Four-lepton LHC events from MSSM Higgs boson decays into neutralino and chargino pairs
Mike Bisset, Jun Li, Nick Kersting, Ran Lu, Filip Moortgat, Stefano Moretti
aa r X i v : . [ h e p - ph ] S e p TUHEP-TH-07161SCUPHY-07002SHEP-07-12DFTT 40/2009
Four-lepton LHC events fromMSSM Higgs boson decaysinto neutralino and chargino pairs
Mike Bisset ∗ , Jun Li Center for High Energy Physics and Department of Physics,Tsinghua University, Beijing, 100084 P.R. China
Nick Kersting ∗ Physics Department, Sichuan University, Chengdu, 610065 P.R. China
Ran Lu ∗ Physics Department, University of Michigan, Ann Arbor, MI 48109, USA
Filip Moortgat ∗ Department of Physics, CERN, CH-1211, Geneva 23, Switzerland
Stefano Moretti ∗ School of Physics and Astronomy, University of Southampton,Highfield, Southampton SO17 1BJ, UK and
Dipartimento di Fisica Teorica, Universit`a degli Studi di TorinoVia Pietro Giuria 1, 10125 Torino, Italy
Abstract
Heavy neutral Higgs boson production and decay into neutralino and chargino pairsis studied at the Large Hadron Collider in the context of the minimal supersymmetricstandard model. Higgs boson decays into the heavier neutralino and chargino states, i.e. , H , A → e χ e χ , e χ e χ , e χ e χ , e χ e χ , e χ e χ as well as H , A → e χ ± e χ ∓ , e χ +2 e χ − (all lead-ing to four-lepton plus missing transverse energy final states), is found to improve thepossibilities of discovering such Higgs states beyond those previously identified by con-sidering H , A → e χ e χ decays only. In particular, H , A bosons with quite heavymasses, approaching ∼
800 GeV in the so-called ‘decoupling region’ where no clear SMsignatures for the heavier MSSM Higgs bosons are known to exist, can now be discerned,for suitable but not particularly restrictive configurations of the low energy supersym-metric parameters. The high M A discovery reach for the H and A may thus be greatlyextended. Full event-generator level simulations, including realistic detector effects andanalyses of all significant backgrounds, are performed to delineate the potential H , A discovery regions. The wedgebox plot technique is also utilized to further analyze the 4 ℓ plus missing transverse energy signal and background events. This study marks the firstthorough and reasonably complete analysis of this important class of MSSM Higgs bosonsignature modes. In fact, this is the first time discovery regions including all possibleneutralino and chargino decay modes of the Higgs bosons have ever been mapped out. Introduction
Among the most investigated extensions of the standard model (SM) are those incorporatingsupersymmetry (SUSY), and among these the one with the fewest allowable number of newparticles and interactions, the minimal supersymmetric standard model (MSSM), has certainlyreceived considerable attention. Yet, when prospective signals at the Large Hadron Collider(LHC) of the new particle states within the MSSM are considered, there is still much thatneeds clarification. Nothing underscores this more than the MSSM electroweak symmetrybreaking (EWSB) Higgs sector. Included therein is a quintet of Higgs bosons left from thetwo SU (2) L Higgs doublets after EWSB (see [1, 2] for more details): a charged pair, H ± ,the neutral CP -odd A and the neutral CP -even h and H (with M h < M H ). The entireHiggs sector ( i.e. , masses and couplings to ordinary matter) can be described at tree-level byonly two independent parameters: the mass of one of the five Higgs states ( e.g. , M A ) and theratio of the vacuum expectation values of the two Higgs doublets (denoted by tan β ). Thesemust be augmented to include significant radiative corrections which most notably raise theupper limit on the mass of the light Higgs boson from M h ≤ M Z at tree-level to < ∼
140 GeV(150 GeV) with inclusion of corrections up to two loops and assuming a stop-sector scale of M SUSY = 1 TeV (2 TeV) and m t = (178 . ± .
3) GeV according to [3], or < ∼
135 GeV with m t = (172 . ± .
4) GeV by [4] (stop mass range not specified). This definite upper bound willallow experimentalists to definitively rule out such a minimal SUSY scenario at the LHC ifsuch a light Higgs state is not observed. Thus, the possible production and decay modes ofthe h state have understandably been investigated in quite some detail [2]. In contrast, thepossibilities for the other heavier neutral MSSM Higgs bosons have not been so thoroughlyexamined. Yet it is crucial that the avenues for discovery of these other MSSM Higgs bosonsbe well understood since, even if a candidate for h discovery is experimentally identified, itmay be indistinguishable from a SM Higgs boson (this corresponds to the so-called ‘decouplingregion’, with M H , M A ≫
200 GeV and for intermediate to large values of tan β [2, 5]). Thenthe additional identification of heavier Higgs bosons may well be required to establish thatthere is in fact an extended Higgs sector beyond the single doublet predicted by the SM.Finding signatures for these heavier MSSM Higgs bosons has proved to be challenging.Unlike the lone Higgs boson of the SM of similar mass, couplings of these MSSM Higgs bosonsto SM gauge bosons are either absent at tree level (for A ) or strongly suppressed over much ofthe allowed parameter space (for H ). Thus, identification of A and H via their decays intoknown SM particles relies chiefly on decays of said Higgs bosons into the heaviest fermionsavailable, namely, tau leptons and bottom quarks . Identification of hadronic decays/jetshowers of these third generation fermions may be problematic in the QCD-rich environmentof the LHC , so that it is very questionable that the entire parameter space can be coveredwith just SM-like signatures. Fortunately, in the MSSM there is an alternative: decays of theseHiggs bosons into sparticles, in particular the charginos and neutralinos formed from the EWgauginos and Higgsinos. Higgs boson couplings to certain –ino states may be substantial, andthese heavy sparticles may themselves decay — except for e χ which is assumed to be the stable H , A top quark couplings are suppressed relative to a SM Higgs boson of the same mass. In addition, jet-free events from Higgs boson decays to tau-lepton pairs where both tau-leptons in turndecay leptonically also come with considerable background-separation challenges [6]. In the remainder, charginos and neutralinos collectively will be abbreviated by ‘–inos’. H , A → e χ + a e χ − b , e χ i e χ j ( a, b = 1 , , i, j = 1 , , , . (1)Therein only subsequent –ino decays into leptons (which will be taken to mean electronsand/or muons, ℓ = e, µ ) were considered, as this is preferable from the standpoint of LHCdetection. Since relatively light sleptons can greatly enhance [13, 20, 21] the branching ratios(BRs) for such decays, the properties of the slepton sector of the MSSM also need to bespecified. All of the previous works concentrated almost exclusively on the decays H , A → e χ e χ . In addition, the subsequent neutralino decays e χ → e χ ℓ + ℓ − were typically presumed toproceed via three-body decays with an off-mass-shell intermediate Z ∗ or slepton, neglectingthe possibility of the intermediate Z or slepton being on-mass-shell ([22] and [23] delve inconsiderable depth into the distinctions between these cases).In this work , all the decays in (1) are incorporated. In fact, as the presumed mass ofa Higgs boson grows, more such decay modes will become accessible. Therefore, if decaychannels to the heavier -inos are significant, they may provide signatures for heavier neutralHiggs bosons (with masses well into the aforementioned decoupling region). When heavier–ino states are included, it also becomes easier to construct model spectra with slepton masseslying below those of the heavier –inos. Thus, in this work, intermediate sleptons are allowedto be both on- and off-mass-shell (same for the Z ∗ ) ) . More background channels are alsoemulated than in previous studies. The Higgs boson production modes considered herein are gg → H , A (gluon-fusion) and q ¯ q → H , A (quark-fusion). (The second mode is dominatedby the case q = b .)This work is organized as follows. The next section provides an overview of the MSSMparameter space through calculation of inclusive rates for the relevant production and de-cay processes contributing to the signal. Sect. 3 then specializes these results to the morerestrictive minimal supergravity (mSUGRA) scenario for SUSY breaking. Sect. 4 gives thenumerical results for the signal and background processes based upon Monte Carlo (MC) sim-ulations of parton shower (PS) and hadronization as well as detector effects. This includesmapping out discovery regions for the LHC. The recently-introduced ‘wedgebox’ method of[27], which is reminiscent of the time-honored Dalitz plot technique, is utilized in Sect. 5 toextract information about the –ino mass spectra and the –ino couplings to the Higgs bosons.Finally, the last section presents conclusions which can be drawn from this study. The decays H , A → e χ +1 e χ − , e χ e χ were also studied in [7] but found to be unproductive due to largebackgrounds to the resulting di-lepton signals. A preliminary account of this analysis is given in Ref. [24]. Similar studies for charged Higgs boson decays into a neutralino and a chargino, where the charged Higgsboson is produced in association with a t or ¯ t quark are done in [13, 20] (see also Refs. [25, 26]). MSSM parameter space
As noted above, M A and tan β may be chosen as the MSSM inputs characterizing the MSSMHiggs bosons’ decays into SM particles . But when Higgs boson decays to –inos are included,new MSSM inputs specifying the –ino sector also become crucial. To identify the latter, thealready mentioned Higgs/Higgsino mixing mass, µ , and the SUSY-breaking SU (2) L gauginomass, M , in addition to tan β , are required. The SUSY-breaking U (1) Y gaugino mass, M ,is assumed to be determined from M via gaugino unification ( i.e. , M = tan θ W M ). Thiswill fix the tree-level –ino masses (to which the radiative corrections are quite modest) alongwith their couplings to the Higgs bosons.Inputs (assumed to be flavor-diagonal) from the slepton sector are the left and right softslepton masses for each of the three generations (selectrons, smuons, and staus) and thetrilinear ‘ A -terms’ which come attached to Yukawa factors and thus only A τ has a potentialimpact. A priori , all six left and right mass inputs (and A τ ) are independent. However, inmost models currently advocated, one has m e e R ≃ m e µ R and m e e L ≃ m e µ L . Herein these equalitiesare assumed to hold. To maximize leptonic –ino BR enhancement, sleptons should be made as light as possible. Butdirect searches at LEP [28, 29] place significant limits on slepton masses: m e e ≥ . m e µ ≥ . m e τ ≥ . m e ν ≥ . Z pole). Furthermore, the sneutrino massesare closely tied to the left soft mass inputs, and, to avoid extra controversial assumptions, onlyregions of the MSSM parameter space where the LSP is the lightest neutralino rather than asneutrino will be considered . To optimize the –ino leptonic BRs without running afoul of theLEP limits, it is best to set m e ℓ R = m e ℓ L . If all three generations have the same soft inputs(with A τ = A ℓ = 0), then the slepton sector is effectively reduced to one optimal input value(defined as m e ℓ soft ≡ m e ℓ L,R ). However, since –ino decays into tau-leptons are generally notanywhere near as beneficial as those into electrons or muons, it would be even better if thestau inputs were significantly above those of the first two generations. This would enhancethe –inos’ BRs into electrons and muons. In the general MSSM, one is of course free to choosethe inputs as such. Doing so would also weaken restrictions from LEP, especially for highvalues of tan β . Fig. 1 in [20] shows values for this optimal slepton mass over the M – µ plane Several other MSSM inputs also enter into the radiatively-corrected MSSM Higgs boson masses andcouplings of the MSSM Higgs bosons to SM particles, namely, inputs from the stop sector — the soft SUSY-breaking stop trilinear coupling A t plus the stop masses — and the Higgs/Higgsino mixing mass µ . In thepresent work the stop masses are assumed to be heavy ( ≈ A t is fixed to zero. The µ parameteris not crucial for the SM decay modes; however, it will become so when decays to –inos are considered. Further, if a sneutrino were the LSP and thus presumably the main constituent of galactic dark matter, itsstrong couplings to SM EW gauge bosons would lead to event rates probably inconsistent with those observedby Super-Kamiokande. In contrast, the coupling of an –ino to SM EW gauge bosons can be tuned to obtainrates consistent with current experimental limits. Unless this leads to m e ν < m e χ < m e ℓ ± , in which case e χ decays to charged leptons will be suppressed withrespect to e χ decays to neutrinos, to avoid which having m e ℓ R < m e ℓ L is preferred. β = 10 ,
20. Setting the soft stau mass inputs 100 GeV abovethose of the other soft slepton masses, as will often be done herein, complies with currentexperimental constraints and moderately enhances the signal rates [24].
