Search for invisible decays of the Higgs boson produced at the CEPC

The Circular Electron Positron Collider (CEPC), proposed as a future Higgs boson factory, will operate at a center-of-mass energy of 240 GeV and will accumulate 5.6 ab−1 of integrated luminosity in 7 years. In this study, we estimate the upper limit of BR( inv) for three independent channels, including two leptonic channels and one hadronic channel, at the CEPC. Based on the full simulation analysis, the upper limit of BR( inv) could reach 0.26% at the 95% confidence level. In the Stand Model (SM), the Higgs boson can only decay invisibly via , so any evidence of invisible Higgs decays that exceed BR( inv) of the SM will indicate a phenomenon that is beyond the SM (BSM). The invariant mass resolution of the visible hadronic decay system , inv) is simulated, and the physics requirement at the CEPC detector for reaching this is given.


Introduction
Many pieces of cosmological evidence point towards the existence of dark matter (DM), such as rotation curves in galaxies, the masses of clusters of galaxies, and the gravitational lensing of galaxies [1,2]. However, there is no candidate for DM in the Stand Model (SM). In collider physics, the Higgs boson might be the portal connecting the new physics, such as DM and the fourth generation neutrino, and the SM [3][4][5]. In this case, the DM particles, which interact weakly with ordinary matter and are completely invisible to detectors, can be observed indirectly by studying the Higgs decays. In the SM, the Higgs boson can only decay invisibly via , as shown in Fig. 1, and its branching ratio (BR) is 1.06 [6]. Therefore, any evidence of invisible Higgs decays that exceed this BR will indicate a phenomenon that is beyond the SM (BSM).
The search for the invisible decays of the Higgs boson has been performed at the Large Hadron Collider (LHC). The signature for the invisible Higgs decays at the LHC is a large missing transverse momentum recoiling against a visible system. ATLAS and CMS yielded the 95% confidence level (CL) upper limits of 26% [7] and 19% [8], respectively, for the Higgs boson invisible branching ratio (BR( inv)). These results were obtained by the ATLAS and CMS detectors, respectively, using combined 4.7 fb −1 , 20.3 fb −1 , 36.1 fb −1 and combined 4.9 fb −1 , 19.7 fb −1 , 38.2 fb −1 of proton-proton collisions at the center-of-mass energy of 7 TeV, 8 TeV, and 13 TeV at the LHC. Compared with the results reported by the LHC, Higgs boson candidates can be identified using a technique known as the recoil mass method without using its decays at the Circular Electron Positron Collider (CEPC) [6]. An example of the recoil mass method is as follows: in the , inv) channel, fermions (f) can be identified, and their momentum M recoil can be measured. By selecting the fermion pair from the Z boson decay, the mass of the system recoiling against the fermion pair, commonly known as the recoil mass , can be calculated as where and are the total energy and the momentum of the two fermions, respectively, and is the center-of-mass energy. The distribution is expected to exhibit a peak at the Higgs boson mass around 125 GeV for the process. In this way, the properties of the Higgs boson can be measured precisely without reconstructing the Higgs boson from its decay products. Therefore, the Higgs boson production can be disentangled from its decay in a model-independent way. Moreover, the collisions have a much lower hadronic background (Higgs boson channels form the signal) contamination compared with hadron collisions, which allows better exclusive measurements of the Higgs boson decay channels. The electron-positron Higgs factory is an essential machine for understanding the nature of the Higgs boson.
CEPC is a Higgs factory proposed by the Chinese high energy physics community. CEPC is designed for delivering a combined integrated luminosity of 5.6 ab −1 to two detectors in 7 years. CEPC will operate at a centerof-mass energy 240-250 GeV, and over one million Higgs boson events will be produced during this period. Owing to the large statistics, the good beam energy spread of approximately 0.16% [9], and a novel particle flow algorithm [10], the mass and width of the Higgs boson are expected to be measured with high precision. With the SM production rate, the upper limit of BR( inv) could reach 0.26% at the 95% CL, which is an expected improvement of two orders of magnitude over the results of ATLAS and CMS.

