Signals of an invisibly decaying Higgs in a scalar dark matter scenario: a study for the Large Hadron Collider
aa r X i v : . [ h e p - ph ] M a y RECAPP-HRI-2011-004
Signals of an invisibly decaying Higgs in a scalar darkmatter scenario: a study for the Large Hadron Collider
Kirtiman Ghosh , Biswarup Mukhopadhyaya and Utpal Sarkar , Regional Centre for Accelerator-based Particle Physics,Harish-Chandra Research Institute, India. Physical Research Laboratory, India. McDonnell Center for the Space Sciences,Washington University in St. Louis, USA.
ABSTRACT
We consider the collider phenomenology of a singlet Majoron model with softly brokenlepton number. Lepton number is spontaneously broken when the real part of a new singletscalar develops vacuum expectation value. With the additional soft terms violating leptonnumbers, the imaginary part of this singlet scalar becomes a massive pseudo-Majoron whichcan account for the dark matter. In presence of the coupling of the pseudo-Majoron with theStandard Model (SM) Higgs, the SM Higgs mostly decays into a pair of pseudo-Majorons,giving rise to E T / signals at a hadron collider. Since the Higgs visible decay branchingfractions get reduced in presence of this invisible decay mode, the bounds on the SM Higgsmass from the LEP and Tevatron experiments get diluted and the invisible decay channelof the Higgs become important for the discovery of low mass Higgs at the Large HadronCollider. The Standard Model (SM) of strong and electroweak interactions is a well-studied theory.The theoretical pillar of the SM is invariance with respect to the gauge group SU (3) C × SU (2) L × U (1) Y and spontaneous breakdown of the electroweak gauge group SU (2) L × U (1) Y to the U (1) group corresponding to electromagnetism. We see phenomena which apparentlyare results of electroweak symmetry breaking (EWSB): the electroweak gauge bosons namely,the W ± and the Z , get masses and so do the chiral fermions. However, the ultimate sourceof EWSB is still mysterious. In the framework of the SM, EWSB is achieved through ascalar SU (2) doublet which couples to the gauge bosons via the covariant derivative, and tothe fermions via Yukawa couplings. The vacuum expectation value (VEV) of this doubletbecomes responsible for the masses of the W ± , Z -boson and the chiral fermions and onephysical degrees of freedom, namely the Higgs boson , remains in the mass spectrum. Theiggs has so far successfully thwarted all attempts towards its detection. However, fromall other measurements, namely the gauge couplings and the masses of gauge bosons andfermions, the couplings of the Higgs bosons to all SM particles are fixed so is the strengthof its self-coupling once the mass and the VEV of the Higgs are known. Thus, the colliderphenomenology of the SM Higgs boson is completely determined by just one undeterminedparameter, namely the Higgs boson mass.However, the correct theory of EWSB may be different from the SM, atleast in the sensethat the Higgs sector can be richer. Many new models in this direction have been proposedduring last two or three decades. The twin primary goals of the ongoing Large HadronCollider (LHC) experiment are to understand the mechanism for electro-weak symmetrybreaking (EWSB) as well as uncover any new dynamics beyond the SM that may be operativeat the scale of a TeV or so.The signature of the Higgs boson at the LHC has been extensively studied in the frame-work of the SM and its various extensions [1, 2]. However, there may still be possibilitiesleading to qualitatively different signatures for the Higgs boson. In particular, some ex-tensions of the SM may contain a Higgs boson that can decay into stable neutral weaklyinteracting particles, therefore giving rise to invisible final states at collider experiments.Examples of this are Majoron models [3, 4, 5, 6, 7] which are quite popular in the contextof neutrino mass generation and leptogenesis. If neutrinos are Majorana particles, leptonnumber must be broken by the neutrino mass. In the simplest version of the Majoron model[3] allowed by Z -decay