Heavy Neutrino Searches via Same-sign Lepton Pairs at the Higgs Factory
HHeavy Neutrino Searches via Same-sign Lepton Pairs at the Higgs Factory
Yu Gao ∗ and Kechen Wang † Key Laboratory of Particle Astrophysics, Institute of High Energy Physics,Chinese Academy of Sciences, Beijing, 100049, China and Department of Physics, School of Science, Wuhan University of Technology, 430070 Wuhan, Hubei, China
This paper investigates the e + e − → Zh sensitivity for Higgs boson’s rare decay into heavy neutri-nos h → NN at the proposed electron-positron collider, with the focus on multi-lepton final statesthat contain same-sign lepton pairs. h → NN decay can derive from Higgs boson’s mixing with newphysics scalar(s) that is complementary to the contribution from active-sterile neutrino mixings. Weanalyze the semileptonic, fully leptonic and mixed NN decay scenarios, and categorize the signalon the number of leptons in the final state: (cid:96) ± (cid:96) ± plus ≥ j , (cid:96) ± (cid:96) ± (cid:96) plus ≥ j , and e ± e ± µ ∓ µ ∓ plus ≥ j , each containing one or two same-sign dilepton system(s). Selection cuts are optimized forthe presence of the associated Z boson, which leads to additional backgrounds at the e + e − collider.The limits on h → NN branching fractions are derived for signals with 2-4 final leptons assumingthe heavy neutrino masses are between 10 and 60 GeV. With 240 GeV center-of-mass energy and5.6 ab − design luminosity, h → NN branching fraction can be probed to fraction to 2 × − in 2 (cid:96) and 3 (cid:96) channels, and 6 × − in the 4 (cid:96) channel at 95% credence level. 3 (cid:96), (cid:96) channels expect oneor fewer background event, and their sensitivities saturate the statistic limit at 5.6 ab − luminosity.A same-sign trilepton ( (cid:96) ± (cid:96) ± (cid:96) ± ) signal in the 3 (cid:96) channel is also discussed. I. INTRODUCTION
The collider search for massive neutrinos plays an im-portant role in the testing of neutrino mass models thatbase on the seesaw mechanism [1–5]. Mass of the activeneutrino ν is generating by mixing the left-handed neu-trino ( ν L ) of the Standard Model (SM) to the additionalright-handed neutrino N R , resulting in a heavy masseigenstate N that has a small SM ν L component. Theheavy N acquires effective couplings to the SM modelgauge bosons via its weakly charged ν L component [6]and is extensively searched at colliders, see Ref. [7–9] forrecent experimental limits.While a heavy N R mass scale explains the tiny ac-tive neutrino mass, it also suppresses the left-right neu-trino mixing, and makes weak production of heavy neu-trinos difficult in models with small mixings | V (cid:96)N | ∼O ( m ν /m N ). Alternatively, heavy neutrinos can alsobe produced in case they couple to Beyond the Stan-dard Model (BSM) mediators, e.g. extra gauge bosonsor scalars that couple to SM particles. Currently,BSM gauge bosons are stringently constrained by heavyresonance searches [10, 11] and electroweak precisiondata [12, 13]. In comparison, BSM singlet scalar mix-ing with the Higgs boson is less constrained [14], as itis among the major physics goals of future Higgs facto-ries [15, 16].The right-handed neutrino can obtain its mass by cou-pling to BSM scalars with a non-zero vacuum expecta-tion value (vev). Generally such scalars mix with theSM Higgs doublet scalar, so if kinematically allowed,the physical Higgs boson can decay into heavy neutri-nos through its BSM component. As this decay occurs ∗ [email protected] † [email protected] directly through scalar mixing, it is relatively insensi-tive to ν L − N R mixing, and is complementary to | V (cid:96)N | based searches. Typical implementations involve extend-ing the SM’s scalar sector, either as an