Table Of ContentHunting Quasi-Degenerate Higgsinos
Zhenyu Han,1 Graham D. Kribs,1,2 Adam Martin,3 and Arjun Menon1
1Department of Physics, University of Oregon, Eugene, OR 97403
2School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540
3Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA
We present a new strategy to uncover light, quasi-degenerate Higgsinos, a likely ingredient in
a natural supersymmetric model. Our strategy focuses on Higgsinos with inter-state splittings
of O(5−50)GeV that are produced in association with a hard, initial state jet and decay via
off-shell gauge bosons to two or more leptons and missing energy, pp → j + E/ + 2+(cid:96). The
T
additional jet is used for triggering, allowing us to significantly loosen the lepton requirements and
gain sensitivity to small inter-Higgsino splittings. Focusing on the two-lepton signal, we find the
seemingly large backgrounds from diboson plus jet, t¯t and Z/γ∗+j can be reduced with careful
4 cuts,andthatfakebackgroundsappearminor. ForHiggsinomassesmχ justabovethecurrentLEP
1 IIbound(µ(cid:39)110GeV)wefindthesignificancecanbeashighas3σ attheLHCusingtheexisting
0 20fb−1 of 8 TeV data. Extrapolating to LHC at 14 TeV with 100fb−1 data, and as one example
2 M =M =500GeV, we find 5σ evidence for m (cid:46)140GeV and 2σ evidence for m (cid:46)200GeV.
1 2 χ χ
n WealsopresentareinterpretationofATLAS/CMSmonojetboundsintermsofdegenerateHiggsino
a (δm (cid:28)5GeV)plusjetproduction. Wefindthecurrentmonojetboundsonm arenobetterthan
χ χ
J
the chargino bounds from LEP II.
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I. INTRODUCTION
Higgsinos, the superpartners of the Higgs doublets, are a key element in a natural supersymmetric model.
The Higgsino mass is controlled by the µ parameter which, via supersymmetry, directly enters into the
tree-level mass matrix for the Higgs bosons M2. In order for electroweak symmetry breakdown (EWSB)
H
to occur at the correct scale without unnatural cancellations, the µ parameter must lie at the weak scale,
∼ 100GeV [1]. The Higgs mass matrix is also influenced by other supersymmetric particles – squarks,
gluinos, winos, etc., but the Higgsinos are the only superpartners whose effect on M2 enters at tree-level.
H
The fact that Higgsinos play such an important role in the delicate process of EWSB in supersymmetric
theories makes them a desirable target at the LHC. Studying Higgsinos at a hadron collider, however, is
easier said than done.
One way to produce Higgsinos is to produce more massive, strongly coupled particles (i.e. squarks) that
subsequentlydecaytoHiggsinos. Thebenefitsofthisapproacharethelargercrosssectionforcoloredobjects
and the fact that there are lots of different colored sparticles to produce which can decay to Higgsinos
(resulting in a multiplicity factor, essentially). The downside of this method is that it depends on the
detailsofthesupersymmetryspectrumthroughthemassesandbranchingfractionsofthecoloredsparticles.
Furthermore, the easiest colored sparticles to produce are the first generation squarks1, but they couple
weakly to Higgsinos due to their small Yukawa couplings. The amount of information light-flavor squarks
can yield on the Higgsinos depends on the mixing among µ, M , and M . A further problem with using
1 2
light-flavor squarks as a Higgsino source is that they play little role on the Higgs sector and can therefore
naturally have masses well beyond the reach of the LHC.
Unlike light-flavor squarks, top squarks do couple strongly to Higgsinos, but they are more difficult to
produce. The current stop bounds are roughly 700GeV [2–7] assuming a massless lightest supersymmetric
particle(LSP)2 whilethe projected exclusionlimits forsame stopscenarioafter 3000fb−1 ofluminosityata
14TeVLHCareonly∼1.1TeV[9]. Whiletheseextrapolationsareroughandnottailoredtowardscapturing
Higgsinos from stop decays, the relatively small increase in limits given a huge increase in luminosity is a
powerful indication of how hard top squarks are to produce and detect. Clearly, at masses not much higher
than the current limits, top squarks cease to be a useful source for Higgsinos and we must look for directly
produced Higgsinos instead.
Direct Higgsino production has the benefit that it is much less sensitive to the details of the rest of the
spectra. However, direct production of any electroweakinos (wino, bino, Higgsinos) occurs through weak
interactions, so the rates are much smaller than the production of colored superpartners. Traditionally,
directly produced electroweakinos are searched for in trilepton plus missing energy final states, 3(cid:96)+E/
T
(which we will refer to simply as trilepton searches). Trilepton searches target heavier electroweakinos that
decay to the lightest electroweakino by emitting a W/Z.3 Typically, the largest contributing process is
pp→χ±χ0 →3(cid:96)+E/ . A drawback to the trilepton search is that it is only sensitive when there is a large
1 2 T
O(m ,m ) splitting among the electroweakinos. As the inter-state splitting decreases, the intermediate
W Z
gaugebosonsinthedecaychaingooff-shellandtheleptonstheyemitbecometoosofttotriggeronefficiently;
the electroweakino signal is simply lost.