data, global lepton number is spontaneously broken after a com-plex singlet scalar carrying lepton number develops a VEV. Right-handed neutrinos acquireMajorana masses through their Yukawa coupling with this singlet scalar. As a result ofthe spontaneous breaking of global lepton number, a massless neutral pseudoscalar, calledthe Majoron, remains in the spectrum. It can acquire mass and become a massive pseudo-Majoron in some variants of the singlet Majoron model [8, 9, 10]. As for example, one cantake into account the soft breaking of the global lepton number, which gives rise to a pseudoGoldstone boson. It was shown in Ref. [10], that such a massive pseudo-Majoron can ac-count for the cold dark matter content of the universe. Moreover, the quartic coupling of thissinglet scalar with the SM Higgs doublet opens up new decay modes for the Higgs boson,namely, the decay of Higgs boson into a pair of pseudo-Majorons. The pseudo-Majoron, be-ing invisible and stable, gives rise to missing energy signature at colliders. In this article, wehave studied the decay of Higgs boson in to a pair of pseudo-Majorons and its consequencesin the context of the Large Hadron Collider (LHC).At the LHC, the Higgs search strategies are modified considerably and in fact becomemore challenging in presence of invisible Higgs decay modes. This is in contrast to an e + e − collider where, via the production channel e + e − → ZH , even an invisible Higgs shows up as aresonance recoiling against a Z -peak [11, 12]. In order to detect the signature of an invisiblydecaying Higgs boson at the LHC, one still has to look for some associated productionchannel. The dominant production process there for a not-too-heavy Higgs is gluon-gluonfusion ( gg → H ). If the Higgs decays invisibly, one can look for the production of Higgs inassociation with a hard jet ( gg → H + jet). The resulting signature would be then a high p T jet and missing transverse energy ( E T / ). However, this monojet in association with missingtransverse energy signal is overwhelmed by the QCD background. The next dominant Higgsproduction channel is vector boson fusion ( qq → qqV ∗ V ∗ → qqH ). Here the final state will2onsist of two energetic high rapidity jets and missing- E T [13, 14]. In this work, we haveconsidered a relatively subdominant production channel, namely the production of the Higgsboson in association with a W or a Z -boson ( q ¯ q ( ′ ) → HZ ( W ± )) followed by the leptonicdecay of W and Z -boson, where the leptons in the final state make the signal relativelycleaner [15, 16].This paper is organized as follows. In the next section, we briefly discuss the pseudo-Majoron model and invisible decay of the Higgs boson. Section 3 contains the main charac-teristics of the signal and backgrounds and cuts chosen to enhance the signal to backgroundratio. Our numerical results are presented at the end of that section. We summarise andconclude in section 4. In addition to the SM fields, the model [10] under investigation includes two types of addi-tional singlet fields: one is a scalar ( ξ ) and the other set contains three right-handed neutrinos( N R ). Since SM leptons carry the lepton number L = 1, same lepton number is assigned tothe right-handed neutrinos. On the other hand, L = − ξ .The part of the Lagrangian involving neutrinos can be written as: L Y ⊃ − y ν ¯ ψ L φN R − hξ ¯ N cR N R + H.c. , (1)where, ψ L and φ , are the SM lepton and Higgs doublets respectively. The scalar potential isgiven by, V ( ξ, φ ) = − µ ξ † ξ + λ ( ξ † ξ ) − µ φ † φ + λ ( φ † φ ) + 2 λ ξ † ξφ † φ , (2)where λ , > λ > − p λ λ to guarantee the potential bounded from below.When the singlet scalar acquires a vacuum expectation value (VEV), it breaks leptonnumber and gives Majorana masses to the right-handed neutrinos. Spontaneous breaking oflepton number would then give rise to an unwanted massless Majoron. For this reason, softbreaking of the lepton number is taken into account with the following term, V soft = − µ ( ξ + H.c.) / . (3)As a consequence, the massless Majoron becomes a massive pseudo-Majoron. All other softlepton number violating terms can be forbidden by appropriate discrete symmetries such asa Z symmetry, under which φ → φ , ξ → − ξ , f → if , where f stands for the SMfermions and the right-handed neutrinos.We now expand the singlet scalar field in terms of its real and imaginary components ξ = ( σ + iχ ) / √