Figs. 1, 2 and 3 show the LHC rates (in fb) for σ ( pp → H ) × BR( H → ℓN ) + σ ( pp → A ) × BR( A → ℓN ), where N is any number (including zero) of invisible neutral particles(in the MSSM these are either neutrinos or e χ LSPs) obtained for tan β = 5, 10, and 20,respectively . (Hereafter this sum of processes will be abbreviated by σ ( pp → H , A ) × BR( H , A → ℓN ).) Each figure gives separate scans of the µ vs. M plane most relevant tothe –ino sector for (from top to bottom) M A = 400, 500, and 600 GeV — covering the rangeof Higgs boson masses of greatest interest [24]. This is in the region of the MSSM parameterspace where observation of h alone may be insufficient to distinguish the MSSM Higgs sectorfrom the SM case ( i.e. , the decoupling region). The darkened zones seen around the lower,inner corner of each plot are the regions excluded by the experimental results from LEP.First observe that these ‘raw’ or ‘inclusive’ ( i.e. , before applying selection cuts to the basicevent-type) rates may be sufficiently large. For an integrated luminosity of 100 fb − , thepeak raw event number is around 4000(1700) events for M A = 400(600) GeV and tan β = 20,irrespective of the sign of µ . Also observe that low values of | µ | and M yield the highest signalrates, though significant event numbers are also found when one but not the other of theseparameters is increased (especially | µ | ; rates do fall rapidly when M increases much beyond500 GeV). These numbers are substantial (especially at high tan β ) and, if experimentalefficiencies are good, they may facilitate a much more accurate determination of some massesor at least mass differences in the -ino spectrum as well as the Higgs-ino mass differences thanthose achieved in previous studies based solely on H , A → e χ e χ decays.Note the color coding of the three figures depicting what percentage of the signal eventsare coming from Higgs boson decays to e χ e χ : >
90% in the red zones, from 90% down to 50%in the yellow zones, from 50% to 10% in the blue zones, and <
10% in uncolored regions. Ifthe events are not coming from e χ e χ , then they are almost always from Higgs boson decaysincluding heavier neutralinos, i.e. , H , A → e χ e χ , e χ e χ , e χ e χ , e χ e χ , e χ e χ (possibly also withcontributions from H , A → e χ ± e χ ∓ , e χ +2 e χ − which are also taken into account here). Also notethat the main source of events at the optimal location in the –ino parameter space shifts from e χ e χ to heavier –ino pairs as M A grows from 400 to 600 GeV. Irrespective of the heavier Higgsboson masses, Higgs boson decays to e χ e χ are the dominant source of signal events in regions These figures are generated using private codes; however, these have been cross-checked against those ofthe ISASUSY package of ISAJET [30] and the two are generally consistent, exceptions being a few codingerrors in ISASUSY and the latter’s inclusion of some mild radiative corrections for the slepton and –inomasses which are not incorporated into the codes used here. These caveats are noteworthy since results fromthe output of the ISASUSY code will be used as input for the simulation work that follows. These smalldistinctions may cause a shift in the parameter space locations of particularly-abrupt changes in the ratesdue to encountered thresholds, though the gross features found in this section and in the ISASUSY-basedsimulation studies are in very good agreement. Finally, note that higher-order corrections to the Higgs boson–ino –ino couplings are incorporated into neither ISASUSY nor the private code. A recent study[31] indicatesthat these generally enhance the partial decay widths by O ( G e V )
15 12108642 61 .1 .1 .1.1
42 1 .1
86 4 2 1 1 .1
64 21 .1 .1.1 .1 .1.1.1 m (GeV) Figure 1: σ ( pp → H , A ) × BR( H , A → ℓN ) (in fb), where ℓ = e ± or µ ± and N representsinvisible final state particles, also showing where the percentage from H , A → e χ e χ is >
90% (red), 50% – 90% (yellow), 10% – 50% (light blue), <
10% (white), with tan β = 5, M A = 400 GeV (top), 500 GeV (middle), 600 GeV (bottom). Optimized slepton masses (withstau inputs raised 100 GeV) are used, and with m t = 175 GeV, m b = 4 .
25 GeV, m e q = 1 TeV, m e g = 800 GeV, A τ = A ℓ = 0. The cross-hatch shaded areas are excluded by LEP.5 ( G e V ) .1 .1 .1 .1 .1 .1 .1.1 m (GeV) Figure 2: σ ( pp → H , A ) × BR( H , A → ℓN ) (in fb), where ℓ = e ± or µ ± and N representsinvisible final state particles, also showing where the percentage from H , A → e χ e χ is >
90% (red), 50% – 90% (yellow), 10% – 50% (light blue), <
10% (white), with tan β = 10, M A = 400 GeV (top), 500 GeV (middle), 600 GeV (bottom). Optimized slepton masses (withstau inputs raised 100 GeV) are used, and with m t = 175 GeV, m b = 4 .
25 GeV, m e q = 1 TeV, m e g = 800 GeV, A τ = A ℓ = 0. The cross-hatch shaded areas are excluded by LEP.6 ( G e V )
37 353020151086422 102 .1 .1 .1 .1 .1.1 .1
24 1715 12 108 6 4 2 11 .1.1.1 m (GeV) Figure 3: σ ( pp → H , A ) × BR( H , A → ℓN ) (in fb), where ℓ = e ± or µ ± and N representsinvisible final state particles, also showing where the percentage from H , A → e χ e χ is >
90% (red), 50% – 90% (yellow), 10% – 50% (light blue), <
10% (white), with tan β = 20, M A = 400 GeV (top), 500 GeV (middle), 600 GeV (bottom). Optimized slepton masses (withstau inputs raised 100 GeV) are used, and with m t = 175 GeV, m b = 4 .
25 GeV, m e q = 1 TeV, m e g = 800 GeV, A τ = A ℓ = 0. The cross-hatch shaded areas are excluded by LEP.7ith low M values and moderate to high values of | µ | . But for low to moderate M valuesand low values of | µ | , the dominant source of signal events shifts to the previously-neglecteddecays into the heavier –inos. Thus, inclusion of these neglected modes opens up an entirelynew sector of the MSSM parameter space for exploration. Furthermore, the parameter spacelocations with the maximum number of signal events also shifts to these new sectors as themasses of the Higgs bosons rise. Therefore, the regions in MSSM parameter space wherein σ ( pp → H , A ) × BR( H , A → ℓN ) processes can be utilized in the search for the heavierMSSM Higgs bosons will certainly expand substantially with inclusion of these additionaldecay channels.The rates illustrated in Figs. 1–3 incorporate indirect decay modes. That is, if the Higgsboson decays into a pair of neutralinos, and then one or both of these ‘primary’ neutralinosdecay into other neutralinos (or other sparticles or the light Higgs boson or both on- andoff-mass-shell SM gauge bosons) which in turn give rise to leptons ( with no additional coloreddaughter particles ), then the contribution from such a decay chain is taken into account. Thisremains true no matter how many decays there are in the chain between the primary –ino andthe 4 ℓN final state, the only restrictions being that each decay in the chain must be a tree-level decay with at most one virtual intermediate state (so 1 to 3 decay processes are includedbut not 1 to 4 decays, etc. ). (As already intimated, the intermediate state is expected to bean on- or off-mass-shell SM gauge boson or slepton, charged or neutral.) The decay modesomitted due to these restrictions are never expected to be significant. Thus, effectively alltree-level decay chains allowable within the MSSM have been taken into account. Potentialcontributions from literally thousands of possible decay chains are evaluated and added to theresults.Inspection of Figs. 1–3 supports selection of the following representative points in theMSSM parameter space to be employed repeatedly in this work. These are: Point 1 . M A = 500 GeV, tan β = 20, M = 90 GeV, M = 180 GeV, µ = −
500 GeV, m e ℓ soft = m e τ soft = 250 GeV, m e g = m e q = 1000 GeV. Point 2 . M A = 600 GeV tan β = 35, M = 100 GeV M = 200 GeV µ = −
200 GeV, m e ℓ soft = 150 GeV, m e τ soft = 250 GeV, m e g = 800 GeV, m e q = 1000 GeV.(Also recall that m e ℓ soft ≡ m e ℓ R = m e ℓ L and A τ = A ℓ = 0.) Point 1 represents a case wheremost of the signal events result from H , A → e χ e χ decays , whereas Point 2 is a case wheredecays including heavier -inos make the dominant contribution. Here tan β has been set fairlyhigh to enhance rates, as Figs. 1–3 suggest.In Fig. 4, the parameter values of Point 1 (left plot) and Point 2 (right plot) are adopted,save that the parameters M A and tan β are allowed to vary, generating plots in the M A vs. tan β plane. Color shading on the left-side plot clearly shows that the e χ e χ decay modestotally dominate in the production of 4 ℓ signal events for this choice of M , µ -ino inputs outto M A ≃
700 GeV. Similarly, the right-side plot shows that for the –ino inputs of Point 2 the This choice of parameters, including the degenerate soft selectron, smuon and stau inputs, also correspondsto one of the choices adopted in [9]. A (GeV) t a n b * . . M A (GeV) t a n b * Figure 4: σ ( pp → H , A ) × BR( H , A → ℓN ) (in fb), where ℓ = e ± or µ ± and N represents invisible final state particles for Point 1 (left side): M = 90 GeV, M = 180 GeV, µ = −
500 GeV, m e ℓ soft = m e τ soft = 250 GeV, m e g = m e q = 1000 GeV; and Point 2 (right side): M = 100 GeV, M = 200 GeV, µ = −
200 GeV, m e ℓ soft /m e τ soft = 150 /
250 GeV, m e g /m e q =800 / M A ∼ β ∼ M A and de-creasing tan β shown here to the corresponding M A vs. tan β discovery region plots based ondetailed simulation analyses presented in the analysis section to follow.Fig. 5 illustrates how results depend on the slepton mass(es). In the upper plot, showingthe overall rate, σ ( pp → H , A ) × BR( H , A → ℓN ), as a function of m e ℓ soft ≡ m e ℓ L,R , onegenerally sees the naively expected decline in the rate as m e ℓ soft increases. If the –inos decaythrough on- or off-mass-shell sleptons, then the decay products always include leptons (andusually charged leptons). However, as the sleptons become heavier (first becoming kinemati-cally inaccessible as on-mass-shell intermediates and then growing increasingly disfavored asoff-mass-shell intermediates), the EW gauge bosons become the dominant intermediates, inwhich case a large fraction of the time the decay products will be non-leptons, and so the BRto the 4 ℓ final state drops. The plot though also reveals an often far more complex dependenceon m e ℓ soft , with rapid oscillations in the rate possible for modest changes in m e ℓ soft .Note again that Point 1, drawn in red in Fig. 5, represents a case where most of the signalevents result from H , A → e χ e χ decays, whereas Point 2, drawn in blue, is a case wheredecays including heavier –inos make the dominant contribution. This is made clear by thelower plot where the percentage of the inclusive rate from e χ e χ decays is plotted vs. m e ℓ soft .In Fig. 5, the slepton mass is varied. But later in this work the value of m e ℓ soft will be fixed at9 ˜ ℓ soft (GeV) m ˜ ℓ soft (GeV) (cid:27) ( PP ! H ; A ! ` N )( f b ) F r a t i o n v i a f (cid:31) f (cid:31) d e a y s ( a ) red — Point 1 (at location of asterisk)blue — Point 2 (at location of asterisk)dashed — Point 2 but change M A = 400 GeV, tan β = 30dotted — Point 2 but change M A = 400 GeV, tan β = 5 ( b ) labeling same as in ( a ) above Figure 5: Dependence on slepton mass. ( a ) σ ( pp → H , A ) × BR( H , A → ℓN ) (in fb),where ℓ = e ± or µ ± and N represents invisible final state particles, vs. m e ℓ soft ≡ m e ℓ L,R forMSSM parameter Point 1 (red) and Point 2 (blue) as well as some variations based on Point2 (black). Asterisks mark the m e ℓ soft values to be used for Points 1 and 2 later in this work.( b ) percentage of the inclusive rate from e χ e χ decays vs. m e ℓ soft , with other labeling as in ( a ).10he values given earlier for Points 1. and 2. (these locations are marked by asterisks in bothplots in Fig. 5). These choices are fairly optimal, especially for Point 1.Points 1. and 2. show some interesting dependence on m e ℓ soft . This dependence can be mademore acute though by adjusting the input parameters. For instance, the black dotted anddashed curves in Fig. 5 result from lowering the M A value of Point 2 to 400 GeV and changingtan β from 35 to 5 and 30, respectively. Then not only does the inclusive rate undergo rapidvariation with m e ℓ soft , but the percentage of the inclusive rate from e χ e χ decays fluctuatesrapidly as well. Points 1. and 2. were selected for further analysis later in this work in partbecause the results are not strongly affected by a small shift in the value of m e ℓ soft . However,apparently this is not true for all points in MSSM parameter space.Finally, notice that the overall normalization of both processes gg → H , A and b ¯ b → H , A is of 2 → . Each of these gluon- and quark-fusion partonic contributionsis separately convoluted with an empirical set of PDFs (CTEQ 6M [34] in this case) toobtain predictions at the proton-proton level, for which the total center-of-mass energy is √ s = 14 TeV. The cross-section thus defined is computed using the MSSM implementation[35] of the HERWIG program [36] (as available in Version 6.5 [37], with the exception of thechoices m t = 175 GeV and m b = 4 .