BothATLASandCMShavesearchedinthetrileptonchannelusinga“simplifiedmodel”approach[10,11].
These searches have cut a swath through parameter space4, though, as expected from the argument above
the limits rapidly degrade as the inter-electroweakino splitting drops below ∼m . This limitation is set by
W
kinematicsandisnotdependentonthecompositionoftheLSPornearbyelectroweakinos. Theinsensitivity
1 Gluinosproductioncanalsobelarge,butgluinosdonottalktoelectroweakinosdirectly.
2 InRef.[8], wereinterpretedexistingstop/sbottomsearchesinasetupwithHiggsino-likeLSP,andfoundthelimitsarenot
dramaticallydifferent,mt˜(cid:38)700GeV.
3 Leptons can also be produced from chargino/neutralino decays to sleptons, but this requires that the sleptons are lighter
thantheelectroweakinos. Ourfocusisonspectrawithelectroweakinosmuchlighterthanallothersuperpartners,sowewill
ignorethesleptonpossibilityhere.
4 ATLAS and CMS collaborations both use lepton triggers for these events. The CMS analysis uses a dilepton trigger,
requiring pT > 17GeV for the leading lepton, and pT > 8GeV for the subleading lepton. The ATLAS analysis uses a
combination of single- and double-lepton triggers, with thresholds depending on the lepton flavor: p >25GeV for single
T,(cid:96)
leptons, p > 25GeV,p > 10GeV (p > 14GeV) for the asymmetric (symmetric) di-electron trigger, p >
T,(cid:96)1 T,(cid:96)2 T,(cid:96)i T,(cid:96)1
18GeV,pT,(cid:96)2 > 10GeV (pT,(cid:96)i > 14GeV) for the asymmetric (symmetric) di-muon trigger, and pT,e > 14GeV,pT,µ >
10GeV(pT,µ>18GeV,pT,e>10GeV)forthemixeddi-leptontrigger. Attheanalysislevel,bothATLASandCMSrequire
p >10GeVforallthreeleptonsintheevent.
T,(cid:96)
3
tosmallsplittingwillnotbeeasilyremediedwithmoredataorhigherenergy. ProjectionsfromATLASand
CMS collaborations [9, 12, 13], albeit preliminary, show the same blind spot that is present in the existing
limits.
This blind spot exactly corresponds to the electroweakino spectrum one expects in natural supersym-
metry, provided the gravitino is not the LSP. There, the Higgsino must be light from the naturalness
arguments presented earlier, while the wino and bino masses (M and M , respectively) can be much
2 1
heavier. The result is a dominantly-Higgsino LSP, accompanied by one charged and one neutral state,
both O(m2 /M ,m2 /M ) ∼ 5−50GeV heavier than the LSP. The push for natural supersymmetry –
W 1 W 2
in light of the ever-increasing bounds on the first and second generation squark (and gluino) – combined
with the problematically-split electroweakino sectors these models possess, make new search strategies for
nearly degenerate Higgsinos a high priority as we prepare for the 14 TeV LHC run. Even neglecting the
UV motivation for µ (cid:28) M ,M , degenerate Higgsino searches are well-motivated simply because there
1 2
is no LHC bound: there are bounds approaching 800GeV on first and second generation squarks in the
limit of a heavy gluino [14, 15] and ∼ 1.7TeV if m ∼ M [15], stop/sbottom squark bounds are sim-
Q˜ 3
ilar m ∼ m ∼ 700GeV [2–7, 14], and gluinos produced in a heavy squark limit must be heavier than
t˜ ˜b
1.3TeV[15–17]. Meanwhile,aswewillshow,thebestlimitondegenerateHiggsinosstillcomesfromLEPII,
m (cid:38)103GeV [18]. If the Higgsino is absolutely stable, the lightest neutral Higgsino could be dark matter.
χ
Giventhemasshierarchyweconsider,µ(cid:28)M ,M ,theannihilationrateislarge,causingthethermalabun-
1 2
dance of the Higgsino to be well below the cosmological abundance. While safe from cosmological bounds,
there are many ways to obtain a higher abundance without significantly affecting our signal.
In this paper we propose a new search aimed directly at quasi-degenerate Higgsinos. Unlike the trilepton
search,oursearchtargetsHiggsinosthatareproducedinassociationwithahigh-p jet: pp→χχ+j,where
T
χ is any state in the Higgsino multiplets. By producing this final state rather than Higgsinos alone, we
have another object in the event that can be triggered upon. Using the hard initial-state radiation (ISR)
for triggering, we gain the freedom to significantly relax the lepton energy requirements and push to smaller
splittings, first explored in Ref. [19]. Some other recent, alternative studies on electroweakinos can be found
in Ref. [20–22], though these studies do not use the χχ+j channel in the manner we propose.