2, where the real part σ includes its VEV and the physical field, while theimaginary part represents the pseudo-Majoron. We can then rewrite the full scalar potentialin the following form: V = −
12 ( µ + µ ) σ + 14 λ σ −
12 ( µ − µ ) χ λ χ − µ φ † φ + λ ( φ † φ ) + 12 λ σ χ + λ σ φ † φ + λ χ φ † φ , (4)The non-zero VEV of the singlet scalar ξ gives masses to the right-handed neutrinos, whilethe VEV of the SM Higgs doublet φ breaks the electroweak symmetry and give Dirac massesto all the fermions. Together, they give rise to the tiny masses of left-handed neutrinosthrough the seesaw mechanism. Minimising the potential in Eq. 4, one finds non-zero VEVsof these two scalars [10], u = √ h σ i = s λ ( µ + µ ) − λ µ λ λ − λ , (5) v = √ h φ i = s λ µ − λ ( µ + µ ) λ λ − λ . (6)We can redefine the scalar σ and φ as, σ = 1 √ u + Φ) and φ = 1 √ " v + H . (7)The VEV v = 246 GeV has been determined from the electroweak symmetry breaking. Wewill argue in the following that, in order to establish the pseudo-Majoron as an alternativecandidate for cold dark matter, the VEV u should be near grand unified theory (GUT) scale( u ∼ GeV). χ has no mixing with Φ and H because of its zero VEV. As a consequenceof the huge hierarchy between u and v , the mixing between Φ and H is extremely smallso that H can be identical to the SM Higgs boson. The mass terms of the physical Higgsscalars can be written as, L m ⊃ − m Φ − m H H − m χ χ (8)with m ≃ λ u , m H ≃ λ − λ λ ) v , m χ = 2 µ . (9)In order to establish the pseudo-Majoron, χ , as a candidate for cold dark matter, itslifetime should be long enough. The pseudo-Majoron couples to the right-handed neutrinos(see Eq. 1), L ⊃ − i √ hχ ¯ N cR N R + H.c. . (10)For m χ ≪ M N , the pseudo-Majoron will decay into the SM particles through the virtualright-handed neutrinos. Conveniently, we can integrate out the heavy right-handed neutrinosto derive the effective couplings of the pseudo-Majoron to the left-handed neutrinos, L eff = i m ν u χ ¯ ν L ν cL (cid:18) Hv (cid:19) + H.c. . (11)4he effective couplings of the pseudo-Majoron to the left-handed neutrinos are highly sup-pressed by the neutrino mass in the numerator and by the VEV u in the denominator. It wasshown in Ref. [10] that for the VEV u ∼ GeV, the decay width of the pseudo-Majoroninto a pair of SM neutrinos is highly suppressed and the lifetime can be very long. As asuccessful dark matter candidate, its relic density should be consistent with the cosmologicalobservations. It has been shown in earlier works [17, 18, 19] that a stable SM-singlet scalarwith a quartic coupling to the SM Higgs doublet can serve as the dark matter because itcontributes a desired relic density through the annihilations into the SM particles. In thepresent model, the pseudo-Majoron χ also has a quartic coupling with the SM Higgs, V ⊃ λ χ φ † φ ⇒ λ vχ H + 12 λ χ H . (12)This implies that the pseudo-Majoron χ with its very long lifetime can play the role of thedark matter .The coupling of the pseudo-Majoron χ to the SM Higgs H in Eq. 12 not only determinesthe dark matter relic density but also opens a new decay mode for the Higgs boson. When itis kinematically possible, Higgs can mostly decay into a pair of pseudo-Majorons and givesrise to missing energy signature at the LHC. Decay width of the Higgs boson into a pair ofpseudo-Majorons is given by,Γ( H → χχ ) = 18 πm H ( λ v ) (cid:0) m H − m χ (cid:1) , (13)where, m H is the mass of Higgs and m χ is the mass of the pseudo-Majoron. We have usedthe code HDECAY [20] to calculate the decay widths and the branching ratios of the Higgsboson ( H ). In Fig. 1, we present the decay branching fraction of Higgs boson as a functionof Higgs mass for three different values of λ ( λ = 0 . , . . m H <