low-energy ef-fective model, or from UV-complete models such as left-right symmetric models [17], U (1) B − L models [3], nextto minimal supersymmetric model [18], etc.When the Higgs boson decay into heavy neutrinos h → N N , a multi-lepton Higgs rare decay emerges. N can decay to a SM final state through its ν L compo-nent’s weak interaction. The fully leptonic N → (cid:96)(cid:96) (cid:48) ¯ ν andsemileptonic N → (cid:96)jj channels are interesting at collidersearches due to the presence of measurable charged lep-tons in the final state. When N is a Majorana fermion,semileptonic N N decay leads to the characteristic lepton-number violating (LNV) same-sign (SS) dilepton, as re-cently studied as a LNV probe for Higgs-BSM scalar mix-ing [19–22] and supersymmetric scenario [22]. Fully lep-tonic N decay allows up to two pairs of same-sign same-flavor (SSSF) dileptons in different flavors for either Ma-jorana or Dirac N [23].Increased lepton multiplicity and the existence of SSlepton pairs greatly reduce SM background contamina-tion in collider searches, particularly for strong inter-action dominated hadron collisions. At lepton collid-ers, in comparison, hadronic backgrounds are control-lable and the dominant Higgs boson production is in the e + e − → hZ channel. An associated Z boson appears andit provides additional lepton or jets to the final state.Thus it is of interest to study the sensitivity on multi-lepton h → N N searches at future lepton colliders. Alsonote that any decay limit would be statistically cappedby the collider’s luminosity-inverse. The proposed leptoncollider missions, e.g. the CEPC [24], ILC [25] and FCC-ee [26], are currently designed to yield O (10 − ) Higgsevents. Study of the multi-lepton signal and the rel-evant backgrounds helps understanding whether future a r X i v : . [ h e p - ph ] F e b h → N N sensitivity would saturate luminosity limits.This paper is organized as follows: Section II brieflydiscusses a minimal singlet extension to the SM that im-plements the h → N N decay channel. Section III to Vcategorize signal channels on the number of final stateleptons, analyze each channel’s SM background and theevent selection strategies. In Section VI we give the sen-sitivity limits at future Higgs factory.
II. MODEL SETUP
For collider search purposes, we adopt the minimal ef-fective extension to the Standard Model that implementsa Type-I seesaw mechanism. With a scalar S and Ma-jorana fermion N R that are both SM gauge singlets, theaddition to interaction Lagrangian is given by,∆ L⊃ y D ¯ LHN R + y S SN R N R + c.c. + λ | H | | S | + V S . (1)where y D and y S are the couplings that give the Diracand Majorana mass terms after the SM Higgs doublet H and the singlet S obtain vacuum expectation values(vevs). The new scalar potential involves H, S mixingterm and S self-interacting terms. Given a small massterm λv S v H (cid:28) m h , V S minimization does not qualita-tively impact the SM electroweak sector. The scalars mixby a small angle α , (cid:18) h h (cid:19) = (cid:18) cos α − sin α sin α cos α (cid:19) (cid:18) hs (cid:19) . (2)where h, s represent the Higgs doublet and singlet modesaround their vevs. h , h are the physical mass eigen-states, with h dominated by h and it identifies with the125 GeV boson. h is singlet s dominated and it picksup a weakly charged h component via mixing. h is sub-ject to diphoton resonance searches [27, 28] and its massrange is less stringently constrained when the mixing an-gle is small, α = λv H v S | m s − m h | , (3)where m s and m h are the singlet and Higgs doubletmasses. In the H − S small-mixing limit ( λ → | m s − m h | ∼| m h − m h + O (sin α ) | if the scalars are not mass-degenerate. Interestingly, if h