Boosting Invisible Higgs Searches
by Tagging a Gluon Jet for Gluon Fusion Process

Higgs discovery at the LHC in 2012 completed the Standard Model as a description of nature in terms of elementary particles and their interactions (Englert and Brout, 1964; *Higgs:1964ia; *Higgs:1964pj; Aad et al., 2012; *Chatrchyan:2012xdj; *Chatrchyan:2013lba), and the precision measurement of the SM Higgs couplings is one of the most important tasks for probing new physics and the dynamics of electroweak symmetry breaking of the universe at future collider experiments Cheung et al. (2013); *Cepeda:2019klc; *deBlas:2019rxi. However Higgs precision measurements are highly non-trivial tasks in the existence of huge irreducible backgrounds. In particular, production of electroweak vector bosons(EWVBs), such as $W$, $Z$ and $\gamma$, comprise a large portion of the irreducible background. This is because, 1) massive gauge bosons, $Z$ and $W$, are in the mass scales similar with the Higgs, 2) decayed particle contents are the same (or easy to be mis-identified) with the Higgs decays ($H\rightarrow f\bar{f}$), and 3) Higgs also decays to a pair of EWVBs with $BR(H\rightarrow VV)\sim 23\%$.

Among various production mechanism of Higgs at the LHC, Higgs production via gluon fusion (ggH) [(LOinQCD)]Georgi:1977gs; [(NLOinQCD)]Ellis:1987xu; *Dawson:1990zj; *Djouadi:1991tka; *Spira:1995rr has the most dominant contribution ($90\%$) to the total production cross sections. The ggH process is a very unique process in that it can transform between the state of QCD force carriers and electroweak bosons via quark loops, and not leaving any other QCD remnants at leading order (LO), so its event topology can basically be the same with the EWVB productions from the leading orders. In result, tagging the Higgs from gluon fusion has been suffering from the irreducible backgrounds much more than the other sub-dominant productions including vector boson fusion (VBF), Higgsstrahlung (VH), and $t\bar{t}H$, as it does not have associated objects with fixed particle identity good for tagging the whole process.

For this reason the most stringent constraints for probing the Yukawa couplings of Higgs have usually been obtained via the non-ggH processes, e.g. in $H\rightarrow$ $b\bar{b}$ Aaboud et al. (2018a); *Sirunyan:2018koj, $c\bar{c}$ Aaboud et al. (2018b), $\tau^{+}\tau^{-}$ Sirunyan et al. (2019b); *Aaboud:2018pen; *Sirunyan:2017khh, $\mu^{+}\mu^{-}$ Sirunyan et al. (2019c); *Aaboud:2017ojs, $e^{+}e^{-}$ Khachatryan et al. (2015a); *Aad:2019ojw. The same argument also applies to the searches of Higgs pair production via gluon fusion against the EWVB backgrounds, but in this case things can get worse as the dominant ggH contribution increases ($93\%$).

In this paper we revisit and generalize an overlooked property, and investigate a new possibility for boosting Higgs searches via ggH. We focus on the sizeable differences in quark-gluon composition of the central ISR jets between the general ggH productions and their irreducible EWVB backgrounds. Based on such difference, we then show that the tagging the central gluon jets from ISR can provide useful discrimination power to overall Higgs searches. The difference was stated earlier in Choudhury and Roy (1994) without attention, and the new possiblity on the difference was claimed in Lee et al. (2019) for $H\rightarrow\mu\mu$, and studied Kasieczka et al. (2019) for a monojet analysis. As the new method can have big impacts, here we generalize the property for (multiple) Higgs and EWVB productions, emphasizing that in the central region of detector, leading ISR jet from ggH is mostly a gluon jet. To prove its experimental feasibility, then we apply the new method in search for invisible Higgs decays, and show that the limit on the Higgs invisible decay branching ratio can be improved significantly ($60\%\rightarrow 5\%$) for the most dominant gluon fusion, to be the most constraining channel, which has been not so useful compared to the other channels at the LHC.