H →
In a previous study on CEPC, the upper limit of BR( inv) was 0.41% [6]. The previous study used the CEPC-v1 detector, whereas the CEPC-v4 detector is √ s used in this study. The main change from CEPC-v1 to CEPC-v4 is the reduction of the solenoidal field intensity from 3.5 Tesla to 3.0 Tesla and changing the of the collider from 250 GeV to 240 GeV. Moreover, the reconstruction algorithm is different in both studies. Therefore, this study does not involve the comparison of the two results.
This study performs three independent analyses corresponding to , , and channels, for estimating the upper limit on the BR( inv) measurement at the CEPC. This paper is organized as follows. Section 2 presents a brief introduction to the CEPC detector and Monte Carlo simulations. Section 3 presents an introduction to the event selection of the three channels. A method for determining the upper limit, along with dependence of the Boson Mass Resolution (BMR), is discussed in Section 4. Section 5 lists our conclusions.

Detector design and Monte Carlo simulations
One of the physics programs at the CEPC is precision measurement of the Higgs boson properties. The CEPC detector is expected to reconstruct and identify all key physical objects, including charged leptons, photons, jets, missing energy, and missing momentum.
The CEPC-v4 [6] detector was designed using the International Large Detector (ILD) [11,12] as a reference. The detector of CEPC-v4 is simulated using MokkaC [13] and Geant4 [14]. It is composed of a tracking system, Time-Projection-Chamber tracker (TPC), high granularity calorimeter system, solenoid that generates a 3 Tesla magnetic field, and muon detector embedded in a magnetic field return yoke. The tracking system consists of silicon vertexing and tracking detectors. The calorimetry system consists of an electromagnetic calorimeter (ECAL) and an iron scintillator for a hadronic calorimeter (HCAL).
The analysis is performed on Monte Carlo (MC) samples simulated at the CEPC-v4 detector. The Higgs boson signal and SM backgrounds at the center-of-mass energy of 240 GeV, corresponding to the overall luminosity of 5.6 ab −1 , are generated with WHIZARD1.95 [15]. The generated events are then processed with MokkaC, and an attempt is made to reconstruct every visible particle with ARBOR [10]. The cross sections of the major SM processes of the collisions as functions of the center-of-mass energy are used in the simulations, including the Higgs boson production as well as the major backgrounds, where the initial-state radiation (ISR) effect has been taken into account. The Higgs boson signal and backgrounds are processed using Geant4 based full detector simulations and reconstruction. Limited by  All samples are grouped into signal and backgrounds, and the backgrounds are classified according to their final states. For the signal, this paper mainly focuses on the process , which is called the " " process. Then, Z bosons decay into leptons or hadrons, and the Higgs particle decays into two Z bosons, which eventually decay into four neutrinos. For the backgrounds, the major SM backgrounds are divided into 2-fermion processes and 4-fermion processes, according to the final states. The 2-fermion backgrounds are , where f refers to all lepton and quark pairs, except . The 4-fermion backgrounds are divided into 6 types: "single_z, " "single_w," "szorsw," "zz," "ww," and "zzorww," which are shown in Table 1. The processes whose four final states are a pair of electrons and two other fermions, or a pair of electron neutrinos and two other fermions, are named "single_z". The "single_w" processes include one electron, one electron neutrino, and two other fermions. If a final state includes a pair of electrons and a pair of electron neutrinos simultaneously, the corresponding processes are named "szorsw". In addition to the above-mentioned backgrounds, the same four fermions in the final state can be combined into different two intermediate bosons. If the two intermediate bosons can be two Z bosons, the processes are named "zz". The "ww" process is the one in which two intermediate bosons can become two W bosons. If two intermediate bosons can become two Z bosons or two W bosons, the corresponding process is "zzorww".