25 GeV for the top and bottom quark masses) and theMSSM input information produced by ISASUSY (through the ISAWIG [38] and HDECAY[41] interfaces). Sometimes a Higgs boson will be produced in association with jets, and thus,as discussed in Ref. [32], what percentage of the time a Higgs boson is produced with hadronicactivity passing jet selection criteria (as will be applied in the analysis section) is (possibly)sensitive to the type of emulation (2 → →
3) being employed. Note though that inFigs. 1–4 colored fermions are not allowed in the –ino decay chains. This is in fact inconsistentand leads to an over-(under-)estimate of the hadronically-quiet (inclusive, allowing jets) 4 ℓ rates (the under-estimation of the inclusive rates is expected to be modest due to the price ofextra BRs in the decay chains of the neglected channels). To attempt to correct for this byfactoring in results from the simulation runs might obscure what is meant by ’raw’ rates, sothis minor inconsistency is simply tolerated in these estimates. The signal, taken here to be events resulting from heavy MSSM Higgs bosons decaying into–ino pairs, is not the only relevant quantity in this analysis that depends on the position inthe MSSM parameter space — backgrounds from other MSSM processes will also vary frompoint to point. Fig. 1 of [27] shows the competing processes for –ino pair-production viaHiggs boson decays : ’direct’ –ino production ( i.e. , via a s-channel gauge boson) and –inosproduced in ’cascade’ decays of squarks and gluinos. The latter is considered in some detail in There is an alternative 2 → gg/q ¯ q → b ¯ bH , b ¯ bA diagrams.The results of these two approaches have been compared and contrasted in Ref. [32]. A full MC implementationfor the 2 → gg → ggH , ggA and related modes (eventually yielding two jets in the finalstate alongside H or A ) [33]) is as-of-yet unavailable though in public event generators. It is therefore moreconsistent to solely employ complete → incomplete → One could also consider signals from Higgs boson decays to other sparticles, especially sleptons. Thiswas discussed in [39], which demonstrated that the heavier MSSM Higgs boson decays to sleptons only havesufficient BRs for low values of tan β ( < ∼ circa , and the masses of the EW gauge bosons areknown, so the direct channel background cannot be easily removed by restricting the analysisto some subset of the parameter space by means of such a straight-forward assumption.In fact, the location in the parameter space where the raw signal rate is largest sometimesdiffers from that where the ratio of the signal to the leading background from direct –inoproduction is largest. For instance, the plot in Fig. 2 (tan β = 10) for M A = 600 GeV showsa maximum in the inclusive rate at approximately ( µ, M ) = ( −
200 GeV ,
250 GeV). Onthe other hand, the signal-to-background ratio (
S/B ) is largest at ≈ ( −
250 GeV ,
500 GeV).The production cross-section for the Higgs bosons is the same at both points. Thus, tounderstand why the two locations differ so much the BR( H , A → ℓN ) and the direct –inoproduction × BR( -inos → ℓN ) need to be studied. The former drops from ∼
6% to ∼ S/B maximum (thus cutting the overallsignal rate by a factor of 3). The background at the inclusive rate maximum is mostly e χ e χ , e χ e χ and e χ ± e χ ∓ with respective production cross-sections (and BRs into 4 ℓN final states) of4 × − pb (18%), 1 × − pb (8%) and 1 × − pb (2%). At the point where the S/B is amaximum, these (still dominant) backgrounds rates shift to 1 × − pb (16%), 1 × − pb(27%) and 1 × − pb (2%), respectively. So the e χ e χ production rate drops by a factorof 4 while e χ e χ production almost vanishes (which is the main factor), mostly because ofincreased phase space suppression due to larger –ino masses: m e χ ( m e χ )[ m e χ ] { m e χ ± } changesfrom 118(180)[212] { } GeV at the rate maximum to 219(257)[273] { } GeV at the
S/B maximum. The result is that the overall background rate drops by a factor of 5. In short, the
S/B improves because the direct –ino pair-production cross-section falls more rapidly thanthe signal BR into 4 ℓN final states. Analogous plots to those in Figs. 1–3 studying the S/B variation across the parameter space are not presented. Instead, discovery regions for selected–ino input parameter sets will be given in Sect. 4. While favorable MSSM points have beenchosen for the simulation analyses, they were not selected to maximize the
S/B . Therefore,this channel may work even better at points other than those analysed in detail herein.
Augmenting the general MSSM with additional assumptions about the unification of SUSYinputs at a very high mass scale yields the more restrictive ’mSUGRA’ models. Here thenumber of free input parameters is much reduced (hence the popularity of such scenariosfor phenomenological analyses), with said free parameters generally set as tan β , a universalgaugino mass defined at the Grand Unification Theory (GUT) scale ( M / ), a universal GUT-level scalar mass ( M ), a universal GUT-level trilinear scalar mass term ( A ), and the sign of µ (henceforth, sgn( µ )). As already noted, the signal has a strong preference for low values of | µ | . Yet in mSUGRA scenarios, | µ | is not a free parameter, as it is closely tied to the masses ofthe scalar Higgs bosons via the M input. An earlier study of charged Higgs boson decays into The sleptons also cannot be made arbitrarily heavy. Direct slepton pair-production, as studied in [40],will generally lead to dilepton final states rather than the 4 ℓ final state desired here. The smaller contributionsfrom these processes are included in the analyses to follow. an b = 5 M (GeV) M / ( G e V ) tan b = 10 M (GeV) M / ( G e V )
10 20 tan b = 20 M (GeV) M / ( G e V ) Figure 6: σ ( pp → H , A ) × BR( H , A → ℓN ) (in fb), where ℓ = e ± or µ ± and N represents invisible final state particles for tan β = 5 , ,
20 in the mSUGRA M vs. M / plane, with sgn( µ ) = +1 and A = 0. Colors depict the percentage of events stemming from H , A → e χ e χ >
90% (red), 50% – 90% (yellow), 10% – 50% (light blue), <
10% (white). Thedark shaded regions are excluded by theoretical considerations or LEP measurements (saveconstraints from LEP Higgs-strahlung which roughly reach up to the dashed green curves withconsiderable uncertainty — see text). Also shown in purple are the CMS TDR (Fig. 11.32) 5 σ discovery regions (assuming L int = 30 fb − ) for H , A → e χ e χ . The solid purple lines showthe extent of the plots in Fig. 11.32. 13 neutralino and a chargino [20] demonstrated that this was sufficient to preclude detection ofa 3 ℓ + top-quark signal from such processes over the entire reach of the unexcluded mSUGRAparameter space. Here, with the heavier neutral MSSM Higgs bosons, the situation is not sodiscouraging. Fig. 6 shows the values for σ ( pp → H , A ) × BR( H , A → ℓN ) obtained fortan β = 5 , ,
20 and µ >
0. Two disconnected regions of unexcluded parameter space appearwhere the expected number of events (for 100 fb − of integrated luminosity) is in the tens tohundreds (or even thousands). Interestingly, one of these (which includes discovery regionsdepicted in the CSM TDR [14] ) is where e χ e χ is the dominant source of 4 ℓ events while theother is where decays of the heavier –inos dominate. For tan β = 5, rates in the e χ e χ regionare much larger than in the heavier –inos region. However, for tan β = 20, rates in the tworegions become more comparable.Also shown as solid purple zones on the tan β = 5 and tan β = 10 plots are 5 σ discoveryregions from the CMS TDR (Fig. 11.32) [14]. These CMS TDR discovery regions assume anintegrated luminosity of just 30 fb − , and thus would have certainly been considerably largerif a base luminosity of 100 fb − was used instead. This CMS TDR analysis was at a technicallevel comparable to that in this work, but only considered MSSM Higgs boson decays into e χ e χ pairs . Thus, the CMS TDR analysis would not pick up the region where heavier –ino decaysdominate (in fact the plots in Fig. 11.32 in the CMS TDR only showed the regions delineatedby the solid purple lines in Fig. 6). Given that the somewhat lower rates of the higher M ,heavier –ino decays-dominated region may be compensated by assuming a larger integratedluminosity, as well as perhaps finding a higher selection efficiency due to harder daughterleptons, it is difficult to infer from the CMS TDR 5 σ
30 fb − discovery regions whether or notdisjoint discovery regions may develop in this novel region of the parameter space. This iscurrently under investigation [15].The excluded regions shown in Fig. 6 merit some explanation. Note that in each plot thediscovery region from the CMS TDR cuts into the excluded region, whereas in Fig. 11.32of the CMS TDR they do not touch the (more limited) excluded regions shown. This ismainly because the excluded regions in Fig. 11.32 of the CMS TDR only mark off regionswhere the e χ is not the LSP (because the mass of the lighter stau is lower — this removesthe upper left corner of the plots) and where EWSB is not obtained (along the horizontalaxis), while ignoring other experimental constaints — such as the lower limit on the lighterchargino’s mass from the LEP experiments. Such additional experimental constraints areincluded, for instance, in the excluded regions shown in Fig. 20-1 of the ATLAS TDR [16] . These experimental constraints have been updated to represent the final limits from theLEP experiments, accounting for the gross differences between the excluded regions depicted Note: virtually all mSUGRA parameter space plots in the TDR showing excluded regions are for tan β =10; the exceptions being the tan β = 5 plot in Fig. 11.32 and the tan β = 35 plots in Figs. 13.12 & 13.13;and the tan β = 35 plots seem to inaccurately have the tan β = 10 exclusion zones. These latter plots andothers in Chapter 13 do show a chargino lower mass limit (green dotdashed curve) and other supercolliderexperimental bounds which are more consistent with the excluded regions shown in the ATLAS TDR (and inthe present work). Note: virtually all mSUGRA parameter space plots in the TDR showing excluded regions are for tan β = 10and for (the now ruled-out) tan β = 2.
14n the ATLAS TDR and those in the present work . Somewhat crude estimates for theregions excluded by the LEP searches for MSSM Higgs bosons are indicated separately by thedashed green lines based on the empirical formula developed by Djouadi, Drees and Kneur [18].Finally, it must be emphasized that constraints from lower-energy experiments (in particularfrom b → sγ ) and from cosmological considerations (such as LSP dark matter annihilationrates) are not herein considered. In the far more restricted parameter domain of mSUGRAmodels it is more difficult to circumvent such constraints, and they can exclude considerableportions of the allowed parameter space shown in the figures (for further details, see [19]).As was done with the general MSSM parameter space, Fig. 5 enables selection of a coupleof representative mSUGRA points for simulation studies. These are: Point A . M = 125 GeV, M / = 165 GeV, tan β = 20, sgn( µ ) = +1, A = 0. Point B . M = 400 GeV, M / = 165 GeV, tan β = 20, sgn( µ ) = +1, A = 0.Point A is dominated by H , A → e χ e χ → ℓ decays (which account for more than 99% ofthe inclusive signal event rate before cuts) while in Point B the corresponding rates are below30% (the largest signal event channel is now H , A → e χ ± e χ ∓ → ℓ , yielding over 50% of theevents, with significant contributions from H , A → e χ e χ , e χ e χ , e χ e χ → ℓ ). Full MC anddetector simulations for Points A and B will be presented in the next section. These will showthat 4 ℓN signals remain visible in the mSUGRA parameter space, at least at these points. The HERWIG 6.5 [37] MC package (which obtains its MSSM input information from ISASUSY[30] through the ISAWIG [38] and HDECAY [41] interfaces) is employed coupled with privateprograms simulating a typical LHC detector environment (these codes have been checkedagainst results in the literature). The CTEQ 6M [34] set of PDFs is used and top and bottomquark masses are set to m t = 175 GeV and m b = 4 .
25 GeV, respectively.Four-lepton events are first selected according to these criteria: • Events have exactly four leptons, ℓ = e or µ , irrespective of their individual charges,meeting the following criteria: Raising the lower bound on the chargino mass from the circa ∼
65 GeV to ∼
100 GeVraises the approximately horizontal boundary for higher M values, while the rise of the bounds for the sleptonmasses from ∼
45 GeV to m e e , m e µ , m e τ ≃
99 GeV ,
91 GeV ,
85 GeV adds the quarter-circle-like bite seen in thelower-left corner of the tan β = 10 plot in Fig. 6 (which is absent in the ATLAS TDR plots). For reasons detailed in [18], foremost among which is the uncertainty in the calculation of M h . Herein theHiggs boson mass formulæ of ISAJET [30] and [12] are employed. Results here are roughly consistent withFigs. 1 & 2 of [18] (2006 paper). Note that in the case of mSUGRA, unlike in the general MSSM examples inthe current work, the stop and other squark parameters — which make the main contributions to the quitesignificant radiative corrections to M h — are determined from the few mSUGRA inputs without the need toset values by hand for assorted soft SUSY-breaking masses. Certainly, in mSUGRA, the LEP bounds on lightHiggs boson production are strongly-tied to rates for heavy Higgs boson to sparticle decay channels, thoughthis correlation will not be intensively examined in this work. | η ℓ | < . E ℓT > , e, µ (see ATLAS TDR [16]).Each lepton must be isolated. The isolation criterion demands there be no tracks (ofcharged particles) with p T > . r = 0 . .
05 radians < r < . • Events must consist of two opposite-sign, same-flavor lepton pairs.Events thus identified as candidate signal events are then subjected to the following cuts: • Z -veto: no opposite-charge same-flavor lepton pairs may reconstruct M Z ±
10 GeV. • restrict E ℓT : all leptons must finally have 20 GeV < E ℓT <
80 GeV. • restrict missing transverse energy, E miss T : events must have 20 GeV < E miss T <
130 GeV. • cap E jet T : all jets must have E jet T <
50 GeV.Jets are reconstructed using a UA1-like iterative ( i.e. , with splitting and merging, seeRef. [42] for a description of the procedure) cone algorithm with fixed size 0 .