resides in the mass win-dow 2 m N < m h < E COM − m Z , production of Zh iskinematically viable and h → N N decay can also con-tribute significantly to the signal. However, it would alsorequire m h to be comparable to the Higgs boson’s masswhen the center-of-mass energy E COM is limited, particu-larly so if e + e − energy just above the Zh threshold at theHiggs factory. In this work, we assume m S to be gener-ally heavier than this mass window and only focus on h production. Also note that a very light singlet scalar sce-nario m S (cid:28) m H is possible: it which requires a shallow V ( S ) with v S above the weak scale so that m N R ∼ y N v S with y N ≤ O (1) still gives a massive N heavy enough todecay inside the detectors. uul − ¯ d ¯ dl − h NNe − e + Z q ¯ q ′ ννµ − e + e + µ − h NNe − e + Z q ¯ q ′ νuµ − e + ¯ d ′ µ − h NNe − e + Z q ¯ q ′ FIG. 1. Illustrative processes of SS dilepton production fromsemileptonic (upper left), leptonic (upper right) and mixed(lower) decays of the NN system. Note the leptonic andmixed decay scenarios also produce SS dileptons withoutLNV [23]. Unlike Higgs production in pp collision where gluonfusion dominates, the leading production channel in e + e − collision is through s -channel Z with an associated finalstate Z boson, as shown in Fig. 1. The h → N N systemleads to the characteristic rare Higgs decay signals withSS lepton pair(s). Here we do not consider the h → N ν channel [29] as its branching fraction relies on | V (cid:96)N | .The Z boson can decay to a lepton or jet pair and theirinvariant mass reconstructs to m Z . For signal selection,visible decays of the Z boson are favorable as they would:(i) demand SM background to be also companied byone additional Z boson;(ii) remove potential lepton number uncertainty fromneutrinos in case LFV is required in the final state.The h → N N branching fraction is proportional tosin α . In Higgs rare decay searches we would assume m N < m h / h → N N are not furthervirtuality-suppressed. N decays through its ν L compo-nent thus its decay width is | V (cid:96)N | suppressed. N → (cid:96)W ∗ is the dominant N decay channel, its hadronic and lep-tonic W ∗ → jj, (cid:96)ν decays lead to ‘semileptonic’ and‘fully-leptonic’ final states, see [23] for branching fractioncalculations. The N → νh ∗ , νZ ∗ channels are subleadingand they require missing or wrong-sign leptons to formSS dileptons.A major SM background consists of τ -lepton or on-shell W boson decays, where the W (cid:96)ν vertex can coupleto any lepton flavor. Same-sign and same-flavor dileptonrequires the presence of same-sign τ or W pairs, chargeconservation would demand four W ( ∗ ) (cid:96)ν vertices in a SMfinal state. Same-sign, different flavor dileptons can risefrom lepton pair production from neutral bosons, whichcan be vetoed by lepton flavor cuts. Another backgroundrises from wrong-sign leptons or missed leptons that canbe controlled by stringent lepton cuts in event analysis.The following sections will discuss the backgrounds foreach channel.In a final state with three or more leptons, opposite-sign same-flavor (OSSF) lepton pair should be vetoed tosuppress the SM background, which also means that atleast one SSSF lepton pair will be selected. For somesignal processes this requires N couple to more than onelepton flavor, and we would assume N couples equally toboth e and µ flavors in our analyses.We perform cut-and-count analyses on Monte-Carlosimulated signal and background events. Eventsare generated by MadGraph5 [30] and showered byPythia8 [31, 32] package. τ lepton decays are handledby TAUOLA [33] as is implemented in Pythia8. e − e + detector simulation is performed by DELPHES [34] withCEPC parametrization [35]. At event generation level weadopt jet cuts η ( j ) < . , p T ( j ) >