Event selection
The signal in this analysis consists of three different channels, namely inv), inv), and inv). Table 2 lists detailed information about the Higgs boson decay channels. The observed upper limit on BR( inv) at 95% CL at the CMS is 19%, and the CEPC is expected to yield more H → accurate results. In the event selection part, this analysis uses BR( inv) = 10%, and the event selection is based on the distribution of the signal and backgrounds. Event selection for each channel is detailed below.
In the inv) process, owing to the presence of quarks, many final states are expected. The event selection uses the information about all visible particles, and the distributions of the signal and backgrounds are shown in Fig. 2. The comprehensive event selections are as follows. In the inv) process, the mass of the system recoiling against all visible particles from the Z boson is , which can be calculated using Eq. (1) by replacing , with , . and is the total energy and momentum of all visible particles. The peak of the distribution is close to the Higgs boson mass. Considering the resolution of the detector, is limited to (100,150) GeV, as shown in Fig. 2(a). To suppress 2-fermion backgrounds, the transverse momentum of all visible particles is required to satisfy 18 GeV, as shown in Fig. 2(b), and the difference between the azimuthal angles of the two jets should be below 175°. Two jets are reconstructed from Z boson decay particles.
is the energy of all visible particles, which can be described as where is approximately 125 GeV, GeV, and the invariant mass of the visible system ( ) is equal to the Z boson mass, which is 91.2 GeV. should be limited to (85,102) GeV, as shown in Fig. 2(c).
Using the values of the parameters in Eq. (2), should be near 105 GeV, as shown in Fig. 2(d). According to the equation , should be near 52 GeV. Owing to the presence of quarks, the final states may include many charged particles. It is necessary to limit the number of charged particles ( ) with energy greater than 1 GeV to be larger than 5. To suppress the backgrounds from tau particles, a dedicated tau-finding algorithm TAURUS has been developed [16]. Since the inv) process  Table 3 lists the yields of signal ( _inv) and its backgrounds of the cut chain. The value of the significance [17] is used to judge the effect of the cuts. After the event selection, the signal selection efficiency is 60.81%, and the total background rejection efficiency is 99.97%.
The backgrounds, which contain neutrinos and two quarks, account for 95% of the total remaining backgrounds. The compositions of these backgrounds are similar to the signal channel and are difficult to suppress further.   Table 3). The blue arrows mark the cut ranges.
Chinese Physics C Vol. 44, No. 12 (2020) 123001 inv) process are similar, and the two processes will be introduced together. Firstly, it is natural that only a pair of oppositely charged muons or electrons is required in the visible final states. By selecting two muons or two electrons, many related parameters can be used for background suppression. The event selections are as follows. The recoil masses of two muons ( ) and two electrons ( ) can be calculated using Eq. (1). The peak of and distribution should be around the Higgs boson mass 125 GeV. Considering the resolutions of muons and electrons and the distributions of signal and backgrounds as shown in Fig. 3 and Fig. 4, the recoil mass should satisfy 120 GeV 150 GeV or 120 GeV 170 GeV, and the invariant mass of two muons ( ) or two electrons ( ) is closer to the Z boson mass. To suppress the 2-fermion backgrounds, the transverse momenta of the muon pair ( ) and the electron pair ( ) are required to be more than 12 GeV, as shown in Fig. 3(c) and Fig. 4(c). Moreover, the angle between the two muons ( ) should be under 175° or that between the two electrons ( ) should be under 176° to suppress the 2-fermion backgrounds. The visible energy ( ), which is described in Eq. (2), is mainly the energy of two muons ( ) or two elec- trons ( ) from the Z boson decays; the value of is approximately 105 GeV, as shown in Fig. 3(d) and Fig.  4(d). Using the approximate values of and in the relativistic energy-momentum relation , the value of is close to 2, similar to that of .
µµH µµH Table 4 lists the yields for the _inv signal and its backgrounds. The remaining backgrounds containing two muons and two neutrinos account for 61% of the total backgrounds. These backgrounds have similar topology as the signal which is difficult to suppress further. The remaining backgrounds containing the muon, tau, and two neutrinos account for 38% of the total backgrounds. The algorithm TAURUS does not increase the significance of the _inv signal. Table 5 lists the yields for the _inv signal and its backgrounds at the CEPC. The cut Vertex 0.0011, which is the position of the decay vertex, changes the value of significance from 10.91 to 13.79. Since the signal channel does not contain tau, the Vertex of the signal channel is much smaller than the backgrounds from tau. The final states of the remaining backgrounds, which are composed of two electrons and two neutrinos, account for 70% of the total background. These back-  Table 4). The blue arrows mark the cut ranges. grounds are the same as the final particles of the signal channel. The final particles of the remaining backgrounds containing tau, electron, and two neutrinos account for 23% of the total background, and the information about tau particles cannot further suppress these backgrounds. In conclusion, the tau-finding algorithm TAURUS can improve the significance of the Higgs invisible decays to a certain extent, but it cannot com-pletely suppress the backgrounds containing tau.

