# Jet origin identification and measurements of rare and exotic hadronic
decays of Higgs boson at $e^{+}e^{-}$ collider

Hao Liang  Institute of High Energy Physics, Chinese Academy of Sciences,
19B Yuquan Road, Shijingshan District, Beijing 100049, China  University of
Chinese Academy of Sciences,
19A Yuquan Road, Shijingshan District, Beijing 100049, China  Yongfeng Zhu
State Key Laboratory of Nuclear Physics and Technology, School of Physics,
Peking University, Beijing, 100871, China  Yuexin Wang  Institute of High
Energy Physics, Chinese Academy of Sciences,
19B Yuquan Road, Shijingshan District, Beijing 100049, China  China Center of
Advanced Science and Technology, Beijing 100190, China  Yuzhi Che  Institute
of High Energy Physics, Chinese Academy of Sciences,
19B Yuquan Road, Shijingshan District, Beijing 100049, China  University of
Chinese Academy of Sciences,
19A Yuquan Road, Shijingshan District, Beijing 100049, China  Manqi Ruan
<EMAIL_ADDRESS>Institute of High Energy Physics, Chinese Academy of
Sciences,
19B Yuquan Road, Shijingshan District, Beijing 100049, China  University of
Chinese Academy of Sciences,
19A Yuquan Road, Shijingshan District, Beijing 100049, China  Chen Zhou
<EMAIL_ADDRESS>State Key Laboratory of Nuclear Physics and Technology,
School of Physics, Peking University, Beijing, 100871, China  Huilin Qu
<EMAIL_ADDRESS>CERN, EP Department, CH-1211 Geneva 23, Switzerland

###### Abstract

We propose the concept of jet origin identification that categorizes jets into
5 quark species $(b,c,s,u,d)$, 5 anti-quarks
$(\bar{b},\bar{c},\bar{s},\bar{u},\bar{d})$, and gluon. Using full simulation
physics events at the Circular Electron Positron Collider (CEPC) and the
ParticleNet algorithm, we quantify the jet origin identification performance
using an 11-dimensional confusion matrix. This matrix exhibits simultaneously
tagging efficiencies of 91%, 80%, 64%, and jet charge flip rates of 18%, 7%,
16% for $b$ and $\bar{b}$, $c$ and $\bar{c}$, and $s$ and $\bar{s}$ quarks,
respectively. It also shows a gluon jet identification efficiency of 67%. We
use jet origin identification to determine the upper limits on branching
ratios of Higgs rare hadronic decays, namely $s\bar{s}$, $u\bar{u}$, and
$d\bar{d}$, and the flavor-changing neutral current decays, namely $sb$, $sd$,
$db$, $cu$. We conclude that these Higgs decay branching ratios could be
measured with typical upper limits of 0.02%–0.1% at 95% confidence level at
the CEPC nominal parameters. For the $H\rightarrow s\bar{s}$ decay, this upper
limit corresponds to roughly three times the Standard Model prediction.

_Introduction.—_ Quarks and gluons are standard model (SM) particles that
carry color charges of the strong interaction. Due to the color confinement of
quantum chromodynamics (QCD), they cannot travel freely in spacetime and are
confined into composite particles like hadrons. Once generated in high-energy
collisions, quarks and gluons fragment into numerous particles that travel in
directions collinear to the initial colored particles. These collinear
particles are called jets, which are fundamental physical objects in high-
energy collider experiments, see Fig. 1.

Figure 1: Event display of an
$e^{+}e^{-}\rightarrow\nu\bar{\nu}H\rightarrow\nu\bar{\nu}gg$ ($\sqrt{s}$ =
240 GeV) event simulated and reconstructed with the CEPC baseline detector
CEPC_CDR_Phy . Different particles are depicted with colored curves and
straight lines: red for $e^{\pm}$, cyan for $\mu^{\pm}$, blue for $\pi^{\pm}$,
orange for photons, and magenta for neutral hadrons.