5, whereincharged tracks are collected at E T > | η | < . E jet T >
20 GeV.Lastly, application of an additional cut on the four-lepton invariant mass is investigated: • four-lepton invariant mass (inv. m.) cut: the 4 ℓ inv. m. must be ≤
240 GeV . For the signal events, the upper limit for the four-lepton inv. m. will be M H,A − M e χ , andthus its value is dependent upon the chosen point in MSSM parameter space. In the actualexperiment, the value of M H,A − M e χ would be a priori unknown. So one could ask how anumerical value can be chosen for this cut? If too low a value is selected, many signal eventswill be lost. On the other hand, if too large a value is chosen, more events from backgroundprocesses will be accepted, diluting the signal. One could envision trying an assortment ofnumerical values for the four-lepton inv. m. upper limit (one of which could for instance be thenominal value of 240 GeV noted above) to see which value optimized the signal relative to thebackgrounds. However, here sparticle production processes are very significant backgrounds(after application of the other three cuts, only such processes and residual Z ∗ ) Z ∗ ) eventsremain), which, like the signal, may well have unknown rates. Thus, strengthening this cutwould lower the total number of events without indicating whether the signal to backgroundratio is going up or down — unless additional information is available from other studiesat least somewhat restricting the location in MSSM parameter space Nature has chosen. Ifsuch information were available, this cut could indeed lead to a purer set of signal events.One could instead consider all events from MSSM processes to be the signal while the SMprocesses comprise the background. However, the aim of this work is to identify the heavierHiggs bosons, not merely to identify an excess attributable to SUSY.16able 1: Relevant sparticle masses (in GeV) for specific MSSM and mSUGRA parameterpoints studied in the analyses. Point 1 Point 2 Point A Point B M A . . . . M H . . . . e χ . . . . e χ . . . . e χ . . . . e χ . . . . e χ ± . . . . e χ ± . . . . m e ν . . . . m e e . . . . m e µ . . . . m e e . . . . m e µ . . . . m e e − m e e .
59 0 .
96 28 .
46 9 . m e µ − m e µ .
20 4 .
81 28 .
62 9 . ℓ events from H , A → e χ e χ , while MSSM Point 2 and mSUGRA Point B obtain most oftheir 4 ℓ events from Higgs boson decays to heavier –ino pairs ( e χ e χ , e χ e χ e χ e χ , e χ e χ and/or e χ e χ ). The sparticle spectra for these points are presented in Table 1. Table 2 shows results for MSSM Point 1, a H , A → e χ e χ -dominated point. Note that, aftercuts, signal events do make up the majority of events in the sample. The only remainingbackgrounds are from direct neutralino/chargino pair-production (denoted by e χ e χ ), fromslepton pair-production (denoted by e ℓ , e ν ) and from Z ∗ ) Z ∗ ) production. The number ofevents obtained from A decays after cuts is about twice the number obtained from H decays.This is despite the fact that the H and A production cross sections are the same within1%. The ratio of A to H events at this point can be compared to that for inclusive rates The older ISASUSY version which inputs sparticle masses into HERWIG 6.3 lacks D-terms in the sleptonmasses, meaning the smuon masses in the simulation runs equate to the selectron masses given in Table 1.This has a minor effect upon the edges in the Dalitz-like ’wedgebox’ plots to be shown later. See discussionin [27]. Herein final states involving a sparton and a chargino/neutralino are included together with the resultsfor e χ e χ , as designed in HERWIG, though for the points studied here the latter overwhelmingly dominate theformer. − ).Process 4 ℓ events ℓ + ℓ − ℓ ( ′ ) + ℓ ( ′ ) − Z -veto E ℓT E miss T E jet T ℓ inv. m. e q , e g
118 64 49 19 1 0 0 e ℓ , e ν
100 65 46 30 23 13 7 e χ e χ, e q/ e g e χ
34 17 13 10 5 2 1 tH − + c.c. 0 0 0 0 0 0 0 Z ∗ ) Z ∗ ) t ¯ tZ ∗ )
47 23 2 1 1 0 0 t ¯ th H , A signal 20,32 18,31 14,26 13,25 11,22 8,17 6,13(with no cuts) which may be calculated using the BRs obtained from ISASUSY . Includingall possible decay chains, ISASUSY numbers predict A : H = 1 .
83 : 1 .
00 (64 . A events).This is in reasonable agreement with A : H = 1 . . . A events) obtained fromthe 4 ℓ before cuts entries in the first column of Table 2. The different H and A eventrates may then be traced back to differences in the H /A - e χ - e χ couplings (as opposed tothe enhancing or opening up of other H decay modes, such as for instance H → h h ).Study of the inclusive rates based on the ISASUSY BRs also confirmed that over 99% of thefour-lepton signal events resulted from H /A → e χ e χ decays. The percentage of A → ℓ events surviving the subsequent cuts is about 10% larger than the percentage of H → ℓ events surviving.Fixing the –ino input parameters M & µ and the slepton & squark inputs to be those ofMSSM Point 1, tan β and M A were then varied to map out a Higgs boson discovery region inthe traditional ( M A , tan β ) plane. This is shown in red in Fig. 7, where the solid (dashed) redborder delineates the discovery region assuming an integrated luminosity of 300 fb − (100 fb − ).The exact criteria used for demarcating the discovery region is that there be at least 10 signalevents and that the 99%-confidence-level upper limit on the background is smaller than the99%-confidence-level lower limit on the signal plus background. Mathematically, the lattercondition translates into the formula [43]: N signal > (2 . q N bckgrd2 . , (2)where N signal and N bckgrd are the expected number of signal and background events, re-spectively. As with MSSM Point 1, direct neutralino/chargino pair-production, slepton pairproduction and SM Z ∗ ) Z ∗ ) are the only background processes remaining after cuts (the ac-tual number of surviving background events varies modestly with tan β ) at all points tested, These were normalized using HERWIG production cross-sections, though here this is of scant importancesince the H and A production cross-sections are almost the same. Also, for consistency with the HERWIGsimulation analysis, ISASUSY Version 7.56 was used to generate the BRs. − (300 fb − ) of integrated luminosity, depending on the value of tan β , if the four-lepton inv.m. cut is not employed. Adding in this last optional cut changes the required numbers to19-22 (28-34) signal events and shifts the discovery region boundaries to those shown as blue(dashed blue) curves in Fig. 7. This places MSSM Point 1 just outside the upper M A edge ofthe 100 fb − discovery region (whether or not the four-lepton inv. m. cut is used). Lowering M A to 400 GeV raises the number of signal events from 25 to 36. Note that Fig. 4 (left-sideplot) predicts that H , A → e χ e χ decays will generate the bulk of the signal throughout thediscovery region. The lower M A edge of the discovery region closely follows where the (dom-inant) e χ e χ decay becomes kinematically accessible, i.e. , M A ≥ m e χ . The A contributionoutweighing the H contribution was found to be a general result valid for almost all pointsin the ( M A , tan β )-plane tested: events from A equaled or outnumbered those from H . Notefrom Table 2 that MSSM Point 1 at M A = 500 GeV and tan β = 20 yielded A : H = 2 . . A events) after all cuts save the four-lepton inv. m. cut (as comparison to the numbersin the preceding paragraph indicate, A events tend to do slightly better at surviving the cuts,though little reason could be found for this small effect). Lowering M A to 400 GeV shifts thisratio to A : H = 3 . . A events).The preponderance of A events is generally greatest for lower values of M A . For M A < ∼
375 GeV, 90-100% of the signal events are from A . Since M A < M H and M A ≃ m e χ this is mainly a threshold effect. The A event percentage drops to around 70% when M A ≃
415 GeV. For higher M A values inside the 100 fb − discovery region (outside the100 fb − discovery region but inside the 300 fb − discovery region), this percentage rangesfrom ∼
70% down to ∼
55% ( ∼
60% down to ∼ β > ∼ A percentage remains above 70% or even 80%.Inclusion of the four-lepton inv. m. cut with the nominal cut-off value of 240 GeV shiftsthe discovery region boundaries in Fig. 7 from the red curves to the blue ones. There areslight gains for low M A values at high and low values for tan β ; however, the high M A edgesalso recede somewhat. Note also that the highest and lowest tan β values which fall insidethe discovery region are virtually unaltered. Though the cut’s effect on the expanse of thediscovery region is quite modest, inclusion of this cut at included points with lower M A valuescan certainly raise the signal : background. For instance, at ( M A , tan β ) = (400 GeV, 20),this ratio goes from 37 : 19 without the 4 ℓ inv. m. cut to 37 : 12 with it. However, shifting M A to 500 GeV as in MSSM Point 1 is enough to remove any advantage, as can be seen inTable 2.Input parameters for MSSM Point 1 were also chosen to match a point studied in a previousanalysis [9] — which only looked at e χ e χ Higgs boson decays . The light purple contour shown Inside of the discovery region (for 300 fb − ), a couple points along the high M A – lower tan β edge werefound where the rate from H very slightly exceeded that from A . A different simulation of the quark-fusion channel involving b (anti)quarks (in the CMS note the simulationwas performed using gg → b ¯ bH , b ¯ bA ) is adopted here. In addition, the MC analysis in [9] was done withPYTHIA version 5.7 [44], which only implemented an approximated treatment of the SUSY sector, while hereinISASUSY is used in conjunction with HERWIG (though intrinsic differences between the two generators in theimplementation of the PS and hadronization stages should be minimal in our context). Also, the backgroundprocesses tH − + c.c., t ¯ tZ and t ¯ th , which were not emulated in [9], in this study were checked to yield no A (GeV) t a n b MSSM Point 1 * from Ref. [ ](cid:242) Ldt = 100 fb -1 (cid:242) Ldt = 300 fb -1 c c ~~ M A (GeV) t a n b MSSM Point 1 * from Ref. [ ](cid:242) Ldt = 100 fb -1 (cid:242) Ldt = 300 fb -1 Figure 7: Discovery region in red in ( M A , tan β ) plane for –ino/slepton parameters µ = −
500 GeV, M = 180 GeV, M = 90 GeV, m e ℓ soft = m e τ soft = 250 GeV as in MSSM Point1 (whose location is marked by a black asterisk). Here Higgs boson decays to e χ e χ totallydominate. Solid (dashed) red border delineates the discovery region for L int = 300 fb − (100 fb − ). The two green curves are M A , M H − m e χ . Also shown in light purple are analogousresults from a previous study [9] for 100 fb − . The blue contours add the extra cut on thefour-lepton inv. m. for the nominal cut-off value of 240 GeV. background events throughout Fig. 7. H , A → ℓN events (excluding cuts) coming from various –inochannels for MSSM Point 2. (Other channels are negligible.) H → e χ e χ . A → e χ e χ . A → e χ e χ . H → e χ e χ . H → e χ ± e χ ∓ . A → e χ ± e χ ∓ . A → e χ e χ . H → e χ e χ . H → e χ +2 e χ − . H → e χ +2 e χ − . < . M A and dies fortan β values below ∼
5. The latter is primarily due to low tan β strong enhancement of the H ( A )- t -¯ t coupling, which is proportional to csc β (cot β ), increasing the H , A → t ¯ t BRs atthe expense of the –ino BRs . BR( H → t ¯ t ) (BR( A → t ¯ t )) rises from around 0 .
30 to 0 . .
93 (0 .
51 to 0 .
79 to 0 .
96) as tan β runs from 6 to 4 to 2.For MSSM Point 2, Higgs boson decays to the heavier neutralinos and charginos neglected inprevious studies produce most of the signal events. Table 3 gives the percentage contributionsto the signal events among the H , A decay modes based on an inclusive rate study usingBR results from ISAJET (ISASUSY) 7.58 normalized with HERWIG cross-sections. Thisparton-level analysis merely demands exactly four leptons in the (parton-level) final state.According to this inclusive rates study, Higgs boson decays to e χ e χ now contribute less thanone hundredth of one percent of the signal events, in stark contrast to MSSM Point 1 wheresuch decays accounted for virtually all of the signal events. Applying all the cuts at the fullevent-generator level does not alter this. Said numerical results with the application of thesuccessive cuts for MSSM Point 2 are given in Table 4.1.Note that the four-lepton inv. m. cut, with the nominal numerical value of 240 GeV, removesabout 74% of the signal events while only slightly reducing the number of background events.This clearly shows that this cut, while helpful for points with lower M A values in Fig. 7, isquite deleterious at MSSM Point 2. Without the 4 ℓ inv. m. cut, an integrated luminosity of25 fb − is sufficient to meet the discovery criteria; while with the 4 ℓ inv. m. cut, an integratedluminosity of ∼
130 fb − is required. Choosing a higher numerical cut-off would lead to a viable The partial widths for H and A decays to –inos also drop by roughly a factor of 2 in going from tan β = 6to tan β = 2 (at M A = 450 GeV), and the H → h h and A → h Z ∗ ) widths increase by about a factor of2. These also lower the signal rate. On the other hand, decay widths to b -quarks and tau-leptons also dropby a bit over a factor of 2, helping the signal. These effects are overwhelmed by an almost order-of-magnitudeenhancement in the H and A to t ¯ t decay widths. − ).Process 4 ℓ events ℓ + ℓ − ℓ ( ′ ) + ℓ ( ′ ) − Z -veto E ℓT E miss T E jet T ℓ inv. m. e q , e g
817 332 197 96 21 0 0 e ℓ , e ν
12 5 4 4 2 2 2 e χ e χ, e q/ e g e χ
123 74 32 17 13 10 4 tH − + c.c. 76 38 22 15 9 3 1 Z ∗ ) Z ∗ ) t ¯ tZ ∗
47 23 2 1 1 0 0 t ¯ th H , A signal 189,179 156,149 64,80 55,64 43,50 32,37 9,9cut for this point; however, it may prove impossible to a priori decide on an appropriate valuefor the actual experimental analysis (see earlier discussion).Table 4.1 gives a ratio of A → ℓ events to H → ℓ events (before additional cuts) of A : H = 1 : 1 .