20 GeV and use rel-atively lenient lepton cuts η ( (cid:96) ) < . , p T ( (cid:96) ) > . R ( j, j ) , ∆ R ( (cid:96), (cid:96) ) > . III. TWO LEPTON CHANNEL
The h → N N → (cid:96) ± (cid:96) ± + 4 j, (cid:96) = e, µ channel re-quires both N decay to a charged lepton and two jets( W ∗ → ¯ qq (cid:48) ) and one of the N s decays as its own antipar-ticle. This final state has no missing energy and violateslepton number with ∆ L = 2, and it is often consideredthe ‘smoking-gun’ channel of the heavy Majorana neu-trino search with explicit LNV.Note in this channel N N decays to four jets. Unlike be-ing easily contaminated in pp collision, the much cleanerenvironment in e + e − collision is largely free of fake lep-tons from soft jets. However, due to the small energy capbetween the Higgs boson and heavy neutrino, these thefour jets are relatively soft and can be difficult to fullyreconstruct. With fewer jet counting, wrong-sign andunreconstructed leptons become possible backgrounds, inaddition to intrinsic multiple- τ, W backgrounds. The rel-evant background channels are listed in Table I.The background channels contain two or more τ lep-tons or light charged lepton (cid:96) = e, µ , plus Z or W + W − that yield dijet resonance near Z mass. The particle signsare omitted and any even number of τ, (cid:96) and W entriesmust include equal number of opposite-sign particles, e.g.4 τ denote for 2 τ + τ − , and 2 (cid:96) W for (cid:96) + (cid:96) − W + W − , etc.While the SM backgrounds (cid:96)(cid:96) restrict to same-flavor, op-posite sign lepton pairs, leptonic W decay can provideone additional lepton and create a like-sign dilepton com-bination in case one lepton are un-detected. Such chan-nels are marked with † in the table. The signal event contains one SS dilepton, two jetsfrom Z decay and a number of soft jets, plus very littlemissing energy. We select hadronic Z decay by impos-ing charged lepton number N ( (cid:96) ) = 2 to avoid confusionbetween the leptons from Z and those from N N decay.With a jet transverse momentum requirement p T ( j ) > N N system are not alwaysidentifiable, especially when the jets are more collimatedif N is light and relatively boosted. Still, having at leastone extra jet in addition to those from Z can be effectivein background rejection, so we consider an jet countingcut N ( j ) ≥ N ( (cid:96) ) = 2 with p T ( (cid:96) ) > τ leptons, N ( τ ) = 0;(iv) at least three jets, N ( j ) ≥ /E T <
15 GeV.
FIG. 2. Normalized distribution of selected kinematic vari-ables to differentiate signals from the total SM backgroundfor the 2 (cid:96) channel. p T ( (cid:96) ) panels are after selecting N ( l ) = 2, N ( j ) is after cut (ii), /E T , p T ( j ) panels are after cut (iv). The histograms of a few crucial kinetic observables forthe signal with different m N and the total backgroundare shown in Fig. 2. p T ( (cid:96) ) and p T ( (cid:96) ) correspond tothe samples after requiring N ( (cid:96) ) = 2; N ( j ) are afterselecting cuts(i-ii); /E T , p T ( j ) , p T ( j ) are after requiringcuts(i-iv). These distributions illustrate the effectivenessof our selection cuts. The N ( j ) cut can be very effectivein background rejection, and we select N ( j ) ≥ t -quark contamination is not a problem in e + e − collision, b -jet veto is not included; τ veto is still helpfulin removing multi- τ background events. The expected initial cuts(i-ii) cuts(iii-iv) cuts(v)Sig. 10 GeV 10
112 37.4 28.860 GeV 10
121 40.5 30.2Bkg. 4 τ . ×
870 4 . × − . × − † τ Z . × . × † (cid:96)Z . × . × - -4 τ Z . × − τ W . × . × − † (cid:96) τ Z
584 13.8 2.0 0.75 † (cid:96)Z
862 16.5 2.2 2.1 † (cid:96) W . ×