We define the concept of jet origin identification as the procedure to
determine from which colored SM particle a single jet is generated. The jet
origin identification combines the concepts of jet flavor tagging, jet charge
measurements, quark-gluon separation, $s$ and light jet tagging together. The
relevant performances are critical for experimental high-energy experiments.
For instance, experiments at the Large Hadron Collider (LHC) emphasize the
differentiation of quark jets from gluon jets Gallicchio:2011xq ;
LHCHiggsCrossSectionWorkingGroup:2016ypw ; Gauld:2022lem , which is crucial
for determining the relevant Higgs couplings ATLAS:2018kot ; CMS:2018nsn ;
CMS:2022psv . The determination of jet charge Kang:2023ptt ; Cui:2023kqb  is
essential for measurements of the weak mixing angle CMS:2018ktx ;
ATLAS:2018gqq  and time-dependent CP violations Belle:2006dlp ; LHCb:2019nin ,
and can be used to improve the precisions of Higgs property measurements at
LHC Li:2023tcr .

After the discovery of the Higgs boson in 2012 ATLAS:2012yve ; CMS:2012qbp ,
one of the leading scientific objectives is to hunt for new physics (NP)
beyond the SM through precise measurements of the Higgs boson. Electron-
positron Higgs factories produce millions of Higgs bosons, are free of QCD
background, and have signal-to-noise ratios surpassing the LHC by 7–8 orders
of magnitudes CEPC_CDR_Phy ; FCC:2018byv ;
ILCInternationalDevelopmentTeam:2022izu . Compared to the ultimate precision
at the LHC, electron-positron Higgs factories could boost the precision of
Higgs boson property measurements by approximately one order of magnitude
An:2018dwb . The electron-positron Higgs factory is regarded as the highest-
priority future collider project in particle physics European:2720131 ;
CEPCPhysicsStudyGroup:2022uwl .

The identification of jet origin is vital for electron-positron Higgs
factories. The electron-positron Higgs factory could record nearly 100% of the
Higgs boson events, most of which include jets in the final states, and
provide an inclusive description of Higgs boson properties relevant to jets,
which is highly complementary to the LHC. Precise identification of jet origin
could significantly enhance the signal-to-background separation, and grant
access to the Higgs couplings to different species of colored particles and
differential cross-sections. Similarly, the jet origin identification also
enhances physics measurements involving $Z$ and $W$ bosons, and the top quark,
since the majority of those particles also decay into jets.

An $11\times 11$ confusion matrix is used to evaluate the jet origin
identification performance. The matrix elements describe the identification
efficiencies and misidentification rates of given colored particles, namely
$b$, $\bar{b}$, $c$, $\bar{c}$, $s$, $\bar{s}$, $u$, $\bar{u}$, $d$,
$\bar{d}$, and gluon. For simplicity, this confusion matrix is referred to as
$M_{11}$ throughout this Letter.

In this Letter, the ParticleNet algorithm Qu:2019gqs  is applied at the
Circular Electron Positron Collider (CEPC) full simulated data to derive
$M_{11}$. ParticleNet is a graph neural network-based deep learning algorithm
and is utilized in CMS experiments CMS:2022psv ; CMS-DP-2021-017 ; CMS-
DP-2022-005  and future $e^{+}e^{-}$ colliders LI:2021kjh ; Liao:2022ufk ;
Gautam:2022szi ; refId0 . In ParticleNet, jets are represented as particle
clouds, where the angular information of particles defines their coordinates.
The core concept of ParticleNet is the EdgeConv operation Wang:2018nkf , which
implements convolution by aggregating features for each particle and its
nearest neighbors.

