure 6

The differential cross section for Higgs boson production $d{\sigma }_{(e\gamma \to eH)}/d(t/m_h^2)$ (black solid line) together with $d{\sigma }_{(\gamma \gamma )}/d(t/m_h^2)$ (blue dashed line), $d{\sigma }_{(Z\gamma )}/d(t/m_h^2)$ (red dotted line), $d{\sigma }_{(W{\nu }_e)}/d(t/m_h^2)$ (green dot-dashed line) and $d{\sigma }_{(Ze)}/d(t/m_h^2)$ (orange thin solid line) as a function of $-t/m_h^2$ with $\sqrt{s}=400\mathrm{GeV}$ for four cases of polarizations of the initial electron and photon beams, $(P_e=+1,P_{\gamma }=+1)$, $(P_e=+1,P_{\gamma }=-1)$, $(P_e=-1,P_{\gamma }=+1)$ and $(P_e=-1,P_{\gamma }=-1)$. In the plots of $(P_e=+1,P_{\gamma }=-1)$ and $(P_e=-1,P_{\gamma }=+1)$, $d{\sigma }_{(Ze)}/dt$ is too small and is out of the plot range.

Figure 7

Higgs boson production cross section ${\sigma }_{(e\gamma \to eH)}$ (black solid line), together with ${\sigma }_{(\gamma \gamma )}$ (blue dashed line), ${\sigma }_{(Z\gamma )}$ (red dotted line), ${\sigma }_{(W{\nu }_e)}$ (green dot-dashed line) and ${\sigma }_{(Ze)}$ (orange thin solid line) as a function of $\sqrt{s}$ for four cases of polarizations of the initial electron and photon beams, $(P_e=+1,P_{\gamma }=+1)$, $(P_e=+1,P_{\gamma }=-1)$, $(P_e=-1,P_{\gamma }=+1)$ and $(P_e=-1,P_{\gamma }=-1)$. The kinematical cut is chosen such that the allowed angle $\theta$ of the scattered electron in the CM frame is $10^{\circ }\le \theta \le 170^{\circ }$.

Figure 8

Higgs boson production cross section ${\sigma }_{(e\gamma \to eH)}(s,P_e,P_{\gamma })$ for the cases of $(P_e=-1,P_{\gamma }=-1)$ (thick solid line), $(P_e=-1,P_{\gamma }=+1)$ (dashed line), $(P_e=+1,P_{\gamma }=+1)$ (dotted line) and $(P_e=+1,P_{\gamma }=-1)$ (thin solid line). The kinematical cut is chosen such that the allowed angle $\theta$ of the scattered electron in the center-of-mass frame is $10^{\circ }\le \theta \le 170^{\circ }$.

Figure 9

The energy spectra of the scattered photons as a function of $y=\frac{\omega }{E_{e2}}$ for the cases of ($E_{\text{Laser}}=2.33\mathrm{eV}$, $E_{e2}=125\mathrm{GeV}$) and ($E_{\text{Laser}}=1.17\mathrm{eV}$, $E_{e2}=250\mathrm{GeV}$). For both cases, the energy spectra are described by the same graph. The blue and red curves represent the spectra when the initial electron and laser photon have the opposite polarizations ($P_{e2}{P}_{\text{Laser}}=-1$) and the same polarizations ($P_{e2}{P}_{\text{Laser}}=+1$), respectively. The dashed and dotted curves show the helicity-flip ($P_{\gamma }=-P_{\text{Laser}}$) and helicity-non-flip ($P_{\gamma }=P_{\text{Laser}}$) components of the scattered photon, respectively, and the solid curves represent the sum of the two.

Figure 10

Examples of background processes for $e+\gamma \to e+b+\overline{b}$.

Figure 11

Monte Carlo results for the differential cross section $d{\sigma }_{\text{cut}}/d(t/m_h^2)$ for the process $e\gamma \to eH\to e(b\overline{b})$ in $e^{-}\gamma$ collision in an $e^{-}{e}^{-}$ collider for the cases (a) $\sqrt{s_{ee}}=250\mathrm{GeV}$ and (b) $\sqrt{s_{ee}}=500\mathrm{GeV}$. The blue thick, red thin, black thick dashed and green thin dashed lines represent the results for the cases where $(P_{e1},P_{\text{Laser}})$ are $(-1,1)$, $(-1,-1)$, $(1,-1)$ and (1,1), respectively, and $P_{e2}=-P_{\text{Laser}}$.