639 11.7 1.2TABLE I. The expected number of signal and backgroundevents for the 2 (cid:96) channel at future e + e − collider with √ s =240 GeV and 5.6 ab − integrated luminosity. Signal ratesassume a benchmark branching fraction BR( h → NN ) =9 . × − . Background channels marked with † require wrongsign or missing leptons. Non-numeric dashes denote for eventnumbers below 10 − . number of events at different cut stages for signal andbackground channels are listed in Table I. The bench-mark branching fraction BR( h → N N ) is chosen to be9 . × − , so that the pre-cut (‘initial’) signal event rateis around 10 and the signal cut efficiencies can be con-veniently converted. The expected signal event number N s with selection cuts can be calculated from Eq. 4.The major background includes 4 (cid:96)Z, τ Z, (cid:96) τ Z and2 (cid:96) W channels. The 4 (cid:96)Z and 2 (cid:96) τ Z channels can fakea signal by missing two final state leptons with the samesign. In the 2 (cid:96) W channel, W → jj provides the re-quired jets, and one missed lepton with the opposite signcan result in a fake signal event. As shown in Table I,these channels contribute more background events thanthe ‘intrinsic’ 4 τ Z channel, and it shows the complica-tion with selecting only one pair of same-sign leptons.The 2 τ Z background events are likely from one wrong-sign lepton. IV. THREE LEPTON CHANNEL
When one N decays leptonically and the other N de-cays semileptonically, the three leptons in the final state Zh → (cid:96) ± (cid:96) ± (cid:96) + 4 j + /E T may contain one SSSF dilep-ton combination. Compared to the 2 (cid:96) channel, the SSSFdilepton signal occurs with both lepton number violating(∆ L = 2) and conserving (∆ L = 0) decays of N N . The∆ L = 2 process is shown in Fig. 1. When N couple toat least two lepton flavors (e.g. to both e and µ ), The∆ L = 0 process can also obtain the same-sign leptonfrom the secondary leptonic W ∗ → (cid:96)ν vertex instead ofthe primary N → (cid:96)W vertex. Therefore, both the Diracand Majorana N can contribute to this signal. Similar to the 2 (cid:96) channel, the SM background includeschannels with multiple τ and W bosons. The OSSF lep-ton pair (e.g. e ± e ∓ ) should be vetoed to suppress theSM background.We select signal events with the following cuts:(i) exactly three leptons N ( (cid:96) ) = 3 with p T ≥ τ leptons, N ( τ ) = 0;(iv) at least two jets, N ( j ) ≥ FIG. 3. Normalized distribution of selected kinematic vari-ables for the 3 (cid:96) channel. p T ( (cid:96) ) panels are after selecting N ( l ) = 3, N ( j ) is after cut (ii), p T ( j ) panels are after cut(iv). The distributions of selected kinetic variables in the 3 (cid:96) channel are shown in Fig. 3. p T ( (cid:96) ), p T ( (cid:96) ), p T ( (cid:96) ) cor-respond to the samples after requiring N ( (cid:96) ) = 3; N ( j )are after selecting cuts(i-ii); p T ( j ) , p T ( j ) are after re-quiring cuts(i-iv). N ( j ) cut is selected to optimize thesignal significance.Table II lists the expected number of events at differentcut stages for signal with different N masses and back-ground channels. In clear contrast to the 2 (cid:96) channel,the surviving backgrounds are 2 τ W and 2 τ lZ chan-nels. The combination of N ( j ) cut and increased leptonnumber cut effectively remove the contamination fromleptonic W decays, which leads to a smaller total back-ground event rate. Because of both a lower leptonic N decay branching fraction and fewer jets from N N de-cays, the signal event rate is also lower compared to the2 (cid:96) channel.Interestingly, selecting three leptons will pick up asame-sign trilepton final state of (cid:96) ± (cid:96) ± (cid:96) ± that derivesfrom leptonic Z decay, as shown in Fig. 4. The jetsfrom semileptonic N N decay satisfy the jet cuts, (cid:96) ± (cid:96) ± (cid:96) ± initial cuts(i) cuts(ii) cuts(iii-iv)Sig. 10 GeV 10