The jet origin identification method is applied to the simulation study of the
rare and flavor-changing neutral current (FCNC) hadronic decays of the Higgs
boson at CEPC. Specifically, we analyze the rare decays of the Higgs to
$s\bar{s}$, $u\bar{u}$, and $d\bar{d}$. The branching ratio for $H\rightarrow
s\bar{s}$ is predicted to be $2.3\times 10^{-4}$ Duarte-Campderros:2018ouv ,
while $H\rightarrow u\bar{u}$ or $d\bar{d}$ is expected to have a branching
ratio less than $10^{-6}$ ParticleDataGroup:2022pth ; Duarte-
Campderros:2018ouv ; Denner:2011mq ; Herren:2017osy  due to the small masses
of $u$ and $d$ quarks. Additionally, we analyze Higgs decay modes via FCNC,
namely $H\rightarrow sb$, $ds$, $db$, and $uc$, which are forbidden in the SM
at the tree level, with branching ratios smaller than $10^{-7}$ due to loop
contributions Kamenik:2023ytu , where $sb$ denotes $s\bar{b}$ or $\bar{s}b$,
and similarly for $ds$, $db$, and $uc$. This Letter derives the upper limits
for these Higgs decay modes at the CEPC nominal operation scenario of
$\sqrt{s}=240~{}{\rm GeV}$ and integrated luminosity of 20 ${\rm ab}^{-1}$,
corresponding to a yield of 4 million Higgs bosons
CEPCPhysicsStudyGroup:2022uwl ; Gao:2022lew .

_Detector Geometry and Software Tools.—_ This study uses full simulation
samples generated with the CEPC baseline detector and software CEPC_CDR_Phy .
The CEPC baseline detector is a particle flow oriented detector composed of a
high-precision vertex detector, a large volume high-precision main tracker,
high granularity calorimetry, and a large volume solenoid. This detector
concept emphasizes the separation of final state particles and measures their
energies and momenta in the most suitable sub-detectors: charged particles are
measured by the tracker, photons by the electromagnetic calorimeter, and
neutral hadrons by the hadron calorimeter. The CEPC baseline detector enables
highly efficient reconstruction of physics objects and significantly improves
jet reconstruction Arbor  compared to conventional methods that use only
calorimeter information. We use Pythia 6 Pythia_6  as the event generator,
MokkaPlus Mokka_git  as the Geant4-based simulation GEANT4:2002zbu , the
baseline digitization, and reconstruction algorithms to reconstruct all the
final state particles Arbor .

_Jet Origin Identification.—_ For each species of jets, one million
$e^{+}e^{-}\rightarrow\nu\bar{\nu}H,H\rightarrow q\bar{q}/gg$ events are
simulated. An event display is shown in Fig. 1. The final state particles of
each event are clustered into two jets using a modified $e^{+}e^{-}$-$k_{t}$
algorithm Suehara:2015ura ; Catani:1991hj . The coordinates of a particle
within the particle cloud are determined by the difference between their
azimuthal angle and pseudo-rapidity and the corresponding values of the jet.
The features of each particle used for training include the kinematic
parameters (momenta and energies), charge, particle type information (e.g.,
electron, muon, charged kaon, charged pion, proton, neutral hadron, or
photon), and the impact parameters of charged particles, including $d_{0}$,
$z_{0}$, and their uncertainties Kramer:2006zz .

The species information of the final state particles is crucial for jet origin
identification. The CEPC baseline detector can effectively identify leptons,
with a typical efficiency higher than 99.5% and a hadron-to-lepton
misidentification rate below 1%, for leptons with energy larger than 2 GeV
Yu:2020bxh ; Yu:2021pxc . It can also distinguish different species of charged
hadrons ($\pi^{\pm}$, $K^{\pm}$, proton, anti-proton), providing a typical
efficiency and purity of 95% for $K^{\pm}$ identification at hadronic $Z$-pole
events An:2018jtk ; Zhu:2022hyy ; Che:2022dig . Neutral hadrons composed of
s-quarks, such as $K_{S}^{0}$ and $\Lambda$, can be reconstructed, especially
if they decay into tracks KsLambda . To quantify the impact of final state
particle identification, three scenarios are compared. The first scenario
assumes perfect identification of leptons. The second scenario further assumes
perfect identification of charged hadrons. The third scenario, on top of the
second one, assumes perfect identification of $K_{S}^{0}$ and $K_{L}^{0}$. In
this Letter, the second scenario is adopted as the default, as a well-
optimized detector could, in principle, provide both decent lepton and charged
hadron identification. The third scenario is rather optimistic as the
identification of $K_{L}^{0}$ can be subtle, and only serves as a reference
for comparison.