150 GeV), invisible decay mode dominates over the b ¯ b mode for λ = 0 .
01. For larger λ = 0 . . m H − λ space. Non-observability of any Higgs boson signal at the LEPexperiment puts bound on the Higgs mass and its invisible decay branching fraction. In theframework of the present model, Higgs invisible branching fraction is a function of both λ and m H . We have used the package HiggsBounds-2.0.0 [21, 22] which tests theoreticalprediction of models with an arbitrary Higgs sector against the exclusion bounds obtainfrom the LEP and Tevatron. In Fig. 2, we have presented 95% C.L. excluded regions inthe m H − λ plane from the direct detection experiments. At the LEP, the Higgs boson It is important to mention that for a sizable λ , the pattern of present symmetry breaking i.e. u ∼ GeV >> v ∼
264 GeV, requires a fine tuning between λ u and µ so that λ u − µ can be of theorder of v [10]. B r a n c h i ng fr ac ti on s m H [GeV] tt bb ggWWZZ γγ ττ Invisible ← λ =0.01 0.0001 0.001 0.01 0.1 1 150 200 250 300 350 400 450 500 B r a n c h i ng fr ac ti on s m H [GeV] tt bb ggWWZZ γγ ττ Invisible →λ =0.1 0.0001 0.001 0.01 0.1 1 150 200 250 300 350 400 450 500 B r a n c h i ng fr ac ti on s m H [GeV] tt bb ggWWZZInvisible → λ =0.5 Figure 1: Decay branching fraction of Higgs boson as a function of Higgs mass for threedifferent values of λ .is expected to be produced mainly via the Higgs-strahlung process: e + e − → ZH . For lowvalues of λ , invisible decay mode of the Higgs boson is highly suppressed. Therefore, forlow λ ( < . b ¯ b channel [23]. In view of the fact that Higgs boson can decay invisibly,four LEP collaborations performed searches for acoplanar jets ( H → invisible )( Z → q ¯ q )[24]. For larger values of λ , invisible branching fraction dominates over the b ¯ b mode. Fig. 2shows that in this part of the parameter space, Higgs mass is also excluded upto 114 GeVfrom the LEP search for the invisible Higgs boson. However, in the region λ ∼ . b ¯ b andinvisible branching fractions become comparable and the LEP exclusion limit of Higgs massis slightly lower. Direct searches for the standard model (SM) Higgs boson at the Tevatronexclude a new and larger region at high mass between 158 < m H <
175 GeV at 95% C.L.[25]. However, in presence of a invisible decay mode, the Tevatron exclusion limit on theHiggs mass should be modified. One should in particular note that for λ > .
06 Tevatronbound on the Higgs mass does not exist (see Fig. 2).
It has been already demonstrated that in the frame work of the present pseudo-Majoronmodel, a low mass Higgs dominantly decays into a pair of pseudo-Majorons which are stableand elusive at the detector. To extract the signature of such an invisible Higgs at the LHC,we note that the most dominant associated production channels, namely, gluon-gluon fusion( gg → H + jet) and vector boson fusion ( qq → qqV ∗ V ∗ → qqH ) channel, result into purelyhadronic final state together with missing transverse energy. QCD backgrounds becomequite serious for them, although some suggestions have been made in the context of vectorboson fusion [14, 13]. In this work, we consider the production of the Higgs in associationwith a W or Z -boson, where, again from the standpoint of background suppression, we haveconsidered the leptonic decay modes of W and Z -boson.The production of W H is mediated by a virtual W -boson in the s-channel. Leptonic6 λ m H [GeV]LEP: ZH production, H->bbLEP: ZH production,H-> Invisible Tevatron Figure 2: 95% C.L. excluded regions in the m H − λ plane. The colours indicates thechannel for highest statistical sensitivity. Red: LEP e + e − → ZH, H → b ¯ b , Green: LEP e + e − → ZH, Z → invisible, Blue: Tevatron p ¯ p → H + X .decay of W -boson ( W → lν ) and invisible decay of the Higgs ( H → χχ ) gives rise to singlehard lepton + missing transverse energy. q ¯ q ′ → W ∗ → W H → ( lν )( χχ ) (14) • The irreducible SM background to the 1 l + E T / signal arises from W Z production where W decays leptonically and Z decays invisibly. However, this background is suppressedby the invisible branching ratio of the Z -boson. • The most significant background to the single lepton + E T / signal arises from thesingle W production followed by the leptonic decay of the W -boson. The single W -production cross-section at the LHC is huge. However, one can define the transversemass: M T = p p lT p T / [1 − cosφ ( ~p lT , ~p T / )] and demand M T >