Thelayoutoftherestofthispaperisasfollows: webeginwithanexplorationoftheparameterspaceand
propertiesofnearlydegenerateHiggsinosinSec.II.Next, inSec.III,wedetailourstrategyusingamonojet
final state by looking for two soft leptons, pp → j+E/ +(cid:96)(cid:96). The backgrounds for this process are sizable
T
at first, though they can be reduced with cuts. We exploit the fact that the signal leptons are softer than
the backgrounds leptons, which come predominantly from the decays of on-shell gauge bosons, yielding a
distinctm spectrum. Giventhesmallsignalandlow-p objectswearetargeting, Sec.IIIBisdevotedtoa
(cid:96)(cid:96) T
study of fake backgrounds, both from jets that fake leptons and double-parton scattering events that mimic
a single hard collision. In Sec. IV, we reinterprete the monojet plus missing energy signal into a bound on
Higgsinoproduction (thedetails ofour reinterpretationare givenin Appendix A).We findthe reinterpreted
LHC bound is no better than the LEP II bound, though it would be interesting to pursue an optimized
search at the 14 TeV LHC [23]. Finally, we conclude with a discussion in Sec. V.
II. THE PARAMETER SPACE OF DEGENERATE HIGGSINOS
WewishtostudysupersymmetricscenarioswheretheHiggsinomultiplets, consistingoftwoneutralWeyl
fermions and one electrically charged Dirac fermion, are much lighter than the other electroweak fermionic
superpartners (the winos and the bino). In terms of supersymmetry mass parameters, this means we are
interested in the hierarchy
µ(cid:28)M ,M . (1)
1 2
As our focus is entirely on the electroweakino sector of supersymmetric theories, we will assume throughout
this work that all other superpartners – the squarks, sleptons, heavy Higgses, and gluino – are effectively
4
decoupled. Once electroweak symmetry is broken, the Higgsinos mix with the neutral bino, and both the
charged and neutral components of the wino multiplet. This mixing splits the Higgsino multiplets, giving
slightly different masses to the two neutral Higgsino states χ0, χ0 and the charged state χ± and endowing
1 2 1
these three states with a small wino or bino component. The size of the splitting and the hierarchy among
thethreestatesdependsonthesizeofM andM relativetoeachotherandtoµ. Notethat,hadwechosen
1 2
the bino or wino to be the lightest electroweakino, the number of light states would be different; one neutral
state for a light bino, or one neutral and one charged state for a light wino.
To get some idea for the typical splitting size and parametric dependences of the mass splitting, we first
proceed analytically and look in two simple limits, M (cid:29) M > |µ| and M (cid:29) M > |µ|. Throughout this
1 2 2 1
study we will take M and M to be strictly positive. The neutralino mass matrix in the MSSM in the
1 2
(B(cid:101)0,W(cid:102)0,ψ0,ψ0) basis is
d u
M 0 −m t c m t s
1 W θW β W θW β
MN˜0 =−mW0tθWcβ mMW2cβ mW0cβ −m−Wµsβ (2)
m t s −m s −µ 0
W θW β W β
while the chargino mass matrix is
√
(cid:18) (cid:19)
M 2s m
M = √ 2 β W (3)
C˜ 2c m µ
β W
where for simplicity we neglect all CP phases.
Case I: M (cid:29)M >|µ|
1 2
In this case, the heavy bino can be integrated out. Depending on the sign of µ, the mixing angle between
W(cid:102)0 andψ−0 = √12(cid:2)ψu0 −ψd0(cid:3), orW(cid:102)0 andψ+0 = √12(cid:2)ψu0 +ψd0(cid:3), canbeenhancedasM2 approaches±µ. When
m (cid:28)M ∓µ, the splittings between the mostly Higgsino states are
W 2
(cid:12) (cid:12) (cid:12) (cid:12) m2 (1∓s )
(cid:12)m (cid:12)−(cid:12)m (cid:12)≈ W 2β (4)
(cid:12) χ±1 (cid:12) (cid:12) χ01(cid:12) 2(M2+|µ|)
(cid:12) (cid:12) (cid:12) (cid:12) m2 (1±s ) (cid:12) (cid:12) (cid:12) (cid:12) m2 (±|µ|s +M )
(cid:12)m (cid:12)−(cid:12)m (cid:12)≈ W 2β , (cid:12)m (cid:12)−(cid:12)m (cid:12)≈ W 2β 2 (5)
(cid:12) χ02(cid:12) (cid:12) χ±1 (cid:12) 2(M2−|µ|) (cid:12) χ02(cid:12) (cid:12) χ01(cid:12) (M22−|µ|2)
where the ± index corresponds to when µ is positive or negative, respectively. As M approaches |µ| the
2
wino fraction in the lightest neutralino increases, while the wino fraction in the next-to lightest neutralino
remains approximately constant. From Eq. (4) and Eq. (5) it is clear that the lightest neutralino and
chargino are more degenerate than the second neutralino and the lightest chargino.