Results for the upper limit and the boson mass resolution (BMR)
H → s After the event selections, the 95% CL upper limit of BR( inv) is computed within the CL formalism, us-   Table 5). The blue arrows mark the cut ranges. ing the profile likelihood ratio as a test statistic [18], in which systematic uncertainties are ignored. The likelihood ratio method uses S+B, where is the signal strength, S is the signal, and B is the background. First, the signal and background samples are fitted to obtain their distribution functions, which are used for generating Asimov data. The Asimov data provide a simple method for obtaining the median experiment sensitivity of the measurement as well as fluctuations around this expectation. Then, the test statistic distribution generated for signal+background and background-only hypotheses is constructed assuming the signal strength , and each corresponds to the CL value calculated by the ratio of the two hypothesis probabilities [19]. When the CL value is 0.05, the value is its 95% CL upper limit. The corresponding negative logarithmic profile likelihood ratio log(L) as a function of is shown in Fig. 5. The horizontal axis corresponding to log(L) = 2 on the yaxis is approximately 95% CL interval of .
H → H → Table 6 summarizes the expected precision of the measurement of BR( inv) and the 95% CL upper limit on BR( inv), for the dataset of 5.6 ab -1 . The estimated combined 95% CL upper limit of three channels is 0.26%. Any evidence of invisible Higgs decays that exceeds this value will indicate the BSM phenomenon.
The precision of the upper limit is affected by various systematic uncertainties [20], such as the luminosity, beam energy, efficiency of the object reconstruction, and acceptance of the detector. The precision of luminosity can be 0.1%, and the beam energy is expected to be better than 1 MeV, which can be ignored in experimental recoil mass measurements. For tracks within the detector acceptance and transverse momenta larger than 1 GeV, the track finding efficiency is better than 99%. These systematic uncertainties are expected to be small and will be ignored in this study. The BMR of the CEPC detector can reach 3.8% using the ARBOR reconstruction algorithm [10,21]. A fast simulation was performed for quantifying this depend-  ence. The fast simulation took into account the signal of inv) and the main background of inv) after the event selection. Fig. 6 shows the accuracy [16] of inv) for different BMR values. For BMR values between 4% and 20%, the accuracy degrades rapidly with increasing BMR, while for BMR values below 4%, the change in the accuracy is below 0.06%. Based on the fast simulation, it can be concluded that BMR is vital and will affect the measurement precision of the inv) channel. Therefore, the BMR value of 4% can be used as an essential reference upper bound for detector design and optimization.

Conclusion
This paper studied the measurement of the Higgs invisible decays at the CEPC. The upper limit on the Higgs invisible decays was measured using three independent channels inv), inv), and inv). The combined result for the 95% CL upper limit of BR( inv) was 0.26% for the three channels. Compared with the LHC results (26% for ATLAS and 19% for CMS), the result obtained at the CEPC is better by two orders of magnitude. Compared with the High-Luminosity LHC (HL-LHC) result for 14 TeV, which is expected to be 2.5% [22], the result obtained at the CEPC is better by one order of magnitude. The accuracy of the upper limit for the CEPC is significantly better than those for hadron colliders, because the reconstructed Higgs recoil mass spectrum at the electronpositron Higgs factories gives a very clear and distinct signature of the Higgs boson, as well as the high productivity of the Higgs bosons at the CEPC. The CEPC result is consistent with the results for other electron-positron colliders, such as the International Linear Collider (ILC) and the Future Circular Collider (FCC-ee), for which the 95% CL upper limits on BR( inv) were 0.26% for ILC [23] and 0.22% for FCC-ee (5 ab -1 at 240 GeV and 0.19% by combining 365 GeV) [24]. Among these three signal channels, the channel yielded the best result owing to its largest number of events. The precision of the upper limit on the channel strongly relies on the invariant mass of the visible hadronic decay system, and BMR better than 4% provides a clear separation between the Higgs signal and the background, which shall be pursued as one of the key physics requirements for designing future CEPC detectors.