Measurement of the Higgs boson mass and $e^{+}{e}^{-}\to ZH$ cross section using $Z\to {\mu }^{+}{\mu }^{-}$ and $Z\to e^{+}{e}^{-}$ at the ILC

This paper presents a full simulation study of the measurement of the production cross section (${\sigma }_{ZH}$) of the Higgsstrahlung process $e^{+}{e}^{-}\to ZH$ and the Higgs boson mass ($M_{\mathrm{H}}$) at the International Linear Collider (ILC), using events in which a Higgs boson recoils against a $Z$ boson decaying into a pair of muons or electrons. The analysis is carried out for three center-of-mass energies $\sqrt{s}=250$, 350, and 500 GeV, and two beam polarizations $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ and $e_{\mathrm{R}}^{-}{e}_{\mathrm{L}}^{+}$, for which the polarizations of $e^{-}$ and $e^{+}$ are $(P{e}^{-},P{e}^{+})=(-80\%,+30\%)$ and ($+80\%$, $-30\%$), respectively. Assuming an integrated luminosity of $250{\mathrm{fb}}^{-1}$ for each beam polarization at $\sqrt{s}=250\mathrm{GeV}$, where the best lepton momentum resolution is obtainable, ${\sigma }_{ZH}$ and $M_{\mathrm{H}}$ can be determined with a precision of 2.5% and 37 MeV for $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ and 2.9% and 41 MeV for $e_{\mathrm{R}}^{-}{e}_{\mathrm{L}}^{+}$, respectively. Regarding a 20 year ILC physics program, the expected precisions for the HZZ coupling and $M_{\mathrm{H}}$ are estimated to be 0.4% and 14 MeV, respectively. The event selection is designed to optimize the precisions of ${\sigma }_{ZH}$ and $M_{\mathrm{H}}$ while minimizing the bias on the measured ${\sigma }_{ZH}$ due to discrepancy in signal efficiencies among Higgs decay modes. For the first time, model independence has been demonstrated to a sub-percent level for the ${\sigma }_{ZH}$ measurement at each of the three center-of-mass energies. The results presented show the impact of center-of-mass energy and beam polarization on the evaluated precisions and serve as a benchmark for the planning of the ILC run scenario.

Figure 1

The lowest order Feynman diagrams of the three major Higgs production processes at the ILC: (top) Higgsstrahlung process $e^{+}{e}^{-}\to ZH$, (center) WW fusion process $e^{+}{e}^{-}\to \nu \overline{\nu }H$, and (bottom) ZZ fusion process $e^{+}{e}^{-}\to e^{+}{e}^{-}H$.

Figure 2

The Higgs production cross section as a function of $\sqrt{s}$ assuming $M_{\mathrm{H}}=125\mathrm{GeV}$ for the following Higgs production processes: Higgsstrahlung (solid), WW fusion (dashed), and ZZ fusion (dotted). (Figure taken from [3].)

Figure 3

The Feynman diagrams contributing to the major background processes for the Higgs recoil analysis in the ${\mu }^{+}{\mu }^{-}H$ channel: 2f_l background with $\mu \mu$ in the final state and an ISR photon (top), 4f_sl background with ZZ as intermediate state (center), 4f_l background with WW as intermediate state (bottom).

Figure 4

Comparison of the distributions of $M_{l^{+}{l}^{-}}$ (top) and $M_{\mathrm{rec}}$ (bottom) between “correct” and “wrong” lepton pairs. This is an example of the $H\to {\mathrm{ZZ}}^{*}$ decay mode in the ${\mu }^{+}{\mu }^{-}H$ channel at $\sqrt{s}=250\mathrm{GeV}$. The distributions are made using the high statistics samples mentioned in Sec. 3c.

Figure 5

Comparison of the $M_{l^{+}{l}^{-}}$ (two topmost) and $M_{\mathrm{rec}}$ (two bottommost) spectra between the cases with (blue) and without (red) bremsstrahlung/FSR recovery for $\sqrt{s}=250\mathrm{GeV}$. The two bottommost plots show the ${\mu }^{+}{\mu }^{-}H$ and $e^{+}{e}^{-}H$ channels, respectively. The histograms are normalized to unit area.