100 GeV to remove thebackground coming from real W production. However, this cut cannot suppress thebackground coming from virtual W ∗ production which is order of magnitude largerthan the signal. Therefore, detecting the signature of invisible Higgs boson in W H channel is extremely challenging. In our analysis, we do not consider 1 l + E T / assignature of invisibly decaying Higgs.We find it more convenient to use the associated production of ZH followed by theleptonic decay of Z -boson and invisible decay of Higgs gives rise to two unlike sign, sameflavour leptons + missing transverse energy signature at the LHC. q ¯ q → Z ∗ → ZH → ( l ¯ l )( χχ ) (15)7he signal is characterized by a peak in the dilepton ( M ll ) invariant mass distribution atthe Z-boson mass ( m Z ). The dominant backgrounds for the dilepton + E T / signal are listedbelow: • The irreducible background to the signal comes from the pair production of Z -boson( q ¯ q → ZZ ) followed by the leptonic decay of one Z and invisible ( ν ¯ ν ) decay of other.Although the mass of Z -boson and Higgs are different, all other kinematic propertiesof ZH signal and ZZ background are identical. In case of both signal and backgroundleptons come from the decay of Z -boson, dilepton invariant mass distribution cannotbe used to separate the signal. On the other hand, the missing E T for the signal arisesfrom the invisible decay of Higgs and for background, invisible decay of Z -boson givesrise to the missing transverse energy. However, in an environment like LHC wherethe longitudinal boost of the center-of-mass frame is unknown, it is not possible todetermine the mass of the particle decaying invisibly. Therefore, it is not possible tosuppress this background without reducing the signal. • Pair production of W -boson followed by the leptonic decay of both the W also con-tribute to the dilepton + E T / background. Since the signal dileptons are characterisedby a peak (at m Z ) in the dilepton invariant mass distribution, we can suppress thisbackground contribution significantly by putting a cut on the dilepton invariant mass( M ll ). • The production of top anti-top pairs may also give rise to 2 l + E T / when both top andanti-top decays leptonically and two b-jets fall out side detector coverage. • Single Z -boson production can also contribute significantly to the background. Here,missing transverse momentum arises from the high energy ISR jets which get lost inthe beam pipe, and also from the jet energy mismeasurment.In this analysis, we have generated the signal and SM background events with PYTHIA6.421 [26]. We have used the leading order CTEQ6L1 [27] parton distribution functions.The QCD factorization and renormalization scales are kept fixed at √ s . In our analysis, we have introduced a set of basic selection criteria to identify leptons, jetsand missing transverse energy. The object selection is described in brief in the following.
Lepton selection: • p T >
10 GeV and | η ℓ | < p T is the transverse momentum and η ℓ is thepseudorapidity of the lepton (electron or muon). • Lepton-lepton separation: ∆ R ℓℓ ≥ R = p (∆ η ) + (∆ φ ) is the sepa-ration in the pseudorapidity–azimuthal angle plane. • Lepton-jet separation: ∆ R ℓj ≥ . E T >
20 GeV.8
The total energy deposit from all hadronic activity within a cone of ∆ R ≤ . ≤
10 GeV.
Jet selection: • Jets are formed with the help of
PYCELL , the inbuilt cluster routine in PYTHIA. Theminimum E T of a jet is taken to be 20 GeV, and we also require | η j | < Missing transverse energy ( E T / ): The missing transverse energy in an event is calculated using calorimeter cell energy and themomentum of the reconstructed muons in the muon spectrometer. In our analysis, we haveused the following definition for the missing transverse energy: E T / = q ( X p x ) + ( X p y ) , (16)where, the sum goes over all the isolated electrons, muons, the jets as well as the ‘unclustered’energy deposits.We have approximated the detector resolution effects by smearing the energies (transversemomenta) with Gaussian functions. The different contributions to the resolution error havebeen added in quadrature. • Electron energy resolution: σ ( E ) E = a √ E ⊕ b ⊕ cE , (17)where ( a, b, c ) = (cid:26) (0 .