For each jet species, 600k events are used for training, 200k events for
validation, and 200k events for testing. The model is trained for 30 epochs,
and the epoch demonstrating the best accuracy on the validation samples is
selected and applied to the testing sample. The results of the testing samples
are presented in this Letter.

Figure 2: The confusion matrix $M_{11}$ with perfect identification of leptons
and charged hadrons. The matrix is normalized to unity for each truth label
(row).

The ParticleNet predicts 11 confidence scores for each jet, which is then
classified into the category with the highest score. The derived $M_{{11}}$ is
illustrated in Fig. 2. $M_{11}$ is approximately symmetric and block
diagonalized into $2\times 2$ blocks for the quark sector. Each block
corresponds to a quark and its corresponding anti-quark of a specific kind. In
the $2\times 2$ sub-matrix, half of the summation of all 4 matrix elements
represents the corresponding jet tagging efficiency. The ratio of the average
value of off-diagonal elements to the tagging efficiency indicates the jet
charge flip rate. The top-left part of $M_{11}$ corresponds to the
identification of heavy flavor jets: $b$, $\bar{b}$, $c$, and $\bar{c}$, with
identification efficiencies of 91% and 80%, for $b$ and $c$, respectively, and
jet charge flip rates of 18% and 7%. In the default scenario with perfect
lepton identification and charged hadron identification, $s$ jets can be
identified with a flavor tagging efficiency of 64% and a charge flip rate
comparable to that of $b$ jets. The identification efficiencies for $u$,
$\bar{u}$, $d$, and $\bar{d}$ are significantly lower than those for heavy
quarks and $s$ quarks but still remain at a level of 35%–42%. The jet charge
flip rate is significantly higher for the $d$ jets than for the $u$ jets,
since $u$ quark carries twice the charge compared to $d$ quark.

$M_{11}$ also demonstrates that gluon jets can be identified with an
efficiency of 67%, with a misidentification rate of approximately 2% into
heavy quarks and 5% into light ($uds$) quarks. Meanwhile, the
misidentification rates of a light quark jet into a gluon jet are two to three
times larger than the inverse misidentification rates.

Figure 3: Jet flavor tagging efficiency and charge flip rate with
identification of leptons (the first scenario, denoted as $\ell^{\pm}$ in the
legend), plus identification of charged hadrons (the second and default
scenario, denoted as $K^{\pm}$) and neutral kaons (the third scenario, denoted
as $K^{0}_{L/S}$). Figure 4: ROC curves for $S$ vs. $U$ or $D$ with
identification of leptons (the first scenario, denote as $\ell^{\pm}$ in the
legend), plus identification of charged hadrons (the second and default
scenario, denote as $K^{\pm}$) and neutral kaons (the third scenario, denote
as $K^{0}_{L/S}$).

Fig. 3 demonstrates the impact of final state particle identification on jet
origin identification. Feeding ParticleNet with more and more accurate
information on final state particle species, the jet origin identification
performance improves progressively. Compared to the first scenario (only
lepton identification), the second scenario (both lepton and charged hadron
identification) improves the $S$-tagging efficiency from 46% to 64% and
reduces significantly the jet charge flip rates. The third scenario, which
includes neutral kaon information, further enhances the $S$-tagging efficiency
to 70%. However, the jet charge flip rates remain almost the same as in the
second scenario, since $K_{S}^{0}$ and $K_{L}^{0}$ are superpositions of
$\ket{s\bar{d}}$ and $\ket{\bar{s}d}$. Interestingly, this exercise indicates
that the current ParticleNet architecture couldn’t figure out at least some of
the $K_{S}^{0}$ decays into a pair of pions — otherwise the relative
improvement on $S$-tagging would not be significant from the second to the
third scenario. The impact of particle identification is also demonstrated in
Fig. 4, which shows progressive improvements in distinguishing $S$-jets from
$U/D$-jets from the first to the third scenarios.