Figure 6

Top: The $M_{{\mu }^{+}{\mu }^{-}}$ distributions of signal and the major background processes, after a loose precut on $M_{\mathrm{rec}}$. Center: The $p_{\mathrm{T}}^{{\mu }^{+}{\mu }^{-}}$ distributions of signal and the major background processes, after a loose precut on $M_{\mathrm{rec}}$ and a cut on $M_{{\mu }^{+}{\mu }^{-}}$. Bottom: The $\cos ({\theta }_{\text{missing}})$ distributions of signal and 2-fermion background, after a loose precut on $M_{\mathrm{rec}}$ and cuts have been applied on $M_{{\mu }^{+}{\mu }^{-}}$ and $p_{\mathrm{T}}^{{\mu }^{+}{\mu }^{-}}$.

Figure 7

The distributions of the variables $M_{{\mu }^{+}{\mu }^{-}}$, $\cos ({\theta }_Z)$, $\cos ({\theta }_{\text{lep}})$, $\cos ({\theta }_{\text{track},1})$, and $\cos ({\theta }_{\text{track},2})$ used for the training in the multi-variate analysis, as well as the distribution of the BDT response, shown here for the signal and background in the case of the ${\mu }^{+}{\mu }^{-}H$ channel at $\sqrt{s}=250\mathrm{GeV}$, after a loose precut on $M_{\mathrm{rec}}$ and cuts have been applied on $M_{{\mu }^{+}{\mu }^{-}}$, $p_{\mathrm{T}}^{{\mu }^{+}{\mu }^{-}}$, and $\cos ({\theta }_{\text{missing}})$. The histograms are normalized.

Figure 8

The distributions of $E_{\mathrm{vis}}$ (after excluding the dilepton energy) of the signal and the 4f_zzorww_l processes, after a loose precut on $M_{\mathrm{rec}}$ and cuts have been applied on $M_{{\mu }^{+}{\mu }^{-}}$, $p_{\mathrm{T}}^{{\mu }^{+}{\mu }^{-}}$, $\cos ({\theta }_{\text{missing}})$, and the BDT response of the MVA analysis.

Figure 9

The histograms of the recoil mass of the signal and the major residual background processes left in a wide window around the signal $M_{\mathrm{rec}}$ peak, shown here for the ${\mu }^{+}{\mu }^{-}H$ (top) and $e^{+}{e}^{-}H$ (bottom) channels at $\sqrt{s}=250\mathrm{GeV}$, after all cuts described in the main text have been applied.

Figure 10

The recoil mass spectra of events in the signal region 110–155 GeV at $\sqrt{s}=250\mathrm{GeV}$: (a) ${\mu }^{+}{\mu }^{-}H$, $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ (b) ${\mu }^{+}{\mu }^{-}H$, $e_{\mathrm{R}}^{-}{e}_{\mathrm{L}}^{+}$ (c) $e^{+}{e}^{-}H$, $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ (d) $e^{+}{e}^{-}H$, $e_{\mathrm{R}}^{-}{e}_{\mathrm{L}}^{+}$. The fitting functions used for the extraction of ${\sigma }_{ZH}$ and $M_{\mathrm{H}}$ (see Sec. 5a) are superimposed. The black markers are the Monte Carlo (MC) data points, the green, magenta, and blue lines indicate the fitted function for signal, background, and the combination of signal and background, respectively.

Figure 11

The recoil mass spectra of events in the signal region 100–200 GeV for $\sqrt{s}=350\mathrm{GeV}$. Top: ${\mu }^{+}{\mu }^{-}H$, $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ Bottom $e^{+}{e}^{-}H$, $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$. The legend is same as in Fig. 10.

Figure 12

The recoil mass spectra of events in the signal region 100–250 GeV for $\sqrt{s}=500\mathrm{GeV}$. (a) ${\mu }^{+}{\mu }^{-}H$, $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ (b) $e^{+}{e}^{-}H$, $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$. The legend is same as in Fig. 10.

Figure 13

For the case of the ${\mu }^{+}{\mu }^{-}H$ channel and $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ at $\sqrt{s}=250\mathrm{GeV}$, in the region 110–155 GeV: Top: The $M_{\mathrm{rec}}$ spectra of the signal MC events used in analysis plotted together with the kernel function. Center: The $M_{\mathrm{rec}}$ spectrum of toy MC events corresponding to the top plot. Bottom: Toy MC events used for extracting ${\sigma }_{ZH}$ and $M_{\mathrm{H}}$ and their statistical uncertainties, which are generated using the function which fitted the top plot as input. The legend is the same as in Fig. 10.