030 GeV / , . , . , | η | < . , (0 .
055 GeV / , . , . , . < | η | < . . (18) • Muon p T resolution: σ ( p T ) p T = ( a, p T <
100 GeV ,a + b log p T
100 GeV , p T >
100 GeV , (19)with ( a, b ) = (cid:26) (0 . , . , | η | < . , (0 . , . , . < | η | < . . (20) • Jet energy resolution: σ ( E T ) E T = a √ E T , (21)with a = 0 . / , the default value used in PYCELL .9ross-section in fbLHC with √ s = 14 TeVBackgroundProcess Cut-1 Cut-1 Cut-1 Cut-1 Cut-1+ E T / >
100 GeV + E T / >
150 GeV + E T / >
170 GeV + E T / >
200 GeV ZZ W + W − < < tt < < Z × < < < m H Signal120 GeV 17.81 5.05 2.18 1.56 0.99160 GeV 7.08 2.92 1.49 1.16 0.78LHC with √ s = 10 TeVProcess Background ZZ W + W − < < < tt < < < Z × < < < m H Signal120 GeV 12.14 3.21 1.37 1.02 0.66160 GeV 4.81 1.83 0.91 0.69 0.46Table 1: Signal (for m H = 120 and 160 GeV) and the SM background cross-sections after Cut-1 and
Cut-1 + E T / > √ s = 10 and 14 TeV. After introducing the basic object selection criteria and discussing about the signal andbackground characteristics, we are now equipped enough to introduce an additional set ofevent selection criteria which will enhance the signal to background ratio. • We demand exactly one pair of leptons with same flavour and opposite charge and p T >
20 GeV. We reject events with any additional lepton with p T >
20 GeV. • We have considered hadronically quiet opposite sign dilepton events i.e. , we veto eventswith one or more central ( | η | < .
5) jets having p T >
20 GeV. • Since the signal leptons result from the decay of Z -boson, we reject events with | M ll − m Z | >
10 GeV. This cut will reduce the W + W − and t ¯ t background significantly.We collectively refer to the basic isolation cuts (described in section 3.1), the abovementioned p T and dilepton invariant mass cuts as Cut-1 . In Fig. 3, we have presented the missingtransverse momentum distributions for signal (with m H = 120 and 160 GeV) and dominant ZZ background after Cut-1 at the LHC with √ s = 14 TeV. In Fig. 3, we have assumed10 C r o ss - S ec ti on / b i n [f b / G e V ] m H [GeV] SM backgroundm H =120 GeVm H =160 GeV Figure 3: Missing E T distributions for signal (with m H =120 and 160 GeV) and dominant ZZ background after Cut-1 at the LHC with √ s = 14 TeV. In this plot, we have assumedthat Higgs decays invisibly with 100% branching fraction.that Higgs decays invisibly with 100% branching fraction. Fig. 3 shows that differentialcross-section decreases rapidly with E T / , however, there is a clear enhancement of signalto background ratio in the high E T / region. This enhancement is more pronounced forlarger Higgs mass. In Table 1, we have presented the signal (for m H = 120 and 160 GeV)and different SM background cross-sections after Cut-1 and
Cut-1 plus four different E T / ( E T / > √ s =10 and 14 TeV . In viewof the cross-sections in Table 1, we choose Cut-1 + E T / >
150 GeV as our final selectioncriteria.
With the criteria listed already, we obtained the discovery potential of invisible Higgs (inthe frame work of present pseudo-Majoron model) at the LHC, with centre-of-mass energy10 and 14 TeV. The production cross-section of ZH depends only on the mass of the Higgsboson ( m H ). We choose m H as one of the scan parameter. The invisible decay branchingfraction of Higgs depends on both m H and the quartic coupling λ (see Fig. 1). Therefore,the resulting dilepton + E T / signal cross-section depends on both m H and λ . We havechose λ as the second scan parameter. To show the variation of signal with m H and λ ,in Fig. 4, we have presented the signal cross-section as a function of Higgs mass for threedifferent values of λ (=0.5, 0.05 and 0.01). For large values of λ , the invisible decay We have checked that the luminosity planned for √ s = 7 TeV is not sufficient to yield signal of thetype suggested by us. Although, the current plan is to upgrade directly to √ s = 14 TeV, we are nonethelesspresenting results for √ s = 10 TeV and the luminosity required by us there, in case the occasion arises inthe future. C r o ss - S ec ti on [f b ] m H [GeV]LHC with √ s=10 TeVSM background λ =0.01 λ =0.05 λ =0.5 0.01 0.1 1 10 115 120 125 130 135 140 145 150 155 160 C r o ss - S ec ti on [f b ] m H [GeV]LHC with √ s=14 TeVSM background λ =0.01 λ =0.05 λ =0.5 Figure 4: Signal cross-section (after selection cuts) for three