_Benchmark Physics Analyses.—_ The precise measurement of Higgs boson
properties, particularly Higgs couplings, is a central objective for particle
physics. The anticipated accuracies of Higgs measurements at future Higgs
factories have been extensively studied using Monte Carlo (MC) simulation.
These studies show the SM Higgs decay modes can be measured with a relative
accuracy level of 0.1%–1% at electron-positron Higgs factories An:2018dwb ;
CEPCPhysicsStudyGroup:2022uwl ; Asner:2013psa ; Bernardi:2022hny , surpassing
the expected precision at the future High Luminosity-LHC (HL-LHC) by one order
of magnitude Cepeda:2019klc . Meanwhile, the rare and FCNC hadronic decays of
the Higgs boson are of great interest to many NP models Bejar:2004rz , and
many studies have been conducted accordingly Duarte-Campderros:2018ouv ;
Kamenik:2023ytu ; Albert:2022mpk ; CMS-PAS-SMP-22-006 ; Barducci:2017ioq .

In this letter, we explore the anticipated performance of these hadronic
decays, namely $H\rightarrow s\bar{s},\,u\bar{u},\,d\bar{d}$, and FCNC
hadronic decays encompassing $H\rightarrow sb,\,ds,\,db,\,uc$ at the CEPC
Using the jet origin identification technology introduced above. At the CEPC,
the Higgs bosons are mainly produced via the Higgsstrahlung ($ZH$) and vector
boson fusion ($e^{+}e^{-}\rightarrow\nu_{e}\bar{\nu_{e}}H$,
$e^{+}e^{-}\rightarrow e^{+}e^{-}H$) processes Mo:2015mza . Our analyses focus
on the $\nu\bar{\nu}H$, $\mu^{+}\mu^{-}H$, and $e^{+}e^{-}H$ channels. At the
CEPC nominal Higgs operation, 0.926 million, 0.135 million, and 0.141 million
of $\nu\bar{\nu}H$, $\mu^{+}\mu^{-}H$ and $e^{+}e^{-}H$ events are expected.

We begin with the existing analyses of $H\rightarrow b\bar{b}/c\bar{c}/gg$
Zhu:2022lzv ; Bai:2019qwd . These analyses consist of two stages: first
perform event selection to concentrate the Higgs to di-jet signal, and then
differentiate different flavor combinations using flavor tagging tools. In
this study, we re-optimize the event selections of the first stage and replace
the flavor tagging tool using the jet origin identification method introduced
above. After the event selection, the leading SM backgrounds are mainly
$\ell\bar{\nu}_{\ell}W$, $\nu\bar{\nu}Z$, and $\ell^{+}\ell^{-}Z$ events. To
thoroughly use the information from the jet origin identification using
ParticleNet, we train a gradient boosting decision tree (GBDT) classifier
ke2017lightgbm  that combines all the $22$ confidence scores corresponding to
a pair of jets. The combined scores are then used to discriminate the Higgs
signal and the SM background events.

Figure 5: The distributions of combined scores for signal and SM backgrounds,
where the signals are (upper panel) $H\rightarrow s\bar{s}$ and (lower panel)
$H\rightarrow sb$, respectively, in the $\nu\bar{\nu}H$ process, with CEPC
nominal parameters.