This paper is composed as the following. In section II, we discuss the dynamics of the ISR from two main processes, gluon fusion Higgs production and massive vector boson production, quantitatively at the leading order, and investigate on the existence of gluon-enriched kinematic region of leading ISR jet from the ggH process. The discussion is generalized by including the case of general Higgs signal production with $n$ Higgs ($\rm ggH^{n}$+jets) and EWVB production ($V^{n}$+jets). In section III we demonstrate the performance of the event classifier based on the ISR jet properties at detector level, in search for invisible Higgs decay. The performances of various discrimination models are compared with in terms of the upper limit of confidence level on invisible Higgs branching ratio in section IV, and section V is devoted to conclusion. Miscellaneous details about multivariate models using deep neural networks and the others are added in Appendix.

In this section, we discuss about the dynamics of ISR at leading order associated with the ggH and EWVB productions at the LHC. Fig. 1 shows the leading diagrams (in bold) of general Higgs signal productions from gluon fusion (ggHⁿ+jets) and EWVB productions (Vⁿ+jets) as irreducible backgrounds with an emission of ISR(s), for three different initial parton configurations ($gq$, $gg$, $q\bar{q}$). Here the $n$ can be larger than one for multi Higgs/EWVB productions, and additional Higgs or EWVB productions with $n\geq 2$ is also represented. The gluon lines in grey indicate extra gluon emissions and the Vⁿ+jets diagram (bottom-center) from $gg$ initial states is drawn also in grey as it is subleading to the other 5 diagrams in $\alpha_{s}$. By the irreducibility we can assume that the particle IDs from the decays of the Higgs and EWVB are the same or very similar.

From the Fig. 1, it should be first noted that the flavor of ISR(s) emitted in the leading diagrams (in bold) are uniquely fixed since the other final state (Hⁿ/Vⁿ) accompanied with is a colorless non-QCD particle in the 2 to (n+1) processes, for the given initial parton configurations. It is also noticeable that the parton luminosity functions, $\mathcal{L}_{gq,gg,q\bar{q}}$ referring to Fig. 2(a), for the three initial partonic states are hierarchical - $\mathcal{L}_{gq}$ $>$ $\mathcal{L}_{gg}$ $\gg$ $\mathcal{L}_{q\bar{q}}$, e.g. $\mathcal{L}_{gq}$:$\mathcal{L}_{gg}$:$\mathcal{L}_{q\bar{q}}$ $\sim$ $2$:$1$:$0.07$ at $\sqrt{\hat{s}}\sim 100$ GeV, and such a hierarchy persists to higher energy scale as shown in the same plot. Based on these two observations, the dominant flavor of leading ISR jet from the whole ggHⁿ+jets and Vⁿ+jets processes can be predicted and their quark-gluon compositions can be compared.

Let us consider the background process, the production of EWVB, first. In $n=1$ case, the differential partonic cross sections in the center-of-mass frame with respect to Mandelstam variable $\hat{t}$ are given as the following for the respective processes, $q\bar{q}\to Vg$ and $gq\to Vq$:

with the number of colors $N_{c}$, the mass of gauge boson $m_{V}$, strong coupling $\alpha_{3}$, vectorial coupling $g^{q}_{V}$, and axial coupling $g^{q}_{A}$ between $V$ and massless quarks $q$, so e.g. for $Z$-boson case, $g^{q}_{V}$ $=$ $\frac{g_{2}}{\cos\theta_{W}}\left(\frac{1}{2}T^{q}_{3}-Q^{q}\sin^{2}\theta_{W}\right)$ and $g^{q}_{A}=\frac{g_{2}}{2\cos\theta_{W}}T^{q}_{3}$. The $T_{F}$(=1/2) and $C_{F}$(=4/3) are Dynkin index and quadratic Casimir of fundamental representation of QCD. Since the matrix elements corresponding to the cross sections have crossing symmetry with each other, so their angular profiles are not so distinctive in the LAB frame even after the integration with parton distribution functions as can be seen in Fig. 2(b).
However their total cross sections become very different considered with the two main scaling factors - 1) different interaction strengths from different initial states, and 2) hierarchical initial parton luminosity function values. As the $q\bar{q}\to Vg$ process is averaged over two quarks, so the amplitude has $\text{tr}(t_{a}t^{a})/N^{2}_{c}$=$C_{F}/N_{c}$ factor with $t_{a}$ as the $SU(3)_{c}$ generators at fundamental representation, while the $gq\to Vq$ process has $\text{tr}(t_{a}t^{a})/(N_{c}(N^{2}_{c}-1))=T_{F}/N_{c}$. Although $T_{F}<C_{F}$, the hierarchically larger parton luminosity function of $gq$, $\mathcal{L}(gq)$ compared to $\mathcal{L}(q\bar{q})$, makes the hadronic total cross section $\sigma(pp\to Vq)$ much bigger than the $\sigma(pp\to Vg)$ by $\mathcal{O}(10)$ at the LHC.
This property can be generalized also for V${}^{n}(\geq 2)$+jets processes, and in result the leading ISR jet is expected most likely to be a quark jet for general EWVB processes. As a demonstration of the quark jet portion dominance, we checked gluon jet portions, $R^{g}$, of the leading ISR ($|\eta^{j_{1}}|\leq 1$ and $p^{j_{1}}_{T}$ $>100$ GeV) in various EWVB processes, and they are found to be (1) $R^{g}_{(WW,\,WZ,\,ZZ)}$ $\approx$ ($0.20$,$0.16$,$0.30$) for Vⁿ⁼²+jets processes, (2) $R^{g}_{(W,Z)}$ $\approx$ ($0.13$,$0.19)$) for Vⁿ⁼¹+jets, and (3) $R^{g}_{\gamma\gamma}$ $\approx$ $0.15$ for prompt di-photon+jet processes, as in Fig. 3.