Case II: M (cid:29)M >µ scenario
1 2
In this case, the heavy wino component can be integrated out. Similar to the previous scenario, depending
on the sign of µ, the splittings between the lightest neutralinos and the chargino are
(cid:12) (cid:12) (cid:12) (cid:12) m2 t2 (1±s )
(cid:12)m (cid:12)−(cid:12)m (cid:12)≈ W θW 2β (6)
(cid:12) χ±1 (cid:12) (cid:12) χ01(cid:12) 2(M1−|µ|)
(cid:12) (cid:12) (cid:12) (cid:12) m2 t2 (1∓s ) (cid:12) (cid:12) (cid:12) (cid:12) m2 t2 (±|µ|s +M )
(cid:12)m (cid:12)−(cid:12)m (cid:12)≈ W θW 2β , (cid:12)m (cid:12)−(cid:12)m (cid:12)≈ W θW 2β 1 (7)
(cid:12) χ02(cid:12) (cid:12) χ±1 (cid:12) 2(M1+|µ|) (cid:12) χ02(cid:12) (cid:12) χ01(cid:12) (M12−|µ|2)
Since t (cid:39) 0.5, the mixing between the (heavy) bino and the Higgsino is smaller than the mixing of a
θW
(heavy)winoandtheHiggsinoofthefirstcase, leadingtoasmalleroverallsplittingbetweentheneutralinos
andthechargino. Furthermore,unlikethefirstcase,thesplittingbetweenχ0 andχ± isgreaterthanbetween
1 1
χ0 and χ±.
2 1
Numerical Scan of the bino-wino Parameter Space
5
InFig.1weshowtheinter-Higgsinosplittingmoregenerally,asafunctionofbothM andM . Theregions
1 2
of low M and µ are constrained by the LEP II limit m (cid:38)103.5 GeV [18] when the splitting between the
2 χ±
1
lightest two states is larger than 3 GeV (that is true throughout the parameter space we consider).
Several observations can be made from the results of Fig. 1. One observation is the mass hierarchy:
m −m is greater than m −m throughout the parameter space. For M ,M <1TeV, m −m >
χ02 χ01 χ±1 χ01 1 2 χ02 χ01
10GeV, while the splitting between the lightest chargino and lightest neutralino is > 10GeV only for
M ,M (cid:46) 500GeV (for µ = 110GeV). As M or M are lowered, the splitting increases, with a steeper
1 2 1 2
gradient in the M direction. This is especially true for m −m which, because the bino mass does not
2 χ± χ0
1
affect the chargino sector, is largely independent of M . The size and sign of µ also affects the inter-state
1
splitting, as we can see by comparing the top and bottom panels in Fig. 1 (and from Eq. (5,7)). Clearly,
changesinµhavealargereffectontheinter-HiggsinosplittingwheneitherM orM issmall. Additionally,
1 2
larger µ increases the available M ,M parameter space by elevating the lightest chargino above the LEP
1 2
bound. Regarding the sign of µ, for the |µ| and tanβ values we are considering, the net effect of flipping the
sign of µ is a small increase (decrease), (cid:46)5GeV in m −m (m −m ) for all M ,M . Given that the
χ±1 χ01 χ02 χ01 1 2
shift from positive to negative µ is small, and that our results are not tied to any particular UV setup, we
assume µ>0 for the remainder of this work.
AnotherkeyingredientinHiggsinophenomenologyishowtheheavierχ± andχ0 decay. Forthechargino,
1 2
there is only one option: χ± → W∗χ0. For most mass splittings we are considering, the W∗ branching
1 1
ratiosareessentiallythesameasforon-shellW. Theexceptioniswhentheχ±−χ0 massdifferenceisbelow
1
∼2GeV – where the W∗ →c¯s(cs¯) and W∗ →τ±ν decays become kinematically squeezed, causing a slight
increase in the branching fractions to lighter states. For the χ0 state there are three options, i.) decay to χ0
2 1
via an off-shell Z∗, ii.) decay to χ± via an off-shell W∗, and iii.) loop level decay to a photon and χ0. The
1 1
breakdown between the three options depends on composition of χ0, χ0, which determines the couplings,
2 1
and kinematics. Since χ0 can decay to either sign chargino, one might expect the branching fraction to
2
W∗ to be larger than Z∗. However, the decays to chargino are more suppressed kinematically, since we see
from Fig. 1 that m −m is smaller than m −m . The χ0 decays to charginos are also suppressed
χ±1 χ01 χ02 χ01 2
when M is lighter and there is a non-negligible bino component in the neutral χ, since the bino does not
1
interact with electroweak gauge bosons. This can be contrasted with the situation when M is light. There
2
the Higgsinos mix with the wino, an electroweak triplet that possesses stronger couplings to gauge bosons,
generating a larger χ0 →W∗χ0 branching fraction. These tendencies are verified in Fig. 2 below, where we
2 1
plot the χ0 →Z∗χ0 and χ0 →W∗χ± branching ratios for M ,M <1TeV with µ=±110GeV,tanβ =10.
2 1 2 1 1 2
We find the two-body decay χ0 → γχ0 only makes up O(1%) of the total width due to the extra power of
2 1
α it requires5.
em
We have seen that the inter-Higgsino mass splittings m −m ,m −m are O(10GeV) for a wide
χ02 χ01 χ±1 χ01
range of M ,M > |µ| parameter space. Splittings of this size are substantially smaller than what the
1 2
trilepton searches are sensitive to, so all three states χ0,χ0,χ± are effectively invisible for this search – an
1 2 1
‘LSP multiplet’. At the same time, the mass splittings are large enough that the χ0 and χ± decays are
2 1
still prompt. Thus, we return to the question posed earlier: with trilepton searches insensitive, how do we
directly look for nearly degenerate Higgsinos? One way to proceed is to continue trilepton searches but
to look for the heavier electroweakinos, the mostly-bino or mostly-wino states with mass ∼ M or ∼ M ,
1 2
respectively. Thesestatesareheavy,sotheleptonsfromtheircascade-decaysdowntotheLSPmultipletwill
carry sufficient energy to efficiently pass analysis and trigger cuts. However, there are many subtleties one
mustconsiderwhenextrapolatingtrileptonsearchestothescenariowearestudyinghere. Tounderstandthe
subtleties, first consider the situation where the lightest state above the Higgsino multiplet is mostly bino.