different values of λ as afunction of Higgs mass at the LHC with centre-of-mass energy 14 TeV (right) and 10 TeV(left). The total SM background cross-section is also presented in the figure.mode of the Higgs is overwhelmingly dominant over the other decay modes. Therefore, thevariation of signal cross-section with m H for large λ is not very significant. For small λ ,the invisible Higgs decay mode still dominant in the low m H region however, for m H > H → W W ∗ and ZZ ∗ decay modes open up and the invisible decay branching fractiondecreases sharply (see Fig. 1). As a result, in Fig. 4, we observe a sharp fall in the signalcross-section above m H = 150 GeV for λ = 0 . L if [28, 29], • N S √ N B + N S ≥ < N B ≤ N S , (22)where, N S ( B ) = σ S ( B ) L , is the number of signal (background) events for an integratedluminosity L . • For zero background event, we treat the signal as decisive if there are at least fivesignal events. • In order to establish the discovery of a small signal (which could be statistically signifi-cant i.e. N S / √ N B ≥
5) on top of a large background, we need to know the backgroundwith high precision. However, such precise determination of the SM background is be-yond the scope of this present article. Therefore, we impose the requirement N B ≤ N S to avoid such possibilities.In Fig. 5, we have presented the discovery potential of invisible Higgs (in the framework ofthe present pseudo-Majoron) at the LHC with center-of-mass energy 10 TeV (right) and 1412 λ m H [GeV]LHC with √ s = 10 TeV100 fb -1
75 fb -1
50 fb -1 λ m H [GeV]LHC with √ s = 14 TeV 100 fb -1
75 fb -1
50 fb -1
30 fb -1 Figure 5: Discovery reach of invisibly decaying Higgs boson in the frame work of pseudo-Majoron model at the LHC with center-of-mass energy 10 TeV (right) and 14 TeV (left).Different values of the integrated luminosity are assumed. Each line corresponds to 5 σ discovery contour in the m H − λ plane. The shaded regions represent the experimentallyexcluded parts of the m H − λ space (see Fig. 2).TeV (left). We have assumed different values of integrated luminosity ranging from 30 fb − to 100 fb − . Fig. 5 shows the 5 σ discovery contours in the m H - λ plane and the lines referto the different integrated luminosities. With 100 fb − of integrated luminosity and 14 (10)TeV center-of-mass energy of the LHC, the invisible decay of the Higgs boson in the large λ ( > .
1) region can be probed upto m H = 160 (155) GeV. For λ ≤ .
02, the LHC with100 fb − of luminosity and √ s = 14 (10) TeV can discover the invisible Higgs boson upto m H = 140 (135) GeV. We have investigated the collider phenomenology of a particular variant of the singlet Ma-joron model where the pseudo-Majoron is a potential dark matter candidate. This is achievedthrough the soft breaking of global lepton number. The quartic coupling of the pseudo-Majoron with the SM Higgs allows the SM Higgs to decay in to a pair of pseudo-Majoronswhenever it is kinematically possible. We found that for low Higgs mass, the decay of theHiggs into a pair of pseudo-Majorons always dominates over the SM decay modes. Weconsider the production of the Higgs boson in association with a Z -boson followed by theleptonic decay of the Z . Our signal consists of two hard isolated lepton in presence of missing E T . The pair production of the Z -boson is the only irreducible SM background. We havedefine a set of event selection criteria to enhance the signal to background ratio. With thisevent selection criteria, we found that at the LHC with √ s = 14 TeV and 100 fb − integrated13uminosity, the invisible decay of the Higgs can be probed upto m H = 160 GeV for valuesclose to 0 . Acknowledgments
KG and BM was partially supported by funding available from the Department of AtomicEnergy, Government of India, for the Regional Centre for Accelerator-based Particle Physics(RECAPP), Harish-Chandra Research Institute. They also acknowledge the hospitality ofthe Department of Theoretical Physics, Physical Research Laboratory (PRL), Ahmedabad,while the work was in progress. US would like to thank Prof. R. Cowsik, Director, McDonnellCenter for the Space Sciences, Washington University in St. Louis, for arranging his visit asthe Clark Way Harrison visiting professor, where this work has been completed.
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