Take the $H\rightarrow s\bar{s}$ analyses for example, we start from the
$\nu\bar{\nu}H$ channel as it has a much larger statistic compared to that of
$\ell\bar{\nu}_{\ell}H$ channels. In the previous analysis of $\nu\bar{\nu}H$
process Zhu:2022lzv , the event selection in the first stage has a signal
efficiency of 34% for $H\rightarrow b\bar{b}/c\bar{c}/gg$, and reduces the
backgrounds by five orders of magnitude, leading to a background statistics of
69k. Since the $H\to s\bar{s}$ analysis has a much smaller signal yield, we
further optimize the cut chain, leading to a signal efficiency of 24% and a
background statistic of 22k. The distribution of combined scores for $H\to
s\bar{s}$ analysis is illustrated in the upper panel of Fig. 5. We define
signal strength as the ratio of the observed branching ratio to the SM
prediction. The anticipated upper limit on the signal strength of
$H\rightarrow s\bar{s}$ at 95% confidence level (CL) Read:2000ru ; Read:2002hq
as a function of cut value is shown in Fig. 5. With the optimal cut on
$\mathcal{S}$, there remain 37 events of $H\rightarrow s\bar{s}$ and 5.1k
background events, and we can set an expected upper limit of 3.8 on the signal
strength for $H\rightarrow s\bar{s}$ at 95% CL. Performing a direct fit to the
combined score distribution yields an upper limit of 3.5 on the signal
strength. Combined data with $e^{+}e^{-}H$ and $\mu^{+}\mu^{-}H$ allows for
reaching an expected upper limit of 3.2 on the signal strength at 95% CL.

In addition to the $H\rightarrow s\bar{s}$ decay, the decays $H\rightarrow
u\bar{u}$ and $H\rightarrow d\bar{d}$ are also analyzed using the same method.
The results are presented in Table 1. By combining all three channels, the
branching ratios of $H\to u\bar{u}$ and $d\bar{d}$ can be constrained to
0.091% and 0.095% at 95% CL, respectively. These results are less precise than
those for $H\to s\bar{s}$, due to the superior tagging performance for the $s$
quark.

We also calculate the expected upper limits on branching ratios for Higgs
hadronic FCNC decays, namely $H\rightarrow sb$, $ds$, $db$, and $uc$. These
decay modes can be limited with upper limits ranging from 0.02% to 0.1%, see
Table 1. The upper limits for the decay modes with heavy flavor final state
jets are superior to those for $H\rightarrow s\bar{s}$ by at least a factor of
two. These superior results are due to the better tagging performance for
heavier quarks and the absence of SM irreducible background.

Table 1:  Summary of background events for $H\rightarrow b\bar{b}/c\bar{c}/gg$, $Z$, and $W$ prior to the flavor-based event selection, along with the expected upper limits on Higgs decay branching ratios at 95% CL. These expectations are derived based on the background-only hypothesis.  |  Bkg. ($10^{3}$) |  Upper limits on Br. ($10^{-3}$)
---|---|---
| $H$ | $Z$ | $W$ | $s\bar{s}$ | $u\bar{u}$ | $d\bar{d}$ | $sb$ | $db$ | $uc$ | $ds$
$\nu\bar{\nu}H$ | 151 | 20 | 2.1 | 0.81 | 0.95 | 0.99 | 0.26 | 0.27 | 0.46 | 0.93
$\mu^{+}\mu^{-}H$ | 50 | 25 | 0 | 2.6 | 3.0 | 3.2 | 0.5 | 0.6 | 1.0 | 3.0
$e^{+}e^{-}H$ | 26 | 16 | 0 | 4.1 | 4.6 | 4.8 | 0.7 | 0.9 | 1.6 | 4.3
Comb. | - | - | - | 0.75 | 0.91 | 0.95 | 0.22 | 0.23 | 0.39 | 0.86
Figure 6: The upper limits on the branching ratios of Higgs rare decays from
this work are shown in green. The relative uncertainties of Higgs couplings
anticipated at the CEPC CEPCPhysicsStudyGroup:2022uwl  are shown in blue, and
those at HL-LHC Cepeda:2019klc  are shown in orange, both with the kappa-0 fit
scenario deBlas:2019rxi  and scenario S2 of systematics DeBlas:2019qco , as
cited in Ref. CEPCPhysicsStudyGroup:2022uwl .