Since it is neutral, we will denote this state as χ0. A pure bino state does not interact with electroweak
3
gauge bosons, so production at the LHC must proceed via the small Higgsino/wino component of χ0. This
3
mixing renders χ0 pair-production completely negligible, leaving associated production χ0χ0, χ0χ0, χ0χ±
3 3 2 3 1 3 1
as the only possibility. None of these associated production modes, however, lead to a trilepton signal; the
5 The loop-factor suppression in the two-body decay is comparable to the suppression in the three-body decays from extra
phasespacefactors,sothedifferencebetweenthetwo-andthree-bodymodesisprimarilytheextracouplingpowers.
6
mΧ0(cid:45)mΧ0: Μ(cid:61)110GeV,tΒ(cid:61)10 mΧ(cid:177)(cid:45)mΧ0: Μ(cid:61)110GeV,tΒ(cid:61)10
2 1 1 1
1000 1000
900 900
10GeV 5GeV
800 800
(cid:76) (cid:76)
V V
e e
G 700 G 700 1 1
(cid:72) (cid:72) 5 0
M2 15 M2 Ge Ge
600 Ge 600 V V
V
2
0
500 25G GeV 500
e
V
LEPExcluded LEPExcluded
400 400
200 400 600 800 1000 200 400 600 800 1000
M (cid:72)GeV(cid:76) M (cid:72)GeV(cid:76)
1 1
mΧ0(cid:45)mΧ0: Μ(cid:61)150GeV,tΒ(cid:61)10 mΧ(cid:177)(cid:45)mΧ0: Μ(cid:61)150GeV,tΒ(cid:61)10
2 1 1 1
1000 1000
10GeV 5GeV
800 800
1 1
5 0
(cid:76) (cid:76) G G
V 600 V 600 eV eV
e e
G G
(cid:72) (cid:72)
2 2
M M
400 20GeV 400
30GeV
200 50GeV 200
LEPExcluded LEPExcluded
200 400 600 800 1000 200 400 600 800 1000
M (cid:72)GeV(cid:76) M (cid:72)GeV(cid:76)
1 1
FIG. 1. Difference in χ0−χ0 masses (left plots) and χ±−χ0 masses (right plots) and for µ=110GeV (top panels)
2 1 1 1
and µ=150GeV (bottom panels). In all plots, tanβ =10.
χ0, χ0, χ± arm of the production is invisible, while the χ0 can only produce one (χ0 →W±((cid:96)ν)χ±) or two
1 2 1 3 3 1
(χ0 → Z((cid:96)(cid:96))χ0,Z((cid:96)(cid:96))χ0) leptons. The situation is different when the state above the Higgsino multiplet is
3 1 2
a wino. In this case, there is an extra charged state χ± accompanying the neutral state χ0, and both states
2 3
possessfull-strength(notsuppressedbymixing)couplingstoelectroweakgaugebosons. Inthiscase,trilepton
signalsarepossible,i.e. pp→χ0χ± →W((cid:96)ν)Z((cid:96)(cid:96))χ0χ0,butthebranchingratioisnotstraightforward. One
3 2 1 2
complication is that χ± is effectively invisible, so some χ0 decays only give one lepton rather than two, and
1 3
some χ± decays give two leptons rather than one. A more substantial complication is that χ0, χ± decays
2 3 2
to Higgs bosons, coming from the Higgsino-wino-Higgs vertices, become important. Since the majority of
Higgsdecaysarehadronic,anyχ0, χ± decaystoaHiggsbosonreducesthetrileptonrate. ThisroleofHiggs
3 2
decaysfromheavierelectroweakinos,includingprospectsforusingtheHiggsdecaysasadiscoverymode,was
discussedrecentlyinRef.[21]. Giventhesevarioussubtleties,itisfarfromclearhowmuchofthedegenerate
Higgsino parameter space can be carved out by trilepton searches for the heavier states (χ0,χ±), even at a
3 2
14TeV LHC and high luminosity. Alternative strategies are thus warranted for all |µ|(cid:28)M ,M values. In
1 2
7
BR(cid:72)Χ0(cid:174)Χ0Z(cid:42)(cid:76): Μ(cid:61)110GeV,t (cid:61)10 BR(cid:72)Χ0(cid:174)Χ0Z(cid:42)(cid:76): Μ(cid:61)(cid:45)110GeV,t (cid:61)10
2 1 Β 2 1 Β
1000 1000
9 5
9 9
900 0. 98 900 0.
0.