05 (48 . A events). ISASUSY BR studies of the inclusive four-lepton eventrates at this point also predict that H will produce more signal events than A this time, with A : H = 1 : 1 .
36 (42 . A events). Exact agreement between the two methods is certainlynot expected, and it is at least reassuring that both predict more H → ℓ events (unlike atMSSM Point 1). The percentage of A → ℓ events surviving the subsequent cuts is againslightly larger than that for H → ℓ events (21% vs. Z -veto takes a larger portion out of the signal event number for MSSMPoint 2 than it did for MSSM Point 1, with only about 50% surviving for the former whileabout 80% survive for the latter. This is understandable since, for MSSM Point 1, virtually allevents were from e χ e χ pairs, and e χ is not heavy enough to decay to e χ via an on-mass-shell Z . For MSSM Point 2, on the other hand, a variety of heavier –inos are involved, and themass differences between e χ or e χ and e χ do exceed M Z .Again the –ino input parameters M & µ and the slepton & squark inputs are fixed, thistime to be those of MSSM Point 2, and tan β and M A allowed to vary to map out the Higgsboson discovery region in the ( M A , tan β ) plane (using the same criteria as in Fig. 7) shownin red in Fig. 8. As before, the solid (dashed) red border delineates the discovery regionassuming an integrated luminosity of 300 fb − (100 fb − ). Assuming that the four-lepton inv.m. cut is omitted, MSSM Point 2 lies firmly inside the 100 fb − discovery region (with the 15sparticle/charged Higgs boson + 4 Z ∗ ) Z ∗ ) event background, Relation (2) requires 26 signalevents to be included in the 100 fb − discovery region, while 69 signal events are expected).Note that Fig. 4 (right-side plot) predicts that H , A → e χ e χ decays will only generate asubstantial number of signal events when tan β and M A are small (the red and yellow zones inthe plot), with decays to heavier –inos dominating elsewhere. This leads to a disjoint discoveryregion in Fig. 8, consisting of a smaller mainly e χ e χ -dominated portion for lower values oftan β and M A and a novel larger portion at considerably higher M A values that stretches up totan β values well above 50. Note the distance between the lower M A edge of this larger portion22f the discovery region and the curves for M A , M H − m e χ . In concurrence with the percentagecontributions for MSSM Point 2 given above, the lower M A edge of the discovery region abutsthe M A , M H − m e χ − m e χ curves (shown in green in Fig. 8), for tan β > ∼
10. The situation fortan β < ∼
10 and 450 GeV < ∼ M A < ∼
700 GeV (in both the upper and lower disjoint portions of thediscovery region) is more complicated, with e χ e χ and several other decays making significantcontributions.The discovery region shown in Fig. 8 represents a significant extension of LHC MSSM Higgsboson detection capabilities to quite high Higgs boson masses. With 300 fb − of integratedluminosity, there is some stretch of M A values covered for almost all values of tan β (1 < tan β < < ∼ tan β < ∼
6. If the integrated luminosity is dropped to100 fb − , the higher M A portion of the discovery region recedes up to tan β > ∼ − discovery regions from MSSM Higgs boson decays to third generation SMfermions found in the ATLAS [45] and other [46] simulations. The new discovery region hasconsiderable overlap with the so-called decoupling zone, where the light MSSM Higgs bosonis difficult to distinguish from the Higgs boson of the SM, and, up to now, no signals of theother MSSM Higgs bosons were known .Though the number of signal events swells to over 50 (30) per 100 fb − for tan β < ∼ β is lowered. (Note also thoughthat restrictions from LEP experiments exclude the most sensitive region of extremely lowtan β values.) As in Fig. 7, the low M A edge of the lower portion of the discovery region inFig. 8 abuts the M A , M H − m e χ curves.Yet for M A in the vicinity of 350 GeV to 450 GeV, the discovery regions in Fig. 7 and Fig.8 resemble mirror images of each other: the former lies exclusively above tan β ≃ β ≃
5. The reasons behind this stark contrast, thougha bit complicated, critically depend on the different inputs to the slepton sector. In Fig. 8,for M A < ∼
470 GeV, Higgs boson decays to other heavier -inos are kinematically inaccessible,and, for higher tan β values, e χ decays almost exclusively via sneutrinos into neutrinos andthe LSP, yielding no charged leptons. This is not the case in this region of Fig. 7 — here e χ undergoes three-body decays via off-mass-shell sleptons and Z ∗ with substantial BRsinto charged leptons. The situation for Fig. 8 changes as tan β declines below ∼
10 since e χ BRs to charged sleptons, while still much smaller than those to sneutrinos, grow beyond thepercent level — sufficient to generate a low tan β discovery region in Fig. 8. One might expectanalogous behavior in Fig. 7; however, in the low tan β region of Fig. 7 the partial widthsΓ( H , A → e χ e χ ) are much smaller, especially for A , than they are in this region of Fig. 8and decline with falling tan β , whereas in Fig. 8 Γ( H → e χ e χ ) actually increases (though onlymoderately) as tan β falls. The e χ e χ partial widths coupled with the subsequent e χ decays tocharged leptons are large enough in the case of Fig. 8 so that the signal is not overwhelmedby the rising Γ( H , A → t ¯ t ) partial widths as it is in the case of Fig. 7. Also, in Fig. 8 butnot in Fig. 7, as M A increases beyond ∼
450 GeV, contributions from other –ino pairs besides e χ e χ become significant and further enhance the low tan β ℓ signal rate.Differences in the discovery regions at very high tan β values are also attributable to the23 A (GeV) t a n b MSSM Point 2 * (cid:242) Ldt = 100 fb -1 (cid:242) Ldt = 300 fb -1 c c ~~ c c ~~ - - + c c ~~ c c ~~ c c ~~ c c ~~ c c ~~ - Figure 8: Discovery region in red in ( M A , tan β ) plane for –ino/slepton parameters µ = −
200 GeV, M = 200 GeV, M = 100 GeV, m e ℓ soft = 150 GeV, m e τ soft = 250 GeV as in MSSMPoint 2 (whose location is marked by an black asterisk). Here Higgs boson decays to a varietyof higher mass –inos (see text) constitute the majority of the signal events. Solid (dashed)red border delineates the discovery region for L int = 300 fb − (100 fb − ). The green curves are M A , M H − m e χ i m e χ j and M A , M H − m e χ ± k m e χ ∓ ( i, j = 2 , , k = 1 , β = 50,while in Fig. 7 the discovery region is curtailed, ending before reaching tan β = 35. Since thesoft slepton mass inputs for all three generations are degenerate for MSSM Point 1, for hightan β values in Fig. 7 splitting effects with the staus drive one of the physical stau masseswell below the selectron and smuon masses. This leads to lots of –ino decays including tau24eptons, virtually shutting down the decays to electrons and muons. Since the soft stau massinputs are elevated well above the other slepton inputs for MSSM Point 2, this high tan β capis removed in Fig. 8.Comments made above for MSSM Point 2 about the increased severity of the Z -line cutand the inappropriateness of the four-lepton inv. m. cut (with the numerical cut-off set to240 GeV) are also applicable to points throughout the larger portion of the discovery region ofFig. 8. As can be seen from the blue curves in Fig. 8, inclusion of the 240 GeV 4 ℓ inv. m. cuteliminates about half of the 300 fb − discovery region and far more than half of the 100 fb − region, including all points between tan β ≃ β ≃
25 for the latter.Also, in contrast to the discovery region of Fig. 7, in large segments of the Fig. 8 discoveryregion the number of signal events from H decays exceed those from A decays. First considerthe smaller, low tan β , portion of the disjoint discovery region. Herein, to the right of the M A , M H − m e χ − m e χ curves (shown in green in Fig. 8), the percentage of A events ranges from ∼ ∼
40% ( ∼ ∼ β > ∼ < ∼ A event percentagegrows to ∼ ∼
60% for tan β > ∼
2; increasing further to ∼ ∼
80% near the region’s upper lefttip ( M A in the vicinity of 350 GeV and tan β around 3 to 4 .
5) where the signal is dominatedby Higgs-mediated e χ e χ production.In the novel and larger high tan β portion of the discovery region in Fig. 8, where the e χ e χ contribution is minor to insignificant, the H and A contributions to the signal eventsstay within 20% of each other (with the A event percentage ranging from ∼ ∼ M A , M H − m e χ curves. In the finger-like projection between the nearly-vertical M A , M H − m e χ − m e χ and M A , M H − m e χ curves the A percentage drops to < ℓ inv. m. cut) , meaning that the number of events from H tothose from A exceeds 3 to 1. The H dominance in this zone stems from the H - e χ - e χ coupling ( H - e χ - e χ coupling) being two to three times larger (smaller) than the A - e χ - e χ coupling ( A - e χ - e χ coupling), combined with the fact that the e χ e χ decays are about twiceas likely to produce 4 ℓ events as those of e χ e χ . This of course means that e χ has a higherleptonic BR than e χ . This in turn is due to e χ decaying into e χ Z about half the time ( Z gives lepton pairs ∼
7% of the time), while e χ almost never decays this way, instead havinglarger BRs to charged sleptons [and e χ ± W ∓ ] which always [ ∼
21% of the time] yield chargedlepton pairs. The situation changes quickly once the H , A → e χ e χ , e χ +2 e χ − thresholds are(almost simultaneously, see Fig. 8) crossed, thereafter for higher M A values the A and H contributions remain reasonably close to each other as already stated.As with points in Fig. 7, direct chargino/neutralino pair-production and slepton pair-production together with Z ∗ ) Z ∗ ) production make up most of the background survivingthe cuts. Now, however, these are joined by a minor segment due to tH − + c.c. production,which depends on M A in addition to tan β .Results showed gb → tH − + c.c. could yield several events at points in the discoveryregion. Since the presence of a charged Higgs boson would also signal that there is an extendedHiggs sector, these events could easily have been grouped with the signal rather than withthe backgrounds. Clearly though the set of cuts used in this work is not designed to pickout such events. The jet cut typically removes roughly two-thirds to three-quarters of these Here are some results from specific points in this region: for M A = 510 GeV and tan β = 10 , , ,
40, thepercentage of A signal events (again, after cuts, excluding the 4 ℓ inv. m. cut), is 23%, 17%, 11 . t ¯ tX events). A more effective set of cuts for tH − , ¯ tH + events is developedin [20], wherein substantially larger numbers of charged Higgs boson events survive the cutstherein at favorable points in the MSSM parameter space. It is also worth noting thoughthat the reach of the discovery region (at a favorable point in the MSSM parameter space) forthe H , A → ℓ signal as described in this work surpasses that of the charged Higgs bosondiscovery regions found in [20]. (or in any other previous work on Higgs boson decays tosparticles).An aspect to be mentioned in this connection, already highlighted in Ref. [24], is thesomewhat poor efficiency for the signals following the Z -veto, especially when combined withthe fact that the Z ∗ ) Z ∗ ) background survives the same constraint. On the one hand, anon-negligible number of events in the signal decay chains leading to 4 ℓN final states actuallyproceed via (nearly) on-mass-shell Z bosons, particularly for MSSM Point 2, in which themass differences m e χ i − m e χ ( i = 3 ,
4) can be very large, unlike the case m e χ − m e χ for MSSMPoint 1 (and in previous studies limited to only e χ e χ decay modes). On the other hand,the rather large intrinsic Z width (when compared to the experimental resolution expectedfor di-lepton invariant masses) combined with a substantial production cross-section impliesthat Z ∗ ) Z ∗ ) events will not be totally rejected by the Z -veto. Altogether, though, thesuppression is much more dramatic for the Z Z background than for the signal, and so thiscut is retained (though the Z -veto will be dropped in some instances in the context of theforthcoming wedgebox analysis). Also, varying the size of the 10 GeV window around M Z didnot improve the effectiveness of this cut. Turning attention briefly to the results within the more restrictive mSUGRA framework forSUSY-breaking, results for mSUGRA Point A and mSUGRA Point B (as defined in Sect. 3)are presented in Tables 5–6. Mass spectra for these parameter sets are given in Table 1. FormSUGRA Point A ample signal events are produced and survive the cuts to claim observationof the Higgs boson at 100 fb − . The largest background is from direct slepton production, withdirect neutralino/chargino production also contributing significantly, whereas SM backgroundsare virtually nil. Note how the E jet T cap suffices to eliminate the background from coloredsparticle (squarks and gluinos) production.Recall that for mSUGRA Point A the signal is dominated by H , A → e χ e χ decays,whereas for mSUGRA Point B heavier –inos make major contributions. Thus, a wedgeboxplot analysis of the former is expected to show a simple box topology, while in the case of thelatter there unfortunately may be too few events (even with 300 fb − of integrated luminosity)to clearly discern a pattern. For mSUGRA Point B, 9(10) signal events survive after all cuts(save the 4 ℓ inv. m. cut), while 6 background events survive, assuming 100 fb − of integratedluminosity. This is insufficient to claim a discovery by the criterion of Relation (2). However,when the integrated luminosity is increased to 300 fb − , then the raw number of signal eventssuffices to cross the discovery threshold. Unfortunately though, for mSUGRA Point B thebackground from colored sparticle production is not removed by the upper limit imposed on E jet T . One can however stiffen the E jet T cut, capping the allowable jet transverse energy at260 GeV rather than 50 GeV and thus eliminate much of this background without diminishingthe signal rate significantly. Then, with 300 fb − of integrated luminosity the discovery criteriacan be met.An earlier ATLAS study [47, 16] also sought to map out the discovery reach of the Higgsboson to neutralino four-lepton signature within the mSUGRA framework transposed onto the( M A , tan β ) plane. Though some statements to the contrary are included in this ATLAS study,it does seem to have been focused on the e χ e χ contributions (analogous to previously-discussedgeneral MSSM studies of this signature), thus apparently omitting parameter sets such asmSUGRA Point B considered herein. Thus, the viability of mSUGRA Point B indicatesan enlargement of the signal discovery region to higher values of M A (and the mSUGRAparameter M ) at intermediate values of tan β ( i.e. ,in the ‘decoupling’ region) from thatreported in this ATLAS study (akin to the enlargements shown in the general MSSM case,though the extent of this enlargement in the case of mSUGRA models will not be quantifiedherein).Table 5: Event rates after the successive cuts defined in the text for mSUGRA Point A(assuming an integrated luminosity of 100 fb − ).Process 4 ℓ events ℓ + ℓ − ℓ ( ′ ) + ℓ ( ′ ) − Z -veto E ℓT E miss T E jet T ℓ inv. m. e q , e g