For the ggH signal, since $\mathcal{L}_{q\bar{q}}$ is much smaller than the others, $q\bar{q}\to Hg$ process can be ignored for the estimation. Relevant partonic differential cross sections, $d\hat{\sigma}_{Hq}/d\hat{t}$ from $gq\to Hq$ and $\hat{\sigma}_{Hg}/d\hat{t}$ from $gg\to Hg$ process, computed at NLO with massless five quarks and finite top-mass effect, are given Ellis et al. (1988); *Dawson:1990zj; *Djouadi:1991tka; *Spira:1995rr as the following:

Here $m_{H}$ is mass of Higgs, and $C_{A}$ is quadratic Casimir of adjoint representation of $SU(3)_{c}$ so that $C_{A}=N^{2}_{c}-1$ is 8. $A_{2}$, $A_{4}$ and $A_{5}$ are loop functions of which definitions are in Appendix A. From $\mathcal{L}_{gg}<\mathcal{L}_{gq}$, one may think that the hadronic cross section $\sigma(pp\to Hq)$ is larger than the other one, $\sigma(pp\to Hg)$, but there is a difference in associated color factors. It makes $C_{A}/C_{F}=9/4$ enhancement on $\sigma(pp\to Hg)$, and two cross sections are compatible with each other. Therefore the quark-gluon portion of leading ISR jet can highly depend on the dynamics of the leading ISR from the two dominant signal processes, especialy on their transverse momentum and angular distributions.
To understand the differences on the $p_{T}$ profiles of the two processes, let’s consider the infinite-top-mass ($m_{t}\to\infty$) limit. This limit is safe as long as $|\hat{s}-m^{2}_{H}|/(4m^{2}_{t})\lesssim 1$, with mass of top-quark, $m_{t}$. In this limit, loop functions are approximated as

and

also for all the other permuted arguments. The effective differential cross sections, $d\hat{\sigma}^{\rm HEFT}_{Hg}/d\hat{t}$ and $d\hat{\sigma}^{\rm HEFT}_{Hq}/d\hat{t}$ are

Note that, each Mandelstam variable at the lowest order of transverse momentum $p_{T}$ is given by, $\hat{s}\simeq m^{2}_{H}$,

where $\Delta y\equiv y_{b}-y_{j}$ is the rapidity difference of the two initial parton system ($y_{b}$) and the jet ($y_{j}$) in the LAB frame. Therefore,

which implies that a gluonic leading ISR jet is likely to have softer $p_{T}$ than a quark ISR jet.
The angular dependence can also be figured out by considering $s$-wave scattering of two processes. If the orbital angular momentum is zero, the spin of outgoing gluon should be aligned along the direction perpendicular to the beam, otherwise the total angular momentum is not conserved. However, the outgoing quark is likely to be backward to the incoming quark for angular momentum conservation in $gq\to Hq$. Then, combined with the balanced momentum profile of the initial $gg$ state at the LHC, the gluon jets are likely to be emitted more in central rapidity region with soft $p_{T}$, in comparison to the quark jet as can be seen in Fig. 2(c).