800 800
V(cid:76) V(cid:76) 0.85
e e
G 700 G 700
(cid:72) (cid:72)
2 2
M 0.97 M
600 600
500 500 0.75
0.96
LEPExcluded LEPExcluded
400 400
200 400 600 800 1000 200 400 600 800 1000
M (cid:72)GeV(cid:76) M (cid:72)GeV(cid:76)
1 1
FIG. 2. Contours of the branching ratio χ0 → Z∗χ0 for µ = ±110GeV in the (M ,M ) parameter space. The
2 1 1 2
branching fraction χ0 → W∗χ± is approximately given by 1−BR(χ0 → Z∗χ0), up to a small O(1%) branching
2 1 2 1
fraction for χ0 →γχ0.
2 1
the following sections we will forget the heavier (χ0,χ±) electroweakinos and explore new ways to directly
3 2
probe the Higgsino LSP multiplet.
III. HUNTING QUASI-DEGENERATE HIGGSINOS: pp→j+E/ +(cid:96)(cid:96)
T
In this section we exploit the small, but nonzero splitting between χ±, χ0 and χ0 that we outlined in the
1 2 1
previous section. As already emphasized, the problem with small inter-Higgsino splitting is that there are
no objects in the pp → χχ final state that are energetic enough to trigger upon efficiently. A simple fix
for this conundrum is to look at associated production pp → χχ+X, rather than pp → χχ alone. There,
the associated object X can be used for triggering, turning a previously “invisible” event into something
that can be retained for study. There are many possibilities for what triggerable object can be produced
in association with Higgsino pairs – jets, photons, W/Z, etc. – however χχ+j has the highest rate. As
rate is a precious commodity when looking at electroweak-strength production, we focus on this possibility,
effectively searching for a Higgsino signal in a monojet-triggered event sample.
MonojetsearcheshavebeenperformedbyboththeATLASandCMScollaborations[24,25]. Theirresults
areusuallycastintheparameterspaceofextra-dimensionalmodels,and,morerecently,intermsofoperators
controllingdarkmatter(DM)pairproduction[26–29]. Therearetwopossibilities. Iftheinter-Higgsinomass
splitting m −m ,m −m ≡ δm (cid:28) 5GeV, the basic monojet E/ +j signal is the only option to
χ02 χ01 χ±1 χ01 χ T
search for such highly degenerate Higgsinos. We defer consideration of this possibility to Sec. IV, where we
reinterpret the existing bounds in terms of Higgsino production.
On the other hand, when the intra-Higgsino mass splitting is larger, δm ∼ 5 − 50GeV, we propose
χ
looking (offline) for the soft leptonic decay products created as heavier Higgsinos decay to the lightest state
via off-shell W/Z. Depending on the Higgsinos that are produced, a χχ+j event can have between 0 and
4 soft leptons. While we briefly discuss the 1 and 3 lepton possibilities later in Sec. IIIC, here we focus on
the signal with 2 isolated leptons pp→j+E/ +(cid:96)(cid:96).
T
8
ThereareseveralpossibleHiggsinoproductionprocessesthatcancontributetothej+E/ +(cid:96)(cid:96)finalstate:
T
1.)pp→χ±χ∓+j →(cid:96)+(cid:96)(cid:48)−νν¯χ0χ0+j
1 1 1 1
2.)pp→χ0χ0+j →(cid:96)+(cid:96)−χ0+j
2 1 1
3.)pp→χ±χ0+j →(cid:96)+(cid:96)−jjχ0χ0+j, (cid:96)+(cid:96)−(cid:96)(cid:48)±νχ0χ0+j, (8)
1 2 1 1 1 1
where we have omitted χ0χ0 + j production since it has a very small cross-section. By adding several
2 2
subprocesses the total signal is enhanced, though the actual enhancement depends on the cuts imposed and
onthesizeoftheχ±−χ0 andχ0−χ0 masssplittings. Thedominantbackgroundsforthisfinalstateare: tt¯,
1 1 2 1
Z/γ∗(τ+τ−)+j with both taus decaying leptonically, and diboson plus jet. All diboson plus jet processes
thatcontributeto(cid:96)(cid:96)+E/ +j areincluded(W+((cid:96)ν)W−((cid:96)ν)+j,Z(ν¯ν)Z((cid:96)(cid:96))+j,andZ(ν¯ν)γ((cid:96)(cid:96))+j),though
T
WW +j is by far the dominant contribution.
Tostudyandcomparethesignalandbackgrounds,weturntoMonteCarlo. Wesimulatethehardprocesses
for the signal in Eq. (8) and the major backgrounds with Madgraph 5 [30]6. The neutralinos and charginos
are fully decayed in Madgraph 5, and therefore the spin correlation is always retained. The background
processes include j(cid:96)+(cid:96)−νν¯ (dominated by WW+jet), jττ in the dileptonic decay channels (dominated by
j+Z,Z →ττ) and tt¯in the dileptonic channels. The parton-level events are then showered and hadronized
with Pythia 8 [31]. In order to estimate the effect of experimental resolutions, which is important especially
forthejetmomentumandmissingmomentummeasurements,wegrouptheparticlesin0.1×0.1calorimeter
cells on the (η,φ) plane, roughly corresponding to the HCAL granularities.
Theeventisreconstructedbyfirstfindingtheisolatedleptonsthatsatisfythefollowingcriteria: thesumof
alltracks’p within∆R=0.2aroundtheleptonislessthan1.8GeV. Nosmearingisappliedtotheisolated
T
leptons. The isolated leptons are then removed from the calorimeter cells which are used for jet clustering.