927 504 312 280 174 0 0 e ℓ , e ν
326 178 145 117 100 71 58 e χ e χ, e q/ e g e χ
567 294 203 179 121 29 21 tH − + c.c. 1 0 0 0 0 0 0 Z ∗ ) Z ∗ ) t ¯ tZ ∗ )
47 23 2 1 1 0 0 t ¯ th H , A signal 46,140 40,123 38,122 38,120 30,83 24,66 24,66Table 6: Event rates after the successive cuts defined in the text for mSUGRA Point B(assuming an integrated luminosity of 100 fb − ).Process 4 ℓ events ℓ + ℓ − ℓ ( ′ ) + ℓ ( ′ ) − Z -veto E ℓT E miss T E jet T ℓ inv. m. e q , e g e ℓ , e ν
309 169 134 110 94 67 57 e χ e χ, e q/ e g e χ
579 302 206 174 115 32 27 tH − + c.c. 1 1 0 0 0 0 0 Z ∗ ) Z ∗ ) t ¯ tZ ∗ )
47 23 2 1 1 0 0 t ¯ th H , A signal 43,130 38,118 37,116 37,116 29,93 23,75 23,7527 Wedgebox analysis of Higgs boson decays to –inopairs
The wedgebox plot technique was introduced in a previous work [27] which focused on neu-tralino pairs produced via colored sparticle production and subsequent ‘cascade’ decays. An-other work [48] has just recently focused on neutralino pairs produced via EW processes,including via a Z ∗ ) boson or via H , A production; the former is termed ‘direct’ productionwhile the latter is ‘Higgs-mediated’ production. A jet cut was found to be fairly efficient inseparating these two neutralino pair-production modes from cascade production assuming thecolored gluinos and squarks are fairly heavy.To utilize the wedgebox technique, the criteria for the final four-lepton state are furthersharpened by demanding that the final state consist of one e + e − pair and one µ + µ − pair .The wedgebox plot then consists of the M ( µ + µ − ) invariant mass plotted versus the M ( e + e − )invariant mass for all candidate events. If a given neutralino, e χ i , decays to the LSP, e χ , and acharged lepton pair via a three-body decay mediated by a virtual Z ∗ or virtual/off-mass-shellcharged slepton, then M ( ℓ + ℓ − ) is bounded from above by m e χ i − m e χ (and from below by0 if lepton masses are neglected). Given a sufficient number of events, the wedgebox plotof the signal events will be composed of a superposition of ‘boxes’ and ‘wedges’ [27], in the M ( e + e − )- M ( µ + µ − ) plane resulting from decay chains of the form: H , A → e χ i e χ j → e + e − µ + µ − e χ e χ . (3)If e χ i ( e χ j ) decays into an e + e − ( µ + µ − ) pair, then M ( e + e − ) ( M ( µ + µ − )) is bounded above by m e χ i − m e χ ( m e χ j − m e χ ). On the other hand, if e χ i ( e χ j ) decays into a µ + µ − ( e + e − ) pair,then these M ( e + e − ) and M ( µ + µ − ) upper bounds are swapped. Superposition of these twopossibilities yields a ‘box’ when i = j (which will be called an ‘ i - i box’) and a ‘wedge’ (or‘L-shape’) when i = j (this will be called an ‘ i - j -wedge’).A heavy neutralino, e χ i , could instead decay to the e χ + leptons final state via a pair oftwo-body decays featuring an on-mass-shell charged slepton of mass m e ℓ . Events containingsuch decays will lead to the same wedgebox pattern topologies as noted above; however, theupper bound on M ( ℓ + ℓ − ) is modified to [50] M ( ℓ + ℓ − ) < m e χ i vuuut − m e ℓ m e χ i vuut − m e χ m e ℓ ! . (4)The M ( ℓ + ℓ − ) spectrum is basically triangular in this case and sharply peaked toward the upperbound, while the former three-body decays yield a similar but less sharply peaked spectrum.The two-body decay series alternatively could be via an on-mass-shell Z , resulting in an M ( ℓ + ℓ − ) = M Z spike.Additional complications can arise if the heavy neutralino e χ i can decay into another neu-tralino e χ j ( j = 1) or a chargino which subsequently decays to yield the e χ final state. These In fact, this extra restriction is not strictly necessary, since recent preliminary work shows same-flavorfour-lepton final states can be correctly paired with a reasonably high efficiency for at least some processesand some points in the MSSM parameter space [49]. Note that this is the physical slepton mass, not the soft mass input. e χ i to e χ j ( j = 1) decay chains involving e χ → ℓ + ℓ − e χ , e χ → ℓ + ℓ − e χ , and/or e χ → ℓ + ℓ − e χ will generate additional abrupt eventpopulation changes or edges, termed ‘stripes,’ on the wedgebox plot. One can imagine quiteelaborate decay chains, with e χ → e χ → e χ → e χ for instance. However, such elaborate chainsare very unlikely to emerge from any reasonable or even allowed choice of MSSM input param-eters. Further, each step in such elaborate decay chains either produces extra visible particlesin the final state or one must pay the price of the BR to neutrino-containing states. The lattertends to make the contribution from such channels insignificant, while the former, in additionto also being suppressed by the additional BRs, may also be cut if extra restrictions are placedon the final state composition in addition to demanding an e + e − pair and a µ + µ − pair. Theaforementioned extra visible particles could be two more leptons, meaning that all four leptonscome from only one of the initial -inos, e χ i → ℓ + ℓ − e χ k → ℓ + ℓ − ℓ ′ + ℓ ′− e χ , while the other –ino,which must yield no leptons (or other visible final state SM particles forbidden by additionalcuts), decays via e χ j → ν ¯ ν e χ or e χ j → q ¯ q e χ . Again though such channels will be suppressedby the additional required BRs. A further caveat is that decays with extra missing energy(carried off by neutrinos, for example) or missed particles can further smear the endpoint.The presence of charginos may also further complicate the wedgebox picture. Heavier –inoscan decay to the LSP + lepton pair final state via a chargino, e χ i → ℓ + ν e χ − → ℓ + νℓ ′− ¯ ν ′ e χ ,or a Higgs boson itself may decay into a chargino pair, with one chargino subsequently yield-ing three leptons while the other chargino yields the remaining one (such events are called‘3+1 events’ [48]). The chargino yielding three leptons will typically decay via a e χ , resultingin a re-enforcement of the solely –ino-generated wedgebox plot topology. A single chargino-generated lepton paired with another lepton from a different source produces a wedge-likestructure but with no definite upper bound. For a more in-depth discussion of these nuances,see [48].The right-hand plot in Fig. 9 shows the wedgebox plot obtained in the case of MSSM Point1, assuming an integrated LHC luminosity of 300 fb − . Criteria for event selection are as givenin the previous section, save that the more restrictive demand of an e + e − µ + µ − final state isapplied while the Z -veto and four-lepton invariant mass cuts are not applied. Both signaland background events are included; the former are colored black. The latter consist of bothSM backgrounds (on- or off-mass-shell Z -boson pair-production — Z ∗ ) Z ∗ ) , 83 events, and t ¯ tZ ∗ ) , largely removed by the missing energy and jet cuts, 2 remaining events; these eventsare colored red and purple, respectively, in Fig. 9 ) and MSSM sparticle production processes(‘direct’ neutralino or chargino production, 4 events, and slepton pair-production, 22 events;such events are colored green and blue, respectively, in Fig. 9). No events from colored sparticleproduction survive the cuts, particularly the jet cut — this is a crucial result. Signal eventsconsist of 14 H events and 25 A events, yielding a signal to background of 39 : 111 = 1 : 2 . S/ √ B = 3 .
7, this is not good enough to claim a discovery based on Relation (2). If theinput CP-odd Higgs boson mass is lowered to M A = 400 GeV, whose wedgebox plot is the left-hand plot of Fig. 9, then the number of signal events rises to 14 + 52 = 66 H and A events(runs for MSSM backgrounds gave 2 ‘direct’ neutralino-chargino events and 26 slepton-pairproduction events), yielding S/ √ B = 6 . A -generated events. Comparing the M A = 500 GeV (MSSM Point 1)plot ( b ) and the M A = 400 GeV plot ( a ) in Fig. 9 shows how the increased number of signalevents in ( a ) more fully fills in the 2-2 box whose outer edges (dashed lines in the figure) are29 ( m + m - ) ( G e V ) M(e + e - ) (GeV) m A = 400 GeV m A = 500 GeV (a) (b) Figure 9: Wedgebox plot for MSSM Point 1 inputs with M A = 500 GeV ( b ) and shifting to M A = 400 GeV ( a ), assuming an integrated luminosity of 300 fb − . Neither the Z -veto cutnor the 4-lepton invariant mass cut are enabled. Black-colored markers are for the H and A signal events. SM background events from Z ∗ ) Z ∗ ) (where either one or both of the Z ’sare permitted to be off-mass-shell are red), while the two surviving t ¯ tZ ∗ ) events are purple.MSSM background events from slepton production or direct neutralino/chargino productionare in blue and green, respectively. The horizontal and vertical dashed lines forming a boxare at the location m e χ − m e χ . MSSM Point 1 –ino and slepton inputs are µ = −
500 GeV, M = 180 GeV, M = 90 GeV, m e ℓ soft = m e τ soft = 250 GeV.given by m e χ − m e χ = 86 . e χ decays into on-mass-shell sleptons.A key observation is that the distributions of the signal and the background events differmarkedly . All but one of the signal events lie within the 2-2 box . The majority of theslepton pair-production events (19 out of 26 events for ( a ) and 17 out of 22 events for ( b )),the dominant MSSM background, lie outside the 2-2 box. The topology of these ‘3+1’ eventsis a 2-2 box plus a wedge lacking a clear outer edge extending from said box (see [48]). Thefew ‘direct’ neutralino and chargino production events happen to all lie within the 2-2 box;however, these events are actually due to e χ e χ pair-production and thus, for a larger sample, On the other hand, the distributions of A and H events show no substantial systematic differences intheir distributions’ wedgebox plot topologies. Note that a similar result is found in Fig. 16 of [9]. There, however, only signal events were shown,and, since a priori only H , A → e χ e χ events were considered, the vast array of other potential wedgeboxtopologies was not brought to light. If direct neutralino pair-production produces a significant number of events, then the dominant source ofsaid events is always e χ e χ production; e χ e χ production is heavily suppressed. See discussion in [48]. This M ( e + e − ) and/or M ( µ + µ − ) equals M Z , which unfortunately is close to the outer edges of the 2-2 box. Usingthe unfair advantage of color-coded events, one can correctly choose to place the edges ofthe box so as to exclude most of the SM background events. Experimentalists may have amore difficult time deciding on wedgebox edges that lie too close to M Z . Though, at theprice of perhaps losing some of the signal events , one could make a selection rule of aneffective 2-2 box with edges sufficiently within M Z in such cases. Correct identification ofthe outer edge value for the 2-2 box removes all but 11 of the 85 SM background events.The signal:background is then 39 : 20 for ( b ) and 66 : 19 for ( a ), an immense improvementin the purity of the samples — both points now certainly satisfy the Relation (2) criterion.Accepting only points lying within a box with outer edges at 80 GeV, more safely eliminatingSM Z ∗ ) Z ∗ ) events, leads to a signal:background of 33 : 12 for ( b ) and 59 : 14 for ( a ). Notethat one can also select points lying well outside the 2-2 box to get a fairly pure sample (atthis point in the parameter space) of slepton pair-production events. Even if one does notknow where Nature has chosen to reside in the MSSM input parameter space, the selectionof only events occupying one distinct topological feature of the experimental wedgebox plotmay yield a sample pure enough (though one may not know exactly what purified sample onehas obtained!) to be amenable to other means of analysis (perhaps entailing some additionreasonable hypotheses as to what sparticles might be involved) [51].Fig. 10 in turn examines several related choices for input parameter sets, including MSSMPoint 2 — which is plot ( c ) therein, in which H and A have large BRs into heavier –ino pairssuch that the majority of the 4 ℓ signal events do not arise from e χ e χ decays for all points savethat of plot ( b ). Plot ( d ) differs from MSSM Point 2, plot ( c ), only in that the Higgsino mixingparameter µ is shifted from µ = −