_Discussion and Summary.—_ We propose the concept of jet origin identification
that distinguishes jets generated from 11 types of colored SM particles, by
combining the conventional concepts of jet flavor tagging, jet charge
measurement, gluon-quark distinguish, and s-quark tagging. Using state-of-the-
art deep learning techniques and full simulated samples at CEPC baseline
detector geometry, we demonstrate the jet origin identification performance
using a confusion matrix $M_{11}$. $M_{11}$ shows that jet flavor tagging
efficiencies range from 80% to 91% for heavy quarks and exceed 60% for $s$
quarks and gluon jet identification, and jet charge flip rates vary from 7% to
20% for all species of quarks. The $c$ quark jets have the lowest jet charge
flip rate since $c$ quark is heavy and has twice the absolute charge compared
to down-type quarks.

We analyze the impact of final state particle identification on jet origin
identification and find that charged hadron identification is critical for jet
flavor tagging and jet charge measurement. The identification of neutral kaons
further enhances the jet tagging performance but does not have a significant
impact on jet charge measurement.

Utilizing jet origin identification, we estimate the upper limits for seven
rare Higgs and FCNC hadronic decay modes. We conclude that these decay modes
could be limited to branching ratios of 0.02%–0.1% at 95% CL at CEPC Higgs
operation with an integrated luminosity of 20 ${\rm ab}^{-1}$ and using
$\nu\bar{\nu}H$ and $\ell^{+}\ell^{-}H$ events, see Fig. 6. For the
$H\rightarrow s\bar{s}$ decay, this upper limit corresponds to roughly three
times the SM prediction and improves by a factor of 3 compared to previous
studies Duarte-Campderros:2018ouv ; Albert:2022mpk . The upper limits for
$H\rightarrow u\bar{u}/d\bar{d}$ can be interpreted as $\kappa_{u}<101$ and
$\kappa_{d}<37$, improved by roughly one order of magnitude compared to
existing analyses deBlas:2019rxi . Regarding the Higgs FCNC decay, a Delphes
fast simulation indicates that $H\rightarrow sb/db$ could be limited to
$10^{-2}$ with an integrated luminosity of 30 ${\rm ab}^{-1}$
ILYUSHIN2020114921 , while our results show an improvement by two/one order of
magnitude. We also quantify the upper limits for $H\rightarrow uc$ and
$H\rightarrow ds$. Including the $q\bar{q}H$ channel could further improve
those limits significantly.

Multiple systematic and theoretical uncertainties are relevant to this study,
for example, the detector performance especially its acceptance and stability,
the influence of beam-induced background, the scaling behavior of jet origin
identification performance and jet energy and polar angle, the impact of
different hadronic fragmentation modes and jet clustering algorithms, etc.
Dedicated efforts are needed to profoundly understand and model the behavior
of jet origin identification performance with different conditions. Meanwhile,
we are confident that many of those experimental systematic uncertainties
could be well controlled using huge statistics of di-jet events at CEPC
$Z$-pole operation. Similar analyses could also be performed for FCNC decays
of $Z$ boson, while the relevant experimental systematic uncertainty control
would be much more challenging.

Supported by advanced algorithms and cutting-edge detector technology, we
demonstrate that jet origin identification is feasible and has encouraging
results. We think that jet origin identification will play an increasingly
important role in the exploration of high-energy colliders. In an optimistic
scenario, with future developments in detector technology and advanced
algorithms like ParticleNet, the electron-positron Higgs factories could well
access $g(Hs\bar{s})$ with relative accuracies of $\mathcal{O}(1)$, and could
probably promote jet origin identification performance approaching to that of
particle identification.

_Acknowledgement.—_ We would like to thank Christophe Grojean and Michele
Selvaggi for the delightful discussions, and Gang Li and Congqiao Li for their
support with the software tools. This work is supported by the Innovative
Scientific Program of the Institute of High Energy Physics, the National
Natural Science Foundation of China under grant No. 12042507, and the
Fundamental Research Funds for the Central Universities, Peking University. We
appreciate the Computing Center at the Institute of High Energy Physics for
providing the computing resources.

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