Jet clustering is done with FastJet 3 [32, 33] using the anti-k algorithm (R=0.4). After obtaining the jets,
t
we calculate the missing transverse momentum by summing over the momenta of all isolated leptons and
jets. We then apply the following cuts, which we find effectively differentiate signal from background.
• large E/ . All signal events end in two massive LSP neutralinos. When both neutralinos are forced
T
to recoil against another hard object in the event – a jet in the case here – they lead to a large E/
T
signature. We require E/ >100GeV.
T
• exactly 1 hard jet: The topology we are interested in is a nearly invisible Higgsino system recoiling
against initial-state radiation, so a single hard jet will suffice. The tt¯background, on the other hand,
is characterized by at least two hard jets. By restricting the number of final state jets to a single
light-flavor(antib-tagged)jet,wecanremovethevastmajorityofthett¯backgroundwithoutaffecting
the signal. The diboson and Z/γ∗ backgrounds are also insensitive to the jet restriction. In practice,
we require exactly one jet (jets with p less than 30 GeV are not counted), p >100GeV, |η |<2.5.
T T,j j
We use 100GeV to satisfy ATLAS/CMS single-jet or, in combination with the E/ cut above, the
T
jet+E/ trigger requirements, at least at the 8TeV LHC. If the jet is b-tagged, the event is vetoed. We
T
will assume a b-tag efficiency of 80% and neglect the possibility of light jets faking b’s. Reinstating
b-fakes would have a very minor impact on our results, since the signal and the dominant WW +j
background would both decrease by the same small amount. Actually, given that the jet composition
of the signal and dominant background are so similar, a more aggressive tagging/fake point may be
even better – for example, a 10% fake rate may be tolerable if we could remove 90% of the t¯t – but we
did not attempt any such optimization in this work.
• two isolated leptons: If more than two isolated leptons are found, the two leading ones are used
in the following steps. We use a lower transverse momentum threshold of 7GeV (regardless of the
6 Wegenerateeventsusingthefollowingparton-levelcuts: pT,j >80GeV,|ηj|<5.0,E/T >80GeV, pT,(cid:96) >5GeV,|η(cid:96)|<2.5,
and∆R >0.1. Weset∆R >0.4forallbackgroundsexceptW +γ∗+j,whereweuse∆R >0.1. Thesecutsare
(cid:96)−(cid:96) j−(cid:96) j−(cid:96)
slightlysofterthantheanalysis-levelcuts.
9
signal
jllvv
V 103 t t
Ge jt t
0
1
s /
nt 102
e
v
e
of
r
e
b 10
m
u
N
1
0 50 100 150 200 250 300 350 400 450 500
m(t , t ) (GeV)
FIG. 3. The reconstructed m , as defined in the text, for the backgrounds and a typical signal mass point: µ =
ττ
110GeV,M = 200GeV,M = 1000GeV (stacked). The last bin contains the overflow for all events with m >
1 2 ττ
500 GeV.
lepton flavor), and require all leptons to lie within the tracker |η | < 2.5. The lower limit of 7GeV is
(cid:96)
comparabletotheoff-lineleptonidentificationthresholdsinATLAS/CMS[34–36]. Moreprecisevalues
of the thresholds depend sensitively on the particular detector and detection region (e.g. in η), as well
as the desired purity of the lepton sample. This level of precision is beyond the scope of this paper,
however we emphasize that the offline lepton identification thresholds are the primary limitation to
considering even smaller Higgsino mass splittings (larger M ,M ).
1 2
• reconstructed m > 150GeV. The dilepton plus E/ that arises from the Z/γ∗(τ+τ−) background,
ττ T
unlike in the signal, originates from a single particle. If we assume the intermediate tau leptons from
Z/γ∗ are highly energetic, we can approximate their leptonic decays as collinear. This assumption
allowsustoreconstructthetwopairsoftentativeneutrinosinanyττ →(cid:96)(cid:96)+E/ event,andfromthere
T
we can reconstruct the would-be m distribution7. Specifically, we assume the missing energy is due
ττ
to four neutrinos, each pair with momentum collinear to a lepton: p(cid:126) = ξ p(cid:126) , p(cid:126) = ξ p(cid:126) . Using
ν,1 1 (cid:96),1 ν,2 2 (cid:96),2
themeasuredE/ onecansolveforξ ,ξ ,whichcanthenbeusedtoreconstructp orp =p +p ,
T 1 2 ν,i τ,i (cid:96),i ν,i
which we combine to form m 8. The Z/γ∗ background should have a narrow peak in m , while the
ττ ττ
signal distribution should be fairly featureless. Cutting out the Z region using this variable, we can
reducetheZ/γ∗ substantially–anabsolutenecessitygiventheenormouscrosssectionofthejZ →jττ
process. In practice we find that a broad, one-sided cut m > 150GeV is better than a cut focused
ττ
right around the Z-peak. The m distributions for the backgrounds and a sample signal point are
ττ
illustrated in Fig. III, where we can clearly see the reconstructed Z peak in the jττ background. Note
thatwehavetousealogarithmicscaleforthenumberofeventsinordertoseethesmallcontributions
from the signal and the other two backgrounds.