200 GeV to µ = −
250 GeV. Yet even this modest changedrastically alters the topology of the resulting wedgebox plot. This is illustrative of how thewedgebox plot may be useful in extracting fairly detailed information about the –ino spectrumand corresponding MSSM input parameters. In plots ( a ) and ( b ) of Fig. 10 the EW gauginoinput parameters are raised from M = 200 GeV in plots ( c ) and ( d ) to M = 280 GeV (recallthe assumption used herein that the value of M is tied to that of M ). Also tan β is loweredfrom 35 to 20, while µ values of plots ( c ) and ( d ) are retained. Again, these shifts in inputparameters radically alter the resulting wedgebox topology. Plots ( a ) and ( b ) clearly showwedge-like topologies. Note again the markedly different event distributions for the signal andbackground events in all four plots, but particularly striking in plot ( a ). Note how the fourMSSM parameter set points yielding the wedgebox plots depicted in Fig. 10 all might crudelybe categorized as high tan β , low | µ | , low to moderate M , and light slepton points. Yet theassociated wedgebox plots come out decidedly different.Taking advantage of knowing which points in MSSM parameter space are being simulated leads to the general conclusion that, with a jet cut in place to remove cascade events from colored sparticledecays, the appearance of a disproportionately strong (densely populated) box on a wedgebox plot is highlyindicative of the presence of Higgs-boson-generated events. The caveat to this being that chargino productioncan generate a box-shape in some rather limited regions of the MSSM input parameter space. Again, see [48]for further discussion. Correct edge values from which to reconstruct information on the –ino mass spectrum would also be lost. ( m + m - ) ( G e V ) (a) M(e + e - ) (GeV) tan b = 20 tan b = 20M = 280 GeV M = 280 GeV m = -200 GeV m = -250 GeV (b) M ( m + m - ) ( G e V ) M(e + e - ) (GeV) (c) tan b = 35 tan b = 35M = 200 GeV M = 200 GeV m = -200 GeV m = -250 GeV (d) Figure 10: Wedgebox plot for MSSM Point 2 inputs ( c ) and shifting to M A = 400 GeV(left), assuming an integrated luminosity of 300 fb − . Neither the Z -veto cut nor the 4-lepton invariant mass cut are enabled. Black-colored markers are for the H and A signalevents. SM background events from Z ∗ ) Z ∗ ) (where either one or both of the Z ’s arepermitted to be off-mass-shell) are red, while the two surviving t ¯ tZ ∗ ) events are purple.MSSM background events from slepton production or direct neutralino/chargino productionare in blue and green, respectively. The horizontal and vertical dashed lines forming a boxare at the location M e χ − M e χ . MSSM Point 1 –ino and slepton inputs are µ = −
500 GeV, M = 180 GeV, M = 90 GeV, m e ℓ soft = m e τ soft = 250 GeV. Also indicated by dashed lines onthe plot are the 2-2, 3-3 and 4-4 box edges found from relation (4) — save for the 2-2 boxedges for ( c ) which are from m e χ − m e χ . 32able 7: Percentage contributions to H , A → ℓ events from the various neutralino and charginopair-production modes for the four MSSM Parameter set points given in Fig. 10. Based uponISAJET(ISASUSY) 7.58 [30] with no consideration given to any cuts. Decays that are kinematicallynot allowed are marked by a 0; contributions below 0 . neg ). H , A → Z ∗ ) Z ∗ ) , H → h h and A → h Z ∗ ) make negligible contributions in all cases. Also given arethe number of H , A signal events and the number of background events, assuming 300 fb − ofintegrated luminosity as in the figure. Decay Pair ( a ) ( b ) ( c ) ( d ) e χ e χ .
6% 70 .
6% 0 . . e χ e χ .
1% 4 .
5% 0 .
05% 13 . e χ e χ .
1% 13 .
0% 0 .
05% 1 . e χ e χ .
5% 0 .
4% 2 .
7% 0 . e χ e χ .
1% 5 .
0% 45 .
0% 9 . e χ e χ .
6% 7 . e χ ± e χ ∓ .
6% 6 .
5% 11 .
3% 31 . e χ +2 e χ − .
4% 0 . e χ e χ . . neg . e χ e χ . neg neg . H , A evts. 305,423 276,473 122,105 182,140bckgrd. evts. 683 257 132 186(something the experimentalist cannot know in the actual experiment) allows comparisonbetween the assorted calculated production rates at the four points and the observed featureson the wedgebox plots. Table 7 gives such theoretical estimates based on analysis of ISAJET(ISASUSY) 7.58 results for the four points . It must be borne in mind though that effectsfrom cuts may alter the percentage contributions found on the wedgebox plots from thosegiven in Table 7.The first thing to notice from this table is the virtual absence of events stemming from e χ to e χ decays for MSSM Point 2 = plot ( c ) relative to the other three points. This is due tothe fact that, for this input parameter set, the sparticle spectrum satisfies the condition that m e ν < m e χ < m e ℓ ± , meaning that e χ mainly decays via an on-mass-shell sneutrino ‘spoiler’mode, e χ → e ν ¯ ν → e χ ν ¯ ν , and its BR into a pair of charged leptons is highly suppressed. Forthe other three points, m e χ > m e ℓ ± , m e ν . Actually, of the four wedgebox plots shown in Fig. 10,the one for MSSM Point 2 most closely resembles a simple box. However, Table 7 indicatesthat (before cuts) 45 .
0% of the events are from e χ e χ , 39 .
6% of the events are from e χ e χ , and12 .
7% of the events are from e χ ± e χ ∓ , e χ +2 e χ − .In Fig. 10, charged sleptons are now light enough so that the neutralino to slepton decaychains, which make significant contributions to the four-lepton signal events, may proceedvia on-mass-shell charged sleptons. So while the outer edges of the 2-2 box in Fig. 9 was Table 3 given previously corresponds to column ( c ) in Table 7 with the H and A contributions listedseparately. e χ - e χ mass difference, here Relation 4 brings the slepton masses intoplay . In plot ( a ), virtually all e χ i to e χ decays proceed via on-mass-shell sleptons, butonly the e χ to e χ decay edge is significantly altered (by more than a couple GeV) — from m e χ − m e χ = 185 GeV to 151-156 GeV (at this point, 18% of four-lepton events are from e χ e χ according to Table 7). On the other hand, in plot ( b ), where the e χ i also decay to e χ viaon-mass-shell sleptons, edges are shifted from m e χ i − m e χ = 82 , ,
192 GeV to 76-78 , , i = 2 , ,
4, respectively , with i = 2 , , c ), the shift in the e χ to e χ decayedge is only 3 . e χ to e χ edge is virtually unchanged. This accounts for 87 . e χ is slightly complicated: e χ canonly decay into e χ via an on-mass-shell e µ , and this would lead to a tremendous shift in theedge position (from 61 GeV to 15 GeV); however, this is so close to the kinematical limit thatdecays through off-mass-shell Z ∗ should be competitive (again placing the edge at ∼
61 GeV).
But , since e χ decays lead to only a tiny fraction of the four-lepton events, note how thereis no visible edge or population discontinuity at this location (the innermost dashed box) onthe wedgebox plot. Lastly, with plot ( d ), again on-mass-shell slepton decays totally dominatefor i = 2 , ,
4, but only the e χ to e χ decay edge is significantly shifted (from 75 . . . . But, by Table 7, this decay is the most important contributor to the signalevents.For plot ( a ) of Fig. 10, the expected 2-4 wedge stands out clearly among the signal events,with outer edges at the expected location. The background is mostly from direct e χ e χ directproduction, giving the 2-3 wedge shown in green (direct neutralino-neutralino production ispredominantly e χ e χ at all interesting points in the MSSM parameter space, with direct e χ e χ production always highly suppressed [48]). The proximity of this wedge’s outer edges to the red M Z lines may complicate the experimental analysis; however, if the SM Z ∗ ) Z ∗ ) backgroundis well-modeled, a subtraction technique to clear up this zone may be feasible. Note thatselecting only events with 100 GeV < M ( e + e − ) <
150 GeV, 0 < M ( µ + µ − ) <
50 GeV or0 < M ( e + e − ) <
50 GeV 100 GeV < M ( µ + µ − ) <
150 GeV, corresponding to the legs of the2-4 wedge lying beyond the 2-3 wedge and the Z -line, changes the signal:background ratiofrom 728:683 seen on the plot to 128:15. This is an example of a cut that can be applied aposteriori based on the examination of the wedgebox plot — as opposed to assuming a priori extra knowledge about where in the MSSM parameter space Nature has chosen to sit.Plot ( b ) of Fig. 10 mainly shows a densely-populated 2-2 box whose edges are well insidethe M Z lines. A faint 2-3 or 2-4 wedge is also discernible (in fact Table 7 shows this to be a Unfortunately, the physical slepton masses input into HERWIG 6.5 are generated by ISASUSY 7.58 [30],which neglects a left-right mixing term ∝ m ℓ µ tan β (see [27]). While this term is negligible for selectrons, itdoes shift the physical smuon masses by as much as a few GeV. Neglecting this term results in degenerate softslepton inputs leading to degenerate physical selectron and smuons masses (so the smuon masses for MSSMPoint 2 given in Table 1 are changed into the mass values given there for the selectrons), which in turn maynoticeably under-estimate the mass splitting between smuons and thus the thickness of the edges shown onthe plots. Later versions of ISAJET correct this oversight, as do private codes employed in Sect. 2. Due to the program oversight mentioned in the last footnote, the thicknesses of these edges shrink to75 . . , . . , . . Again, this feature is lost in HERWIG 6.5/ISAJET 7.58 . In HERWIG 6.5/ISAJET 7.58 this width shrinks to 55 . . e χ e χ and e χ e χ decays are present while e χ e χ are absent (further suggesting that saiddecay mode is kinematically inaccessible, which helps pin down the relative masses of theheavy Higgs bosons and the heavier neutralinos).Plot ( c )’s most obvious feature is an outer box, which in fact is a 4-4 box. Topology alonedoes not distinguish this from a plot dominated by a 3-3 box or a 2-2 box, though the locationof the outer edges well beyond M Z might give pause for entertaining the latter possibility. A3-4 wedge may also be discerned from the somewhat diminished event population in the upperright-hand box in the plot. Comparison of this plot with the other three quickly points out theabsence of a dense event-population in this plot. Seeing such a wedgebox plot experimentallystrongly hints that leptonic e χ decays are being suppressed, perhaps with a mass spectrumfavoring sneutrino spoiler modes as noted above.Like plot ( b ), plot ( d ) shows a 2-2 box, but with outer edges at a very different location.Plot ( d ) also has more signal events outside of the 2-2 box than does plot ( b ), and said eventsare more scattered in ( d ). A lot of these events are from H , A decays into e χ ± e χ ∓ pairs. Thus,the alignment of the wedgebox features to the dashed lines derived from neutralino featuresshown is less compelling.In both Fig. 9 and Fig. 10, note how closely the wedgebox plot features, obtained by the fullevent generator & detector simulation analysis, conform to the dashed-line borders expectedfrom the simple formula 4. This strongly supports the assertion that a wedgebox-style analysisis realistic in the actual experimental situation. Recapping the findings presented herein:
For many interesting choices of the basic input parameters of the MSSM, heavier Higgs bosondecay modes of the type H , A → e χ i e χ j , with i, j = 1 are potentially important LHC signalmodes. The neutralinos’ subsequent leptonic decays, typified by e χ i → ℓ + ℓ − e χ , can yield afour-isolated-lepton (where here ℓ refers to electrons and/or muons) plus missing-transverse-energy signature. Such leptonic neutralino decays may proceed via either an intermediatecharged slepton or via an intermediate Z ∗ ) , where in either case this intermediate statemay be on- or off-mass-shell. The present study presents for the first time a systematicinvestigation of the potential for discovering such a signature at the LHC, including all possiblesuch neutralino pairs: e χ e χ , e χ e χ , e χ e χ , e χ e χ , e χ e χ , and e χ e χ . Other Higgs boson decays thatmay lead to the same signature are also incorporated, including: decays to chargino pairs H , A → e χ ± e χ ∓ , e χ +2 e χ − , in which case e χ ∓ yields three leptons while the other chargino givesthe fourth; H , A → e χ e χ , e χ e χ , where the e χ or e χ must provide all four leptons; and H → h h , Z ∗ ) Z ∗ ) , A → h Z ∗ ) , & H , A → e ℓ + e ℓ − , all three of which yield negligiblecontributions in all cases studied. This surpasses previous studies which restricted virtuallyall of their attention to H , A → e χ e χ , and also did not consider the possibility of neutralino35ecays to on-mass-shell sleptons (with the incorporation of the heaviest neutralinos as is doneherein this assumption becomes particularly restrictive).Naturally, at least some of the –inos must be reasonably light for this H , A → ℓ + E miss T signature to be seen. Parameter-space scans studying the potential scope of such a signalindicate that the –ino parameter M needs to be relatively low while the Higgsino mixingparameter µ need not be so constrained (however, if | µ | is not also relatively low, then thesignal is dominated by the e χ e χ mode). Relatively light slepton masses are also quite helpful,and the slepton mass spectrum plays a crucial rˆole in determining for what values of the otherMSSM input parameters large rates may occur. Said large rates are possible throughoutmost of the phenomenologically-interesting value ranges of the Higgs-sector parameters M A and tan β , depending of course on the accompanying choice of other MSSM inputs, as thediscovery regions delineated herein illustrate. To clearly demonstrate the potential importance of the H , A → ℓ + E miss T signature in thehunt for the heavier Higgs bosons, Figs. 11 and 12 again show the discovery regions associatedwith MSSM Point 1 and MSSM Point 2 neutralino input parameter sets (as depicted before inFigs. 