102 24.9 12.750 GeV 10
112 27.3 14.160 GeV 10
115 28.2 14.4Bkg. 4 τ . ×
614 155 3 . × − † τ Z . × . ×
350 - † (cid:96)Z . × . ×
121 -4 τ Z . × − τ W . × † (cid:96) τ Z
584 46.5 1.1 0.44 † (cid:96)Z
862 132 0.27 1 . × − † (cid:96) W . × . × . × − TABLE II. Similar to Table I but for the 3 (cid:96) channel. Back-ground channels with † require missing leptons. uul − ¯ d ¯ dl − h NNe − e + Z l − l + (missed) FIG. 4. SS trilepton emerges when Z decay leptonically andthe oppose-sign lepton misses detection. emerges once the opposite-sign (cid:96) ∓ misses detection.Among (cid:96) ± (cid:96) ± (cid:96) ± events, about 25% have the same fla-vor for all three leptons (i.e. SSSF trilepton e ± e ± e ± and µ ± µ ± µ ± ). When m N = 60 GeV, this (cid:96) ± (cid:96) ± (cid:96) ± finalstate is 7.6% of the (cid:96) ± (cid:96) ± (cid:96) signal events after selectingcuts(i-ii). In comparison, SM events would need at leastthree missed or wrong-sign leptons to fake such a pro-cess. The SSSF trilepton background rate is found to beabout 0.1% of the original 3 (cid:96) background event rate aftercut (ii). If capped by luminosity limits, SSSF trileptonsignal doesn’t necessarily yield stronger sensitivity as itsexpected signal event rate is small. V. FOUR LEPTON CHANNEL
The fully leptonic
N N decay leads to four chargedleptons. When N couple to both the first and secondlepton generations, two SSSF dileptons e ± e ± µ ∓ µ ∓ canemerge, and the two pairs must be in different flavors toavoid the OSSF dilepton pairs. Due to the presence of(anti)neutrinos, this final state does not guarantee LNV,and receives contribution from both LNV and non-LNVdecays of N . Therefore, both the Dirac and Majorana N can contribute to this signal.The fully-leptonic branching fraction is lower than thesemileptonic branching fraction due to the smaller lep-tonic W ∗ → lν branching compared to the hadronic W ∗ → jj branching, plus the requirement that the twodileptons must differ in flavor. Having two SSSF dilep-tons can provide major reduction on backgrounds, and itis shown that the SM background can be below single-event level in pp collision [23]. At e + e − collision, evenlower background is expected, and it would be interest-ing to check at what luminosity level the backgroundsare relevant.Similar to the semileptonic case, the SM backgroundrise from multiple τ, W channels with one associated Z boson. We consider the following selection cuts in eventanalysis:(i) exactly four leptons, N ( (cid:96) ) = 4 with p T ( (cid:96) ) ≥ e ± e ± µ ∓ µ ∓ lepton pairs;(iii) veto τ leptons, N ( τ ) = 0;(iv) at least one jet, N ( j ) ≥ FIG. 5. Normalized distribution of selected kinematic vari-ables for the 4 (cid:96) channel. p T ( (cid:96) ) panels are after selecting N ( l ) = 4, N ( j ) is after cut (ii), p T ( j ) panels are after cut(iv). The kinetic distributions of selected observables for thesignal with different N masses and the total backgroundare shown in Fig. 5. p T ( (cid:96) ), p T ( (cid:96) ), p T ( (cid:96) ), p T ( (cid:96) ) cor-respond to the samples after requiring N ( (cid:96) ) = 4; N ( j ) isafter selecting cuts(i-ii); p T ( j ) is after requiring cuts(i-iv).The expected number of events at different cut stages initial cuts(i) cuts(ii) cuts(iii-iv)Sig. 10 GeV 10 τ . × † τ Z . × . × † (cid:96)Z . × . × - -4 τ Z . × − . × − τ W . × † (cid:96) τ Z
584 13.8 1 . × − . × − † (cid:96)Z
862 116 7 . × − - † (cid:96) W . ×