• Finally, we cut on the dilepton invariant mass, m . The leptons from the cascade decays χ± →
(cid:96)(cid:96) 1
W∗((cid:96)ν)χ0, χ0 → Z((cid:96)(cid:96))χ0 are soft, limited by the inter-Higgsino splitting, while the leptons in the
1 2 1
diboson plus jet background come predominantly from on-shell gauge bosons and are more energetic.
7 The collinear approximation notoriously does not work when the taus are back-to-back. As we are always interested in
Z/γ∗+j,sothetau-tausystemisalwayssomewhatboosted,thislimitationisnotanissuehere.
8 Whilethespatialmomentaisscaledwithξi,wescaletheenergyby|ξi|topreventunphysicalnegativeenergyfortheneutrinos
if ξi < 0 (and negative energy for the parent τi if ξi < −1). Large negative ξi occur if the missing energy vector points
oppositetoaleptonand|E/ |>|p |–afairlycommonconfigurationforthesignalorWW +j background.
T T,(cid:96)
10
σ(fb) at 8 TeV σ(fb) at 14 TeV
j(cid:96)(cid:96)νν tt¯ jττ signal j(cid:96)(cid:96)νν tt¯ jττ signal signal
(µ=110GeV) (µ=110GeV) (µ=150GeV)
pj, E/ >100GeV 19.0 9.6 130.4 5.2 48.4 30.8 339.0 14.0 5.8
T T
two isolated leptons 17.8 8.8 46.5 0.8 45.2 28.0 120.9 2.2 0.9
m >150GeV 17.3 8.6 3.7 0.6 43.9 27.6 9.7 1.7 0.7
ττ
TABLEI.Crosssections(infb)aftereachcut,forthemajorbackgrounds,andthesignalfortanβ =10,M =M =
1 2
500GeV,andµequalto110or150GeV.Thecutsinthefirstrowincludetheb-jetvetoandavetooneventswitha
second jet with p >30GeV. Also, the t¯t cross section has been scaled by a factor of 0.2, the probability to fail to
T
tag a b-jet.
Thesoftnessofthethesignalleptonscanbeseeninindividualleptondistributionslikep ,butitalso
T,(cid:96)
shows up in observables constructed, such as m ,m(cid:96)(cid:96) , etc. that are constructed from both leptons
(cid:96)(cid:96) T,2
in the event. By focusing on low values for p ,m , etc. we can reject a large fraction of the diboson
T,(cid:96) (cid:96)(cid:96)
plusjetbackgroundwhileretainingthesignal. Theoptimalsizeofthem windowforcapturingsignal
(cid:96)(cid:96)
and rejecting background depends on the Higgsino mass splittings.
To show the relative size of the processes we are dealing with, in Table I we show the background cross
sections at various stages of the analysis, up to the final m cut. We also show the cross section for a few
(cid:96)(cid:96)
example parameter choices. The cross sections used in Table I and in all plots are the leading order (LO)
values. The signal and the WW +j background are initiated by the same partonic subprocess and have
similarproductionkinematics(asµ∼m ),soweexpectthehigherordercorrectionsfortheseprocesses(K-
W √
factors) to be nearly identical [37]9. Including higher-order corrections would therefore increase the S/ B
√
by ∼ K. However, our analysis has also neglected several experimental details, such as lepton momentum
smearing. Therefore, in an effort to compensate for the crudeness of our analysis and present a conservative
result, we use the leading order cross sections10.
A. Results
Having outlined the search strategy and identified the important backgrounds, we are ready to present
our results. We break up our search for quasi-degenerate Higgsinos into three regions, corresponding to the
three parameter sets discussed in Section II,
1. Case I: M (cid:29)M >|µ|. We fix µ=110GeV, M =1TeV, and vary M from 150GeV to 1TeV.
1 2 1 2
2. Case II: M (cid:29)M >|µ|. We fix µ=110GeV, M =1TeV, and vary M from 150GeV to 1TeV.
2 1 2 1
3. Case III: M ∼M >µ. We fix M =M =500GeV and vary µ from 110GeV to 200GeV.
1 2 1 2
The µ value is fixed to 110GeV for the first two cases to ensure that there is ample parameter space safe
from the LEP II bound, and we will assume that µ > 0. Unless otherwise stated, we assume tanβ = 10.
From Eq. (5),(7) we see that all splittings scale as (1±s ) or (1∓s ) which asymptote to 1 for large
2β 2β
tanβ. Finally, the effect of raising |µ| is captured by case III.
We start from case I, where M is allowed to vary with M fixed to 1TeV. Depending on the M value,
2 1 2
there can be a sizable mass gap between the Higgsino states. A larger inter-Higgsino splitting means the
leptons in the final state are more energetic so the efficiency (and therefore rate) for the signal events is
9 Next-to-leading-order(NLO)dibosonplusjetfornon-VBFtopologiesiscurrentlyonlyknowntoleadingorder.
10 TheK-factorfort¯tisO(2)[38]andpotentiallylargerthanthesignalorWW+j. Howevergiventhatitisaminorbackground
(andtheonlyonesubjecttob-vetoandrelateduncertainties),weretaintheleadingordercrosssection.