7 and 8, respectively), but this time with a logarithmic scale for tan β and also showingthe expected reaches, assuming 300 fb − of integrated luminosity at the LHC, of Higgs bosondecay modes into SM daughter particles as developed by the ATLAS collaboration [45] .Clearly, the new neutralino decay mode signature can extend the discovery reach for theheavier MSSM Higgs bosons to much higher values of M A , and also offer at least partialcoverage of the so-called ‘decoupling region’ where only the lightest Higgs state h could beestablished in the past (through its decays into SM objects) and where said h may be difficultto distinguish from the sole Higgs boson of the minimal SM. Thus, a more complete analysisof the H , A → e χ i e χ j modes as is presented here may be crucial to the establishment of anextended Higgs sector. The inclusion of the heavier neutralinos, e χ and e χ , absent in previousstudies, is essential in extending the reach of the H , A → ℓ + E miss T signature up to thehigher Higgs boson masses unattainable by the SM decay modes.It should be noted that the ATLAS discovery contours presented in Figs. 11 and 12 are not obtained using the same choice of MSSM input parameters as are the H , A → e χ i e χ j discoveryregions developed in the present work. In fact, the ATLAS discovery regions used input choicesdesigned to eliminate, or at least minimize, the Higgs boson decays into sparticles. Thus, thereach of the ATLAS discovery contours essentially represents the maximum expanse in theMSSM parameter space achievable through these Higgs boson decays to SM particles underthe (unsubstantiated) assumption of a very heavy sparticle sector. Stated another way: werethe ATLAS discovery regions to be generated for the same set of neutralino input parametersas the H , A → e χ i e χ j discovery regions presented herein, the former may well shrink in size(and certainly not increase ), further emphasizing the importance of thoroughly studying the H , A → ℓ + E miss T signature. It would certainly be desirable to re-do the SM-like signaturereaches of MSSM Higgs bosons in the presence of light sparticle spectra identical to those ATLAS collaboration discovery region contour lines in Figs. 11 and 12 have been remade to match asclosely as possible those in the original plot. (GeV) A M100 200 300 400 500 600 b t a n
10 1111 LEP 2000 (GeV) A M100 200 300 400 500 600 b t a n (cid:242)(cid:242) -1 Ldt = 300fb -1 Ldt = 100fb
Figure 11: Discovery regions in the ( M A , tan β ) plane, here with a logarithmic tan β scale,assuming MSSM Parameter Set 1 –ino inputs and for L int = 100 fb − and 300 fb − , for the(lower plot) MSSM Higgs bosons’ 4 ℓ signals from their decays into neutralino or chargino pairs(here H , A decays to e χ e χ totally dominate). This is shown juxtaposed (upper plot) with300 fb − regions for MSSM Higgs boson signatures from decays to SM particles based uponLEP results and ATLAS simulations [45], where labels represent: 1. H → Z Z ∗ → t → bH + , H + → τ + ν + c.c.; 3. t ¯ th , h → b ¯ b ; 4. h → γγ and W ± h /tth , h → γγ ;5. b ¯ bH , b ¯ bA with H /A → b ¯ b ; 6. H + → t ¯ b + c.c.; 7. H /A → µ + µ − ; 8. H /A → τ + τ − ;9. g ¯ b → ¯ tH + , H + → τ + ν + c.c.; 10. H → h h → b ¯ bγγ ; 11. A → Z h → ℓ + ℓ − b ¯ b ;12. H /A → t ¯ t . Note that SM discovery regions are not for the same input parameters:they presume a very heavy sparticle spectrum; identical MSSM inputs to those used for thelower plot may well yield smaller SM discovery regions in a revised upper plot. For the 4 ℓ signals from e χ i e χ j , e χ + m e χ − n decays, the MSSM Parameter Set 1 –ino/slepton parameters are µ = −
500 GeV, M = 180 GeV, M = 90 GeV and m e ℓ soft = m e τ soft = 250 GeV.37 (GeV) A M100 200 300 400 500 600 700 800 b t a n
81 9 LEP 2000 (GeV) A M100 200 300 400 500 600 700 800 b t a n (cid:242)(cid:242) -1 Ldt = 100fb -1 Ldt = 300fb (cid:242)(cid:242) -1 Ldt = 100fb -1 Ldt = 300fb
Figure 12: Discovery regions in the ( M A , tan β ) plane, here with a logarithmic tan β scale,assuming MSSM Parameter Set 2 –ino inputs and for L int = 100 fb − and 300 fb − , for the(lower plot) MSSM Higgs bosons’ 4 ℓ signals from their decays into neutralino or charginopairs (here Higgs boson decays to higher-mass neutralinos typically dominate). This is shownjuxtaposed (upper plot) with 300 fb − regions for MSSM Higgs boson signatures from decaysto SM particles as in Fig. 11. For the 4 ℓ signals from e χ i e χ j , e χ + m e χ − n decays, the MSSM ParameterSet 2 –ino/slepton parameters are µ = −
200 GeV, M = 200 GeV, M = 100 GeV, m e ℓ soft =150 GeV and m e τ soft = 250 GeV. Here Higgs boson decays to a variety of higher mass –inos(see text) constitute the majority of the signal events. Note that, as in Fig. 11, since ATLASdiscovery regions presume a very heavy sparticle spectrum, SM discovery regions made for thesame MSSM input parameters as used in the lower plot may well yield smaller SM discoveryregions in a revised upper plot. 38tudied herein for the Higgs-to-sparticle decay channels; however, this is clearly beyond thescope and capabilities of this study. It also must be emphasized that the diminution of theexpected signatures from SM decay modes of the MSSM Higgs bosons was investigated in [7]and thus is fairly well-established as well as inherently sensible.Previous studies exploring Higgs-to-sparticle decay channels, whether for neutral Higgsbosons ( e.g. , CMS [9]) or for charged Higgs bosons ( e.g. , ATLAS [52], CMS [20]), — andcomparing, to some extent, SM and SUSY decay modes — have not re-scaled the reachesof previously-studied SM decay channels (done by the same collaboration) to allow a rea-sonable comparison to the new-found sparticle decay modes; nor have the SM decay modesbeen re-analyzed for the same set of MSSM input parameters. Yet clearly such comparisonsare absolutely essential to gauge the scope and impact of the new sparticle-decay channels.Certainly, the comparisons presented in Figs. 11 and 12 are less than optimal; however, theyare far from un-informative.It is also important to keep in mind that the assumptions inherent in the ATLAS (andCMS) discovery regions for the SM decay modes of the MSSM Higgs bosons are no lessrestrictive than the choices of MSSM input parameters made to generate the two 4 ℓ + E miss T discovery regions in this study. The parameter space scans of Sect. 2 further enable the readerto put the two discovery regions shown here into a wider perspective. The new H , A → ℓ + E miss T discovery regions have been mapped out using a full eventgenerator-level analysis utilizing HERWIG coupled with a detector simulation on a par withexperimental analyses. All significant backgrounds have been included in the analysis, somefor the first time in the study of such a signature. The importance of the restriction onjet activity employed herein is particularly noteworthy. Without such a cut the Higgs signalcould be swamped by the cascade decays of colored sparticles (gluinos and squarks), unless saidsparticles are a priori assumed to be quite heavy (at or above the TeV scale). The ultimatelimit of this type of jet cut, to demand that events be ‘hadronically quiet’ quickly springsto mind as an attractive search category. Yet care must be taken here since, in Higgs bosonproduction via gg → H , A and b ¯ b → H , A , jets emerge in the final state alongside the Higgsbosons due to PS effects, though such additional jets tend to be rather soft and collinear to thebeam directions. In addition, rather than emulating Higgs boson production via gg → H , A and b ¯ b → H , A , one could instead consider gg → ggH , ggA and gg → b ¯ bH , b ¯ bA processes,in which case one might worry about stronger jet activity emerging. The true signal rate isthe sum of these and the previous process types, after making a correction for the overlap(as discussed previously). HERWIG simulations of gg → b ¯ bH , b ¯ bA at selected points inthe parameter space indicate that the these processes are in fact removed by the jet cutimposed herein. To better optimize the level of hadronic activity that should be allowed, fullimplementation of 2 → gg → ggH , ggA and other channels yielding twolight jets and a H , A in the final state) into HERWIG must be completed (work in progress[53]).The BRs of H and A to the assorted –ino pairs can certainly differ markedly in regionswhere the signal is large, as seen for instance in Table 3; thus one must not assume thatthe two contribute a roughly equal number of events to the 4 ℓ + E miss T signal rate. On the39ther hand, results also show that only in quite narrow low- M A threshold regions within thediscovery areas (wherein the small M H - M A mass difference is crucial) do events due to one orthe other Higgs boson (in this case the lighter A ) totally dominate, producing in excess of90% of the signal events. General statements beyond this concerning the H and A admixturepresent in the signal seem elusive. Throughout the e χ e χ -dominated discovery region of Fig.7, A produced the majority of the events (though in some cases only slightly more than H ); whereas in Fig. 8 there were substantial zones in which H events dominated (as well aslarge segments wherein the two Higgs boson contributions were within ∼
20% of each other).Finally, though the cuts did typically eliminate slightly more H events than A events, thiseffect was of little significance. Note that in comparing the signal with the MSSM backgrounds, the present study followsthe standard procedure of comparing signal and background rates at the same point in theMSSM parameter space. One could well ask whether or not larger backgrounds at a differentpoint in parameter space could lead to the number of excess events attributed to the signalat the designated point in the MSSM parameter space. One way of addressing this issueis to look at the distribution of the signal+background events on a M ( e + e − ) vs. M ( µ + µ − )wedgebox plot in addition to merely asking what is the raw rate. To wit, analyses of selectedpoints in parameter space, again at the full event generator + detector simulation level, arepresented illustrating that: (1) small changes in the MSSM input parameters can lead tosignificant topological changes in the pattern observed on the wedgebox plot; (2) the signaland background events often have markedly different distribution patterns on the wedgeboxplot, pointing toward the possibility of further purifying cuts (perhaps in conjunction withextra information garnered from other studies or additional assumptions to clarify of whatone is obtaining a purer sample) such as the example presented for plot ( a ) of Fig. 10; and(3) the composition of the H , A → ℓ + E miss T signal, that is, what percentages are due to H , A → e χ i e χ j for different i and j , may be ascertained to some level. The basic topologicalfeatures of the wedgebox plot provide strong, often easily interpreted, leads as to which modesare the dominant contributors. The locations of the edges of such features on the wedgeboxplot also provide information about the sparticle spectrum. The densities of event points ineach component of wedgebox checkerboard can also be used to distinguish wedgebox plotswith the same topological features/edges, such as, for instance, telling a wedgebox plot witha 2-3 wedge and a 2-2 box from one with only a 2-3 wedge. Further, these point densitydistributions may be used to reconstruct information about the relative production rates ofthe different H , A → e χ i e χ j processes, though extracting such ‘dynamical’ information maywell be far more complicated than is the task of extracting ‘kinematical’ information aboutthe sparticle spectrum from the locations of the edges. All of this is further complicated bythe remaining background events, and a more holistic study looking at both the Higgs bosonproduced signal and the MSSM backgrounds together may be most appropriate [48].40 ote Motivated in part by the earlier archival submission of this work, a similar analysis waseventually carried out by a member of ATLAS [54], also aiming at mapping out MSSM Higgsboson discovery regions via H , A → e χ i e χ j decays. Results of this ATLAS analysis areessentially consistent with those presented herein, though the actual shapes of the discoveryregions obtained differ somewhat. These differences are in part attributable to adoptingdifferent selection criteria and employing different simulation tools. Of particular note are the t ¯ t and b ¯ bZ ∗ ) backgrounds which are quite significant in the case of the ATLAS analysis butyield no background events in this study . This is mainly due to the more stringent leptonisolation criteria adopted for this study which are very effective at removing leptons producedin these two would-be background processes from B -mesons decays. The restrictions on E ℓT ,which are absent from [54], also aid in removing residual background events. Acknowledgments
The authors thank the organizers of the 2003 Les Houches workshop in association withwhich earlier stages of this work were performed. We also thank Guang Bian for assistancein preparing a couple of the figures. Communications with Simonetta Gentile are gratefullyacknowledged. This work was supported in part by National Natural Science Foundation ofChina Grant No. 10875063 to MB and a Royal Society Conference Grant to SM, who is alsosupported in part by the program ‘Visiting Professor - Azione D - Atto Integrativo tra laRegione Piemonte e gli Atenei Piemontesi’.
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