Like as the two quark jets in forward region from the VBF, and as the extra Z/W from the VH, now the ggHⁿ + jets also has such a unique property accompanied - the gluon-like ISR jets in central region. In this regard, if some relevant techniques using quark-gluon tagging of ISR jets are employed, one can improve the constraints from the most dominant gluon fusion channel for a broad range of Higgs signatures which are buried in the irreducible EWVB backgrounds matched with.

In order to demonstrate experimental feasibility, here we utilize the gluonic ISR jet from the ggH for constraining invisible decays of Higgs where the decayed particles from the Higgs and irreducible EWVB are electrically neutral and invisible. Historically, there had been lots of studies on the possibility of invisible Higgs decays along the developements of the Standard Model and the beyonds. The early proposals include the models in diversity e.g. with MajoronsChikashige et al. (1981); *Gelmini:1980re; Shrock and Suzuki (1982); *Li:1985hy; *Jungman:1991sh; *Joshipura:1992ua; *Joshipura:1992hp, supersymmetries Griest and Haber (1988); *Gunion:1988yc; *Romao:1992zx; *deCampos:1995ten; *Djouadi:1996mj; *Djouadi:1997gw; *Belanger:2001am; *Hirsch:2004rw; *Antoniadis:2004se; *Chang:2005ht; *Draper:2010ew; *Cao:2012im; *Butter:2015fqa; *Barman:2017swy; *Wang:2020dtb; *Barman:2020vzm, heavy neutrinos with radiatively generated masses Pilaftsis (1992), large extra dimensions Arkani-Hamed et al. (1998); Dienes et al. (1999); *ArkaniHamed:1998vp; *Giudice:2000av; *Battaglia:2004js; *Datta:2004jg; *Dominici:2009pq, the 4th generations Fargion et al. (1999); *Khoze:2001ug; *Belotsky:2002ym; Belotsky et al. (2004); Frere et al. (2006); *Kribs:2007nz; *Eberhardt:2012sb, and so on, while the recent interpretations are mainly based on the effective singlet extensions of the SM, in the context of so-called Higgs-portal models with dark mattersSilveira and Zee (1985); *Krasnikov:1992zk; *McDonald:1993ex; *Binoth:1996au; *Datta:1997fx; *Burgess:2000yq; *Bento:2001yk Davoudiasl et al. (2005a); *Schabinger:2005ei; *Barbieri:2005ri; *Patt:2006fw; *Cerdeno:2006ha; *OConnell:2006rsp; *Kim:2006af; *BahatTreidel:2006kx; *Barger:2007im; *Bertolami:2007wb; *Kim:2008pp; *Barger:2008jx; *Gonderinger:2009jp; *Cheung:2009wb; *He:2009yd; *Andreas:2010dz; *Kanemura:2010sh; *Englert:2011yb; *Raidal:2011xk; *He:2011de; *Pospelov:2011yp; *Lebedev:2011iq; *Baek:2011aa; *Drozd:2011aa; *Djouadi:2011aa; *Batell:2011pz; *He:2011gc; *Kamenik:2012hn Djouadi et al. (2013); Cline et al. (2013); *deSimone:2014pda; *Baek:2014jga; *Feng:2014vea; *Beniwal:2015sdl; *Han:2016gyy; *Dupuis:2016fda; *Arcadi:2019lka. For these proposals, there exist numerous phenomenological and experimental researches in search for the invisible Higgs decays, via the production channels, including VH Choudhury and Roy (1994); Frederiksen et al. (1994); Davoudiasl et al. (2005b); *Martin:1999qf; *Godbole:2003it; Englert et al. (2012a); Bai et al. (2012); Ghosh et al. (2013); Carpenter et al. (2013); *Goncalves:2016bkl; *Goncalves:2018ptp Aad et al. (2014a); *Aad:2014iia; *Aad:2014vka; *Aad:2015uga; *CMS:2016pps; *Aaboud:2017bja; *Aaboud:2018xdl; Khachatryan et al. (2017); Sirunyan et al. (2018b); Chatrchyan et al. (2014); ATL (2018); Aaboud et al. (2019b), $t\bar{t}H$ Gunion (1994) Choudhury and Roy (1994); Kersevan et al. (2003); *Malawski:2004kg; *Zhou:2014dba; *Craig:2015jba; *Buckley:2015ctj CMS (2019), ggH (monojet) Choudhury and Roy (1994); Davoudiasl et al. (2005b); Fox et al. (2012); Englert et al. (2012a); Bai et al. (2012); Djouadi et al. (2013); Barducci et al. (2017) Chatrchyan et al. (2011); *Aad:2011xw; *Aaltonen:2012jb; *Chatrchyan:2012me; *ATLAS:2012zim; *ATLAS:2012ky; *Khachatryan:2014rra; *Aad:2015zva; *Aaboud:2016tnv; *Sirunyan:2017hci; Khachatryan et al. (2017); Sirunyan et al. (2018b), and VBF Eboli and Zeppenfeld (2000) Davoudiasl et al. (2005b); Bai et al. (2012); Ghosh et al. (2013); Bernaciak et al. (2015); *Goncalves:2017gzy; *Biekotter:2017gyu; *Heisig:2019vcj Di Girolamo and Neukermans (2002); *Aad:2015txa; *Aad:2015pla; *CMS:2016jjx; *Aaboud:2018sfi; *ATLAS:2020cjb; Khachatryan et al. (2017); Chatrchyan et al. (2014); ATL (2018); Sirunyan et al. (2019d); Aaboud et al. (2019b) which has been presented the most sensitive limits on the invisible Higgs decay BR at the LHC. There also have been interesting surveys via diffractive Higgs productions Belotsky et al. (2004), total decay width Low et al. (2012), Higgs rare B decays Kim et al. (2010), di-Higgs Banerjee et al. (2017); *Englert:2019eyl, Higgs off-shell decays Endo and Takaesu (2015); *Craig:2014lda; *Ruhdorfer:2019utl, lepton colliders Eboli et al. (1994); *Searches:2001ab; *Abdallah:2003ry; *Djouadi:2007ik; *Kanemura:2011nm; *Baer:2013cma; *Moortgat-Picka:2015yla; *Kato:2020pyl; *Tang:2015uha, including global analysis Englert et al. (2012b); *Espinosa:2012vu; *Belanger:2013kya; *Bechtle:2013wla; *Curtin:2013fra; *Corbett:2015ksa; *Athron:2018hpc; *Arina:2019tib. Throughout the searches, the dominant $ggH$ channel has never been competitive to the other sub-dominant channels. However, employing the new method we show that the most stringent constraint can be obtained from the ggH channel for the invisible Higgs decays, as is demonstrated in the next paragraphs.