217 - -TABLE III. Similar to Table I but for the 4 (cid:96) channel. Back-ground channels with † require missing leptons or wrong signs. for signal with different N masses and background chan-nels are shown Table III. Due to two SSSF dileptons,two wrong-sign leptons must occur to fake such an event.Missing leptons are also less a problem as it would takea 2 τ e µZ final state with one missed e and one missed µ to fake the signal.The surviving backgrounds are the 4 τ Z and 2 (cid:96) τ Z channels. The lepton flavor and opposite-sign cuts playthe central role in rejecting the background with sameflavor, oppose-sign leptons. Stringent lepton countingremoves the contamination from hadronic τ decays. The2 τ (cid:96)Z channel still contribute to background events, pos-sibly due to wrong sign leptons. VI. RESULTS
We generate signal events with the e + e − → h N N process and then let the Higgs boson and the right-handneutrinos decay inclusively. The signal event rate is, N s = L · σ Zh · BR( h → N N ) · η s (4)where L is the collider luminosity and η s denotes the se-lection efficiencies. At a future Higgs factory with a de-sign luminosity L = 5 . − and σ Zh = 196 fb at 240GeV center-of-mass energy [16], a sample of 1 . × Zh events are expected. Since we let N decay inclusively, η s already includes the N N system’s combined branchingfraction into final states that contribute to each signalchannel, and the formula above does not explicitly con-tain N decay branching fractions. The signal’s statisticsignificance is σ stat = (cid:114) N s + N b )ln(1 + N s N b ) − N s ] . (5)The background event rate in each channel N b are listedin Table I, II and III, respectively. Requiring 2 σ and 5 σ significance levels, the sensitivity limits on BR( h → N N ) are shown in Fig. 6.
FIG. 6. Sensitivity limits on the decay branching ratio ofHiggs boson to NN for 2-4 (cid:96) channels assuming m N between10 and 60 GeV. Zh production assume 240 GeV center-of-mass energy and 5.6 ab − integrated luminosity at fu-ture e − e + colliders. The solid (dotted) curves correspondto 2 σ (5 σ ) significance. Given L · σ Zh ∼ , the BR( h → N N ) η s in Eq. 4 isstatistically limited by N s /N Zh ∼ − N s . The selec-tion efficiency η s is favorably obtained via Monte Carlo,as η s is weighted between different processes that con-tribute to the same final state, e.g. both Z → (cid:96)(cid:96), jj cancontribute to our signal channels.Note the 2 (cid:96) and 3 (cid:96) limits worsen towards lower m N .This is caused by N decaying into collimated leptons andjets when N is more boosted at smaller m N , resulting infewer reconstructed jets, and hard hit by the N ( j ) cut.Relaxing jet counting would help recovering the low m N signal yet at the cost of significantly higher SM back-ground. The 4 (cid:96) channel has the highest background vetoefficiency that can saturate luminosity cap ( N b <
1) upto 10 ab − . Due to sub-unity background event rate,the 4 (cid:96) channel’s sensitivity is less stringent than 2 (cid:96) and3 (cid:96) channels because of its relatively lower signal selectionefficiency.BR( h → N N ) relates to BSM parameters as | sin α · y S | = BR( h → N N ) (6) × (cid:15) · π Γ h m h (cid:32) − m N m h (cid:33) − / , where (cid:15) = 1 for Majorana N and (cid:15) = 1 / N . With the total Higgs boson width Γ h ∼ h → N N )= 10 − would correspond to a sensitivitylimit | sin α · y S | ≤ . × − at m N = 60 GeV, and ≤ . × − towards low N mass 2 m N (cid:28) m h wherethe decay phase space is unsuppressed. y S is a free modelparameter given by v S and m N . For y S ∼ O (1), this limitconstrains | sin α | to be lower than 10 − . This shows thefuture Higgs factory has good sensitivity to tiny effectivemixing angles between the Higgs boson and the BSMscalar, which is comparable to the projected | sin α | ∼ − sensitivity at the LHC [23]. Acknowledgments
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