Assuming the Higgs production cross section of the SM, we perform the analysis in search for the invisible Higgs decays in $E_{T}^{\text{miss}}$+jets signature via the ggH+jets channel. Samples are generated by Monte Carlo simulated pp collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV at the LHC, for 36 fb^-1 using MadGraph5 aMC@NLO v2.6.2 Alwall et al. (2014) interfaced with Pythia v8.235 Sjöstrand et al. (2015) for hadronisation and fragmentation. Delphes v.3.4.1 is used for detector simulation de Favereau et al. (2014). The signal process (ggH+jets) is generated with up to extra 1 jet at LO taking into account finite top mass effects Hirschi and Mattelaer (2015) with $M_{H}=125$ GeV, and backgrounds are generated at NLO in QCD. We use FxFx scheme with $k_{T}$-algorithm and $\Delta R=1$ for jet merging Frederix and Frixione (2012). For jet clustering, FastJet v3.2.1 Cacciari et al. (2012) is used with anti-$k_{T}$ algorithm with $\Delta R=0.4$, and CT10NLO Lai et al. (2010) is used for parton distribution function.

Among the relevant background processes - $V(Z(\nu\nu)$, $W(\ell\bar{\nu}))$+jets, Diboson, top quarks, $Z/\gamma\rightarrow\ell\bar{\ell}$, QCD multijets, where the leptons ($\ell$) in $W/Z/\gamma$ decays are mis-identified, we only included the most dominant irreducible EWVB backgrounds - $V$+jets, while the others take just $O(1)\%$ level for the event selection criteria as follows [(e.g.seeTable.7andFig.5)]Khachatryan:2016whc:

• •

  $p^{j_{1}}_{T}>100\text{GeV}$, $|\eta^{j_{1}}|<2.5$, $E^{\text{miss}}_{T}>200\text{GeV}$, $\min_{j\in\{\text{jets}\}}\Delta\phi(\vec{p}^{\;\text{miss}}_{T},\vec{p}^{\;j}_{T})\geq 0.5$, $N_{\text{jet}}\geq 1$.

The 1st (2nd) cut on the transverse momentum (pseudorapidity) of the leading jet is imposed to suppress all of the backgrounds, the 3rd cut on the missing transverse energy is mainly to reduce the QCD and top quarks, and the 4th cut with the missing transverse momentum, $\vec{p}_{T}^{\;\text{miss}}$ suppresses the QCD multijets very efficiently Sirunyan et al. (2018b).

There also exist contributions from other Higgs productions, VBF and VH with yield rates (ggH:VBF:VH $\sim$ 70:20:10$\%$). However as the leading jets from VBH are most likely quark jets opposed to the gluonic leading jets in the ggH+jets, we checked that the VBF can be easily separated (see Appendix. C) from the ggH+jets by tagging gluonic central leading jet in addition to the forward jet tagging for VBF. As for the VH which also has quark jet like leading ISRs according to the same argument with the V+jets, it can have additional selection criteria (Ellis et al., 2010; Thaler and Van Tilburg, 2011) for identifying jets from hadronically decaying vector bosons. In this regard, to demonstrate the main idea without making event selection scheme too complicated, we simply consider the ggH+jets as the only signal versus the V+jets as the main background in this analysis, without loss of consistency in applying the flavor information for discrimination of gluon-jet rich ggH signal from general quark-jet rich backgrounds.

We use a set of jet substructure variables Larkoski et al. (2020), say $S^{\,\text{jet}}$, in our analysis as the following,

• •

  $S^{\,\text{jet}}$ $\equiv$ $\{$ $n_{\text{tk}}$ (track multiplicity) Gallicchio and Schwartz (2011), Girth Gallicchio et al. (2011); Gallicchio and Schwartz (2011), Broadening Catani et al. (1992), EEC (energy-energy correlation) (Bhattacherjee et al., 2017) with $\beta=0.2$ Larkoski et al. (2013), RMS-$p_{T}$ Gallicchio and Schwartz (2011) $\}$,

which contain the information on jet flavors. It can also be extended to include more raw data, e.g. jet images Komiske et al. (2017); Cogan et al. (2015) for deep learning. Among the five jet substructure variables used, the Girth as the linear radial moment of a jet reflects a fatness/radius of a jet. As gluon jets tend to have more showers and be fatter by the color factor enhancement, $C_{A}$($g\to gg)/C_{F}$($q\to gq$), such a property can be checked in the Girth distribution of the leading jet from ggH and V+jet processes in Fig. 4(b).

Jet substructure observables have been used to build a jet tagger, $\text{P}_{q/g}(S^{\,\text{jet}})$, while the kinematic observables, such as reconstructed four-momenta of jets have been used to build an event classifier, $\text{P}_{\text{S/B}}(\{p^{\,\text{jet}},...\})$. However, as can be seen from $d^{2}\sigma/dp^{\,\text{jet}}_{T}dy^{\,\text{jet}}$ in Fig. 2(c), the flavor of a jet can have a correlation with kinematic information depending on the scattering process. This observation motivates us to build $\text{P}_{\text{S/B}}(\{p^{\,\text{jet}},...\}\cup S^{\,\text{jet}})$, rather than a factorized classifier, $\text{P}_{\text{S/B}}(\{p^{\,\text{jet}},...\})\otimes\text{P}_{q/g}(S^{\,\text{jet}})$.

For S (B) $=$ ggH (V+jets) process, Fig. 4 shows the normalized distribution of (a) $E_{T}^{\text{miss}}$, (b) Girth, (c) $\text{P}_{\text{S/B}}(S^{\,\text{jet}})$, and (d) $\text{P}_{\text{S/B}}$ $(S^{\,\text{jet}}\cup$ $\{E_{T}^{\text{miss}},$ $p_{T}^{\,\text{jet}},$ $\eta^{\,\text{jet}}\})$. The two event classifiers $\text{P}_{\text{S/B}}$ in Fig. 4(c) and 4(d) are obtained by training neural networks with 2-4 layers each with 200-300 nodes with the specified input features. We used one million event samples with Keras Chollet et al. (2015) for building and training the neural network models. More detailed information about using neural network can be found in Appendix. B. It is noticeable that the event classifier using the set of jet substructures alone can provide much better separation of signal and background compared to the one $E_{T}^{\text{miss}}$ as in Fig. 4(c). Combining them all we get the best separation as is clearly seen in Fig. 4(d).

The result obtained up to now can be used to discover invisible Higgs decay or put constraints on the invisible branching ratio of Higgs. After selecting the events with the criteria, we performed the profile likelihood ratio test following the procedure in ATL (2011) with the four template distributions in Fig. 4. The likelihood function is given,

where $n_{i}$ is the number of events (or pseudo events) in $i$-th bin, and $\hat{n}_{i}$ is the number of expected events with branching ratio parameter $\mu=\frac{\sigma}{\sigma_{\rm{SM}}}\times BR(h\to\rm{inv})$ (production x-section of invisibly decaying Higgs over the total x-section of the SM Higgs - $\sigma_{\rm{SM}}$), i.e.,

Here the $P_{s(b)}(i)$ is the expected event rate in $i$-th bin, given the total number of events $N_{s(b)}$ survived the cut, and the $\theta_{s(b)}$ in the Poisson and prior probabilities denotes a nuisance parameter associated to the systematic uncertainty $f_{s(b)}$, of signal (background). As a global variation of event rates in signal and background distributions, we tested the $f_{s(b)}$ in 5-20% Khachatryan et al. (2017), which changes median of expected upper limit in their 3% at most, and set $f_{s(b)}$ to 10%. Signal cross section (ggH+X) is taken from de Florian et al. (2016) computed at NNLO+NNLL QCD and NLO EW, and we applied the efficiency on the selection criteria evaluated using simulated event samples, for the fiducial signal yield. For the background process (V+jets) we take both of the cross section and efficiency from our MC simulation of the $Z$+jets, and the fiducial background yield was obtained by a K-factor (1.53) with respect to the $Z$+jet, to take the $W$+jets into account simply, reproducing the expected limit using missing transverse energy [(e.g.seeTable.4)]Sirunyan:2017jix.

For the four profile likelihood ratio tests with/without the new features of jet flavors (‘Missing $E_{T}$’, ‘Girth’, ‘jet substructure variables’, and ‘All variables’), we obtained the upper limits on the branching ratio of invisible Higgs decays in 95% of confidence level, for the integrated luminosity 36 $\rm{fb}^{-1}$ at the LHC, as in Fig. 5 (right panel), and show them with the existing experimental results (left panel) Sirunyan et al. (2019d) - ‘ggH-tag’, ‘VBF-tag’, and ‘combined’, which did not use jet flavor information. As the results in the two red-boxed columns can directly be compared with under the same features and selection criteria, we summarize our results in Table 1 with the errors rescaled by the correction factors projecting the obtained ‘Missing $E_{T}$’ band to the reference ‘ggH-tag’ band. The result shows that the limit on Higgs invisible decays from the ggH can significantly be improved from $60\%$ down to $5\%$ if sub-jet level information of the leading ISR is employed. It is interesting that the jet substructures alone provides stronger constraints ($8\%$) than the missing transverse energy in Higgs invisible search. Moreover, combining the features in two kinds, we end up with the best sensitive result ($5\%$) only from the ggH, much lower than the one obtained from VBF ($\sim 20\%$).

Though more sophisticated understanding and treatment of systematic errors are necessary to obtain a firm number for the expected limit on the Higgs invisible decays, the exercise we did in this paper strongly suggests that 1% (2%) precision for Higgs invisible branching ratio at the end of the LHC running with 3 $\rm{ab}^{-1}$ (300 $\rm{fb}^{-1}$) is a plausible expectation from the gluon fusion solely. It is also expected that the limit can significantly be improved again if it is combined with the results from VBF and other processes.

We revisited and generalized the property - the gluon rich leading ISR jets in central rapidity region from gluon fusion Higgs productions versus the quark rich EWVB backgrounds, and proposed the idea to improve general Higgs searches produced from ggH by tagging the central gluonic ISR jets. Applying the new method to the searches of invisible decays of Higgs, we showed that the ggH can be the best channel with the improved limit on invisible Higgs decay branching ratio ($60\%\rightarrow 5\%$), significantly exceeding the best limit given by the other channels - VBF ($\sim 20\%$) and VH ($\sim 40\%$). The physics and methods in this analysis can also be applied to a broad range of new resonance and Higgs productions induced by gluon fusion, e.g. in search for exotic/rare Higgs decays and di-Higgs productions, concurrently with their irreducible EWVB backgrounds mostly containing quark jet